N01 · The reciprocal-square identity

Row

row 1

φ² + φ⁻² = 3 (axiom) theory 3 experiment 3 deviation 0 · d = exact Axiom exact

This is an internal identity, not an experimental match. The Scorecard calls the row “Axiom”; LIB2-046 records the identity at the selected spectrum. Those are different descriptions, retained without changing the cell.

Theory value

row 1

The suite prints

The computed internal value is 3, exactly. The reference 3 is the same identity, not a measurement.

Derivation chain

row 1

1. Use the named golden-unit input, AX1: the positive root of the stated quadratic defines the scalar used here. (p0_framework_foundations.tex:521; appendix_x_zero_parameter_input_ledger.tex:62).
2. Evaluate the reciprocal-square identity at that scalar. The supplied source explicitly gives \phi^2=\phi+1 and \phi^{-2}=2-\phi; adding them is the arithmetic check, not a physical selection step. (appendix_i_dynamics_bounce.tex:608-609; appendix_e_vacuum_selector.tex:149-153).
3. Read the result as the spectral corollary. The conditional vacuum-selection hypotheses and the ordered-frame loading remain separate. (appendix_e_vacuum_selector.tex:509).

Registrar sync

row 1

LIB2-046 — Carries the exact reciprocal-square corollary used in the addition step.

Comparator NONE — the reference is internal, structural or adopted, not a supplied experimental ledger entry.

LIB2-082, LIB2-164, LIB2-200 and LIB2-344 concern other predicates; their shared numerals do not carry this identity.

Calculation

Run python3 N01_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N01 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0

# Exact arithmetic in Q(phi), with phi^2=phi+1. A pair is a+b*phi.
def qmul(x, y):
    a, b = x
    c, d = y
    return (a*c + b*d, a*d + b*c + b*d)


def qadd(x, y):
    return (x[0]+y[0], x[1]+y[1])


def qstr(x):
    return str(x[0]) + " + (" + str(x[1]) + ")*phi"

def main():
    print('=== row 1 ===')
    print('Scorecard (verbatim): φ² + φ⁻² = 3 (axiom) theory 3 experiment 3 deviation 0 · d = exact Axiom exact')
    phi = (Fraction(0), Fraction(1))
    inv = (Fraction(-1), Fraction(1))
    square, inverse_square = qmul(phi, phi), qmul(inv, inv)
    result = qadd(square, inverse_square)
    print("phi_squared = " + qstr(square))
    print("phi_inverse_squared = " + qstr(inverse_square))
    print("identity = " + qstr(result))
    assert result == (Fraction(3), Fraction(0))
    print("theory = 3; internal_reference = 3; signed_percent = 0%")
    print("d = exact (identity label, not a statistical distance)")
    print()


if __name__ == "__main__":
    main()

row 1

Actual stdout for this entry; the text blocks in entry order concatenate to N01_stdout.txt.

=== row 1 ===
Scorecard (verbatim): φ² + φ⁻² = 3 (axiom) theory 3 experiment 3 deviation 0 · d = exact Axiom exact
phi_squared = 1 + (1)*phi
phi_inverse_squared = 2 + (-1)*phi
identity = 3 + (0)*phi
theory = 3; internal_reference = 3; signed_percent = 0%
d = exact (identity label, not a statistical distance)

Comparison

row 1

Theory 3; internal reference 3; signed deviation 0%. Unit, experimental uncertainty, renormalization scheme, scale and experimental edition are not applicable. “d = exact” means an exact algebraic check, not an error-normalized statistic.

Tier and what this does not show

Literal tier: Axiom; status: exact. AX1 is consumed. The calculation neither tests the axiom experimentally nor derives the physical vacuum, a mass scale, or a readout.

Sources

LIB2-046; p0_framework_foundations.tex:521; appendix_x_zero_parameter_input_ledger.tex:62; appendix_i_dynamics_bounce.tex:608-609; appendix_e_vacuum_selector.tex:149-153; appendix_e_vacuum_selector.tex:509.

N02 · Unit determinant of the stated vacuum

Row

row 2

det(J vac ) φ·1·φ⁻¹ theory 1 experiment 1 deviation 0 · d = exact Theorem (AX1) exact

The experiment cell is an internal normalization check. It is not an independent measured determinant.

Theory value

row 2

At the printed vacuum,

The script multiplies the diagonal entries exactly and obtains 1.

Derivation chain

row 2

1. Take the working diagonal vacuum and its adjoint/inverse as stated in the Roman-surface paragraph. (p1_peirce_gauge_group.tex:116-119).
2. For this diagonal slice the printed determinant is the product of the entries; substitute the reciprocal pair and the middle unit. (p1_peirce_gauge_group.tex:111; p1_peirce_gauge_group.tex:116-118).
3. Distinguish checking this vacuum from selecting it: Appendix E uses unit determinant as hypothesis H0. (appendix_e_vacuum_selector.tex:39-42).

Registrar sync

row 2

LIB2-047 — States the determinant at the working vacuum and distinguishes it from the normalization hypothesis.

Comparator NONE — the reference is internal, structural or adopted, not a supplied experimental ledger entry.

Calculation

Run python3 N02_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N02 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0

# Exact arithmetic in Q(phi), with phi^2=phi+1. A pair is a+b*phi.
def qmul(x, y):
    a, b = x
    c, d = y
    return (a*c + b*d, a*d + b*c + b*d)


def qadd(x, y):
    return (x[0]+y[0], x[1]+y[1])


def qstr(x):
    return str(x[0]) + " + (" + str(x[1]) + ")*phi"

def main():
    print('=== row 2 ===')
    print('Scorecard (verbatim): det(J vac ) φ·1·φ⁻¹ theory 1 experiment 1 deviation 0 · d = exact Theorem (AX1) exact')
    phi = (Fraction(0), Fraction(1))
    one = (Fraction(1), Fraction(0))
    inv = (Fraction(-1), Fraction(1))
    result = qmul(qmul(phi, one), inv)
    assert result == one
    print("diagonal_product = " + qstr(result))
    print("theory = 1; internal_reference = 1; signed_percent = 0%")
    print("d = exact (identity label, not a statistical distance)")
    print()


if __name__ == "__main__":
    main()

row 2

Actual stdout for this entry; the text blocks in entry order concatenate to N02_stdout.txt.

=== row 2 ===
Scorecard (verbatim): det(J vac ) φ·1·φ⁻¹ theory 1 experiment 1 deviation 0 · d = exact Theorem (AX1) exact
diagonal_product = 1 + (0)*phi
theory = 1; internal_reference = 1; signed_percent = 0%
d = exact (identity label, not a statistical distance)

Comparison

row 2

Theory 1, internal reference 1, signed deviation 0%. Experimental uncertainty, unit, scheme, scale and experimental edition are not applicable. The equality checks the stated normalization only.

Tier and what this does not show

Literal tier: Theorem (AX1); status: exact. The working vacuum and golden-unit input are consumed. Unit determinant alone does not select that spectrum or its physical ordering.

Sources

LIB2-047; p1_peirce_gauge_group.tex:111; p1_peirce_gauge_group.tex:116-119; appendix_e_vacuum_selector.tex:39-42.

N03 · DET-7: evaluation and imposed status

Row

row 3

DET-7 det(Gram) = 7 theory 7 experiment structural deviation — Structural input —

The comparison is “structural,” not an experiment. Computing the Gram determinant at the golden vacuum does not derive why DET-7 must be imposed upstream.

Theory value

row 3

The printed invariant is

On the stated reciprocal spectrum the supplied proof gives s=4 and \det G=s^2-9=7. The computed value is 7.

Derivation chain

row 3

1. Use the working reciprocal spectrum with unit determinant, under the named conditional selector hypotheses. (appendix_x_zero_parameter_input_ledger.tex:63).
2. The supplied DET-7 check uses s=\phi^2+1+\phi^{-2}=4 and \det G=s^2-9. Substitution gives the displayed Gram determinant. (appendix_i_dynamics_bounce.tex:605-609).
3. Keep the logical direction explicit: the algebraic selector imposes DET-7 as a structural postulate. NOT IN SUITE — a first-principles necessity for that postulate; the supplied source itself says it remains open. (appendix_e_vacuum_selector.tex:97-107).

Registrar sync

row 3

LIB2-018 — Carries the imposed-postulate status and the missing necessity, not a physical derivation.

LIB2-019 — Carries the conditional reciprocal golden spectrum used for the evaluation; it does not make DET-7 unconditional.

Comparator NONE — the reference is internal, structural or adopted, not a supplied experimental ledger entry.

LIB2-020 is the alternate arithmetic selector, not needed for this evaluation. LIB2-356 concerns the downstream mismatch identity, not the necessity of DET-7.

Calculation

Run python3 N03_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N03 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0

# Exact arithmetic in Q(phi), with phi^2=phi+1. A pair is a+b*phi.
def qmul(x, y):
    a, b = x
    c, d = y
    return (a*c + b*d, a*d + b*c + b*d)


def qadd(x, y):
    return (x[0]+y[0], x[1]+y[1])


def qstr(x):
    return str(x[0]) + " + (" + str(x[1]) + ")*phi"

def main():
    print('=== row 3 ===')
    print('Scorecard (verbatim): DET-7 det(Gram) = 7 theory 7 experiment structural deviation — Structural input —')
    phi = (Fraction(0), Fraction(1))
    inv = (Fraction(-1), Fraction(1))
    s = qadd(qadd(qmul(phi,phi), (Fraction(1),Fraction(0))), qmul(inv,inv))
    det = qadd(qmul(s,s), (Fraction(-9),Fraction(0)))
    assert s == (Fraction(4),Fraction(0))
    assert det == (Fraction(7),Fraction(0))
    print("s = " + qstr(s))
    print("gram_diagonal = 4; gram_off_diagonal = 3")
    print("det_Gram = 4*4 - 3*3 = 7")
    print("theory = 7; comparator = structural (not a measurement)")
    print("signed_percent = NOT APPLICABLE; d = NOT APPLICABLE")
    print()


if __name__ == "__main__":
    main()

row 3

Actual stdout for this entry; the text blocks in entry order concatenate to N03_stdout.txt.

=== row 3 ===
Scorecard (verbatim): DET-7 det(Gram) = 7 theory 7 experiment structural deviation — Structural input —
s = 4 + (0)*phi
gram_diagonal = 4; gram_off_diagonal = 3
det_Gram = 4*4 - 3*3 = 7
theory = 7; comparator = structural (not a measurement)
signed_percent = NOT APPLICABLE; d = NOT APPLICABLE

Comparison

row 3

Theory 7; comparator structural. No experimental central value or uncertainty exists for this row, so signed experimental deviation and d are not applicable. The supplied suite treats this as an internal invariant and a structural input, not an empirical agreement.

Tier and what this does not show

Literal tier: Structural input; status: —. The spectrum, normalization and trace/Gram construction are used. Evaluating the postulate on its selected spectrum is not evidence that nature selects the postulate.

Sources

LIB2-018; LIB2-019; appendix_x_zero_parameter_input_ledger.tex:63-64; appendix_i_dynamics_bounce.tex:605-609; appendix_e_vacuum_selector.tex:97-107.

N04 · The solar-angle readout in two coordinates

Row

row 4

sin²θ 12 3/(φ⁴+3) theory 0.304442 experiment 0.3088 +0.0067 −0.0066 deviation −1.41% · d = −0.66 Derived-conditional —

row 4′

θ 12 (°) arctan(√3/φ²) theory 33.488 experiment 33.76 +0.42 −0.41 deviation −0.81% · d = −0.66 Derived-conditional —

The candidates LIB2-063, LIB2-064 and LIB2-238 are Cabibbo readouts, not the solar derivation. The supplied ledger record LIB2-227 is an angle in degrees; no supplied comparator record carries the squared-sine cell itself.

Theory value

row 4

The suite prints \tan\theta_{12}=\sqrt3/\phi^2 and \tan^2\theta_{12}=3/\phi^4. Evaluating the Scorecard’s equivalent coordinate gives

at the cell’s precision.

row 4′

The suite’s angle formula is

at Scorecard precision. The coarser source display is 33.49^{\circ}; it is not a different formula.

Derivation chain

row 4

1. Use the golden-unit input and its reciprocal-square identity. (appendix_x_zero_parameter_input_ledger.tex:62; appendix_e_vacuum_selector.tex:149-153).
2. Apply the stated Peirce readout \tan\theta_{12}=\sqrt3/\phi^2, with the normal-ordering, resolvent-ladder and propagation-interface premises. (appendix_e_vacuum_selector.tex:154-156; p3_ckm_pmns_mixing.tex:581).
3. Evaluate the squared-sine coordinate of that angle; this is arithmetic re-expression of the supplied tangent relation, not an additional physical theorem. (p0_framework_foundations.tex:641-647).
4. NOT IN SUITE — a derived identification of the ladder with physical propagation eigenstates; the supplied source calls that interface undeclared. (p3_ckm_pmns_mixing.tex:581).

row 4′

1. Evaluate the same tangent readout in degrees, without using the measured solar angle as input. (appendix_e_vacuum_selector.tex:154-158).
2. The kernel-line passage prints the finer framework angle separately from its coarser display; the physical premises remain those of the solar row. (p3_ckm_pmns_mixing.tex:157; p3_ckm_pmns_mixing.tex:581).

Registrar sync

row 4

LIB2-046 — Carries the reciprocal-square input identity.

LIB2-060 — Carries the solar readout and its unclosed ordering/interface premises.

Comparator NONE — no matching comparator record is supplied for this exact entry; the stated cell is retained without inventing an ID.

row 4′

LIB2-060 — Carries the tangent readout whose degree evaluation is shown.

Comparator LIB2-227 / SL-24 — value 33.76 (+0.42/−0.41) deg · scheme NH global fit · edition 6.1.

Calculation

Run python3 N04_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N04 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 4 ===')
    print('Scorecard (verbatim): sin²θ 12 3/(φ⁴+3) theory 0.304442 experiment 0.3088 +0.0067 −0.0066 deviation −1.41% · d = −0.66 Derived-conditional —')
    value = 3.0/(PHI**4+3.0)
    print("formula = 3/(phi**4+3)")
    print("theory_at_cell_precision = " + shown(value,6))
    compare("full_formula", value, "0.3088", "0.0066", "0.0067")
    compare("printed_cell", "0.304442", "0.3088", "0.0066", "0.0067")
    print()
    print('=== row 4′ ===')
    print('Scorecard (verbatim): θ 12 (°) arctan(√3/φ²) theory 33.488 experiment 33.76 +0.42 −0.41 deviation −0.81% · d = −0.66 Derived-conditional —')
    value = math.degrees(math.atan(math.sqrt(3.0)/PHI**2))
    print("formula = degrees(atan(sqrt(3)/phi**2))")
    print("theory_at_cell_precision = " + shown(value,3))
    print("coarse_suite_display = " + shown(value,2))
    compare("full_formula_deg", value, "33.76", "0.41", "0.42")
    compare("printed_cell_deg", "33.488", "33.76", "0.41", "0.42")
    print()


if __name__ == "__main__":
    main()

row 4

Actual stdout for this entry; the text blocks in entry order concatenate to N04_stdout.txt.

=== row 4 ===
Scorecard (verbatim): sin²θ 12 3/(φ⁴+3) theory 0.304442 experiment 0.3088 +0.0067 −0.0066 deviation −1.41% · d = −0.66 Derived-conditional —
formula = 3/(phi**4+3)
theory_at_cell_precision = 0.304442
full_formula.theory = 0.304441745
full_formula.reference = 0.308800000
full_formula.signed_percent = -1.411351942%; rounded = -1.41%
full_formula.uncertainty_used = 0.0066 (lower)
full_formula.d = -0.660341636; rounded = -0.66
printed_cell.theory = 0.304442000
printed_cell.reference = 0.308800000
printed_cell.signed_percent = -1.411269430%; rounded = -1.41%
printed_cell.uncertainty_used = 0.0066 (lower)
printed_cell.d = -0.660303030; rounded = -0.66

row 4′

Actual stdout for this entry; the text blocks in entry order concatenate to N04_stdout.txt.

=== row 4′ ===
Scorecard (verbatim): θ 12 (°) arctan(√3/φ²) theory 33.488 experiment 33.76 +0.42 −0.41 deviation −0.81% · d = −0.66 Derived-conditional —
formula = degrees(atan(sqrt(3)/phi**2))
theory_at_cell_precision = 33.488
coarse_suite_display = 33.49
full_formula_deg.theory = 33.488005129
full_formula_deg.reference = 33.760000000
full_formula_deg.signed_percent = -0.805672011%; rounded = -0.81%
full_formula_deg.uncertainty_used = 0.41 (lower)
full_formula_deg.d = -0.663402124; rounded = -0.66
printed_cell_deg.theory = 33.488000000
printed_cell_deg.reference = 33.760000000
printed_cell_deg.signed_percent = -0.805687204%; rounded = -0.81%
printed_cell_deg.uncertainty_used = 0.41 (lower)
printed_cell_deg.d = -0.663414634; rounded = -0.66

Comparison

row 4

Theory 0.304442, comparator 0.3088 +0.0067 −0.0066, dimensionless; the supplied paired material identifies NuFIT 6.1, NH global fit. Signed offset rounds to −1.41% and naive d to −0.66, using the lower error. No scheme or running scale is assigned to this fit parameter. Its missing ledger ID is not replaced with the degree-valued record.

row 4′

Theory 33.488°; experiment 33.76 +0.42 −0.41°, NuFIT 6.1, NH global fit (LIB2-227 / SL-24). Signed offset −0.81%; naive d −0.66. These are two coordinate displays of one readout, not independent observations.

Tier and what this does not show

Both literal tiers: Derived-conditional; statuses: —. Normal ordering, the Structural ladder and the propagation attachment are consumed. The calculation does not derive those premises or double the evidence by printing an angle and its squared sine.

Sources

LIB2-046; LIB2-060; LIB2-227; SL-24; appendix_x_zero_parameter_input_ledger.tex:62; appendix_e_vacuum_selector.tex:149-158; p0_framework_foundations.tex:641-647; p3_ckm_pmns_mixing.tex:157; p3_ckm_pmns_mixing.tex:581; s1162.

N05 · Atmospheric mismatch and selected octant registration

Row

row 5

sin²θ 23 7/16 (DET-7) theory 0.4375 experiment 0.470 +0.017 −0.014 deviation −6.91% · d = −2.32 Loaded-correspondence (internal 7/16 identity theorem-grade; octant registration selected against data — A1566, Rev32.6) lower octant

The internal identity and the physical lower-octant correspondence are different claims. The cell’s loaded attachment is preserved; a theorem about the mismatch is not substituted for an octant selector.

Theory value

row 5

The internal relation is \sin^2\theta_{\rm mismatch}=7/16. The selected physical registration uses

Derivation chain

row 5

1. Take the stated golden vacuum, DET-7 and unit normalization. The supplied check gives the norm quantity entering the mismatch denominator. (appendix_i_dynamics_bounce.tex:605-609).
2. Use the internal mismatch corollary, which the supplied ledger distinguishes explicitly from its physical registration. (appendix_x_zero_parameter_input_ledger.tex:69; p3_ckm_pmns_mixing.tex:582).
3. Apply the registered lower-octant map. The current source says this registration was selected against data and is not uniquely supplied by the candidate map. (appendix_x_zero_parameter_input_ledger.tex:69).
4. NOT IN SUITE — a registered selector that excludes the mirror identification. The supplied LIB2-100 quotation identifies this missing map explicitly. (p3_ckm_pmns_mixing.tex:582).

Registrar sync

row 5

LIB2-356 — Carries the internal mismatch corollary.

LIB2-002 — Carries the loaded physical registration and its convention choice.

LIB2-100 — Carries the nonselection of the mirror map, not a derivation excluding it.

Comparator LIB2-003 / SL-25 — value 0.470 (+0.017/−0.014) · scheme NH global fit, lower octant · edition 6.1.

Calculation

Run python3 N05_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N05 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 5 ===')
    print('Scorecard (verbatim): sin²θ 23 7/16 (DET-7) theory 0.4375 experiment 0.470 +0.017 −0.014 deviation −6.91% · d = −2.32 Loaded-correspondence (internal 7/16 identity theorem-grade; octant registration selected against data — A1566, Rev32.6) lower octant')
    value = Fraction(7,16)
    print("internal_fraction = 7/16; value = " + shown(float(value),4))
    print("mirror_registration = 9/16 = " + shown(float(Fraction(9,16)),4))
    compare("selected_registration", float(value), "0.470", "0.014", "0.017")
    print()


if __name__ == "__main__":
    main()

row 5

Actual stdout for this entry; the text blocks in entry order concatenate to N05_stdout.txt.

=== row 5 ===
Scorecard (verbatim): sin²θ 23 7/16 (DET-7) theory 0.4375 experiment 0.470 +0.017 −0.014 deviation −6.91% · d = −2.32 Loaded-correspondence (internal 7/16 identity theorem-grade; octant registration selected against data — A1566, Rev32.6) lower octant
internal_fraction = 7/16; value = 0.4375
mirror_registration = 9/16 = 0.5625
selected_registration.theory = 0.437500000
selected_registration.reference = 0.470000000
selected_registration.signed_percent = -6.914893617%; rounded = -6.91%
selected_registration.uncertainty_used = 0.014 (lower)
selected_registration.d = -2.321428571; rounded = -2.32

Comparison

row 5

Theory 0.4375; NuFIT 6.1 NH global-fit comparator 0.470 +0.017 −0.014, dimensionless (LIB2-003 / SL-25). Signed offset −6.91%; naive d −2.32, with the lower error. This compares the selected physical lower branch; it does not independently test the unregistered internal identity.

Tier and what this does not show

Literal tier: Loaded-correspondence (internal 7/16 identity theorem-grade; octant registration selected against data — A1566, Rev32.6). Status: lower octant. The physical registration is consumed. Disagreement with that registration alone does not refute the internal mismatch theorem.

Sources

LIB2-356; LIB2-002; LIB2-100; LIB2-003; SL-25; appendix_i_dynamics_bounce.tex:605-609; appendix_x_zero_parameter_input_ledger.tex:69; p3_ckm_pmns_mixing.tex:582; s501; s1156; s1157.

N06 · The reactor-angle round-trip formula

Row

row 6

sin²θ 13 sin⁴(π/8) = (3−2√2)/8 theory 0.0214466 experiment 0.02248 +0.00055 −0.00059 deviation −4.60% · d = −1.75 Structural —

Only LIB2-061 carries the retained formula. Historical proposals and the open question are not proofs of the adopted readout. LIB2-228 / SL-26 is a degree-valued angle, not this squared-sine comparator.

Theory value

row 6

The suite prints

at the Scorecard’s precision.

Derivation chain

row 6

1. Take the identified triality half-angle readout and round-trip squaring as the retained construction. (p0_framework_foundations.tex:702-706).
2. Evaluate the trigonometric expression and its printed radical form independently; the script checks that both routes give the same value. (p3_ckm_pmns_mixing.tex:583).
3. NOT IN SUITE — first-principles selection of the readout ray and squaring. The source explicitly withdraws the inference from the substrate half-turn to a canonical mixing half-angle. (appendix_b_independent_verification.tex:177-191; appendix_x_zero_parameter_input_ledger.tex:70).

Registrar sync

row 6

LIB2-061 — Carries the retained formula and the fact that its round-trip readout remains unforced.

Comparator LIB2-226 / SL-23 — value 0.02248 (+0.00055/−0.00059) · scheme NH global fit (IC24) · edition 6.1.

LIB2-252 is superseded wording; LIB2-280–LIB2-282 are archived proposals; LIB2-315 is an open question. None is mapped as the retained derivation.

Calculation

Run python3 N06_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N06 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 6 ===')
    print('Scorecard (verbatim): sin²θ 13 sin⁴(π/8) = (3−2√2)/8 theory 0.0214466 experiment 0.02248 +0.00055 −0.00059 deviation −4.60% · d = −1.75 Structural —')
    trig = math.sin(math.pi/8.0)**4
    radical = (3.0-2.0*math.sqrt(2.0))/8.0
    assert abs(trig-radical) < 1e-14
    print("trigonometric_value = " + shown(trig))
    print("radical_value = " + shown(radical))
    print("theory_at_cell_precision = " + shown(trig,7))
    compare("full_formula", trig, "0.02248", "0.00059", "0.00055")
    compare("printed_cell", "0.0214466", "0.02248", "0.00059", "0.00055")
    print()


if __name__ == "__main__":
    main()

row 6

Actual stdout for this entry; the text blocks in entry order concatenate to N06_stdout.txt.

=== row 6 ===
Scorecard (verbatim): sin²θ 13 sin⁴(π/8) = (3−2√2)/8 theory 0.0214466 experiment 0.02248 +0.00055 −0.00059 deviation −4.60% · d = −1.75 Structural —
trigonometric_value = 0.021446609
radical_value = 0.021446609
theory_at_cell_precision = 0.0214466
full_formula.theory = 0.021446609
full_formula.reference = 0.022480000
full_formula.signed_percent = -4.596933244%; rounded = -4.60%
full_formula.uncertainty_used = 0.00059 (lower)
full_formula.d = -1.751509480; rounded = -1.75
printed_cell.theory = 0.021446600
printed_cell.reference = 0.022480000
printed_cell.signed_percent = -4.596975089%; rounded = -4.60%
printed_cell.uncertainty_used = 0.00059 (lower)
printed_cell.d = -1.751525424; rounded = -1.75

Comparison

row 6

Theory 0.0214466; comparator 0.02248 +0.00055 −0.00059, NuFIT 6.1 NH global fit, IC24, dimensionless (LIB2-226 / SL-23). Signed deviation −4.60%; naive d −1.75, lower error. It is a retained structural readout, not a derived selection result.

Tier and what this does not show

Literal tier: Structural; status: —. The half-angle normalization and squaring are chosen. Numerical agreement does not supply the missing physical readout selection or restore withdrawn canonicality.

Sources

LIB2-061; LIB2-226; SL-23; p0_framework_foundations.tex:702-706; p3_ckm_pmns_mixing.tex:583; appendix_b_independent_verification.tex:177-191; appendix_x_zero_parameter_input_ledger.tex:70; s502.

N07 · The CP-phase orbit time and its physical readout

Row

row 7

δ CP (°) −2π/√5 ≡ 199.003 theory 199.003 experiment 212 +26 −36 deviation −6.13% · d = −0.36 Derived-conditional —

No comparator record or SL identifier for this phase is supplied. The comparator is nevertheless stated in the supplied Paper 7 passage. The negative phase and its positive representative must not be compared on different branches.

Theory value

row 7

The suite prints \delta_{\rm CP}=-t_*=-2\pi/\sqrt5 in radians. On the displayed positive degree branch,

Derivation chain

row 7

1. Take the vacuum-sector frequency \Omega=(\phi+\phi^{-1})/2=\sqrt5/2 and the stated half-turn time t_*=2\pi/\sqrt5. (appendix_a_lagrangian_derivation.tex:168-176; appendix_x_zero_parameter_input_ledger.tex:66-67).
2. Apply the stated \delta=-t_* readout; convert radians to degrees and choose the same positive branch as the comparison. (appendix_b_independent_verification.tex:122-125; p7_precision_tests_falsification.tex:50).
3. NOT IN SUITE — the independently derived propagation/physical-phase interface. The current conditional row explicitly carries its ordering, ladder and interface premises. (p3_ckm_pmns_mixing.tex:584).

Registrar sync

row 7

LIB2-062 — Carries the orbit-time formula and its conditional physical CP-phase attachment.

Comparator NONE — no matching comparator record is supplied for this exact entry; the stated cell is retained without inventing an ID.

Calculation

Run python3 N07_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N07 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 7 ===')
    print('Scorecard (verbatim): δ CP (°) −2π/√5 ≡ 199.003 theory 199.003 experiment 212 +26 −36 deviation −6.13% · d = −0.36 Derived-conditional —')
    negative = -2.0*math.pi/math.sqrt(5.0)
    positive = math.degrees(negative) % 360.0
    print("phase_radians = " + shown(negative))
    print("negative_degree_representative = " + shown(math.degrees(negative)))
    print("positive_degree_representative = " + shown(positive))
    print("theory_at_cell_precision = " + shown(positive,3))
    compare("full_formula_deg", positive, "212", "36", "26")
    compare("printed_cell_deg", "199.003", "212", "36", "26")
    print()


if __name__ == "__main__":
    main()

row 7

Actual stdout for this entry; the text blocks in entry order concatenate to N07_stdout.txt.

=== row 7 ===
Scorecard (verbatim): δ CP (°) −2π/√5 ≡ 199.003 theory 199.003 experiment 212 +26 −36 deviation −6.13% · d = −0.36 Derived-conditional —
phase_radians = -2.809925892
negative_degree_representative = -160.996894380
positive_degree_representative = 199.003105620
theory_at_cell_precision = 199.003
full_formula_deg.theory = 199.003105620
full_formula_deg.reference = 212.000000000
full_formula_deg.signed_percent = -6.130610557%; rounded = -6.13%
full_formula_deg.uncertainty_used = 36 (lower)
full_formula_deg.d = -0.361024844; rounded = -0.36
printed_cell_deg.theory = 199.003000000
printed_cell_deg.reference = 212.000000000
printed_cell_deg.signed_percent = -6.130660377%; rounded = -6.13%
printed_cell_deg.uncertainty_used = 36 (lower)
printed_cell_deg.d = -0.361027778; rounded = -0.36

Comparison

row 7

Theory 199.003°; comparator 212 +26 −36°, NuFIT 6.1, NH with SK, as printed in Paper 7. Signed offset −6.13% and naive d −0.36, using the lower error. These are local, branch-matched arithmetic summaries, not a circular likelihood. Unit: degrees; renormalization scheme and scale are not assigned.

Tier and what this does not show

Literal tier: Derived-conditional; status: —. The frame, normal ordering, Structural ladder and physical readout are consumed. The internal orbit identity alone is not a measurement of the Dirac phase or a construction of its propagation interface.

Sources

LIB2-062; appendix_a_lagrangian_derivation.tex:168-176; appendix_x_zero_parameter_input_ledger.tex:66-67; appendix_b_independent_verification.tex:122-125; p7_precision_tests_falsification.tex:50; p3_ckm_pmns_mixing.tex:584.

N08 · The loaded first-row unitarity value

Row

row 8

|V ud | first-row unitarity theory 0.97429 experiment 0.97367 ± 0.00032 deviation +0.06% · d = +1.94 Loaded —

The candidate LIB2-065 carries the final square root. The prerequisite magnitudes are carried by records supplied with other notes; those records are named below rather than treating a unitarity identity as an independent selection theorem.

Theory value

row 8

The suite prints

The square root is evaluated from the unrounded framework magnitudes, not from measured magnitudes.

Derivation chain

row 8

1. Use the data-selected Route-B input |V_{us}|=\sin(\theta_{12}^{\rm fw})/\sqrt6 and the framework solar angle. (p3_ckm_pmns_mixing.tex:157).
2. Use the retained |V_{cb}|=1/(9\sqrt7) formula and |V_{ub}|=|V_{us}||V_{cb}|/\sqrt6. (p0_framework_foundations.tex:712-719).
3. Substitute these magnitudes into first-row unitarity and take the positive magnitude. The printed source explicitly retains the inherited loading. (p3_ckm_pmns_mixing.tex:145-154).

Registrar sync

row 8

LIB2-063 — Carries the selected Cabibbo input.

LIB2-066 — Carries the adjacent magnitude used in the hierarchy.

LIB2-067 — Carries the hierarchy expression for the small first-row magnitude.

LIB2-065 — Carries the final unitarity square root and inherited loading.

Comparator LIB2-217 / SL-14 — value 0.97367 (+0.00032/−0.00032) · scheme PDG first-row · edition 2026.

Calculation

Run python3 N08_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N08 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))


def ckms():
    solar = 3.0 / (PHI**4 + 3.0)
    vus = math.sqrt(solar) / math.sqrt(6.0)
    vcb = 1.0 / (9.0 * math.sqrt(7.0))
    vub = vus * vcb / math.sqrt(6.0)
    vud = math.sqrt(1.0 - vus*vus - vub*vub)
    return vus, vcb, vub, vud

def main():
    print('=== row 8 ===')
    print('Scorecard (verbatim): |V ud | first-row unitarity theory 0.97429 experiment 0.97367 ± 0.00032 deviation +0.06% · d = +1.94 Loaded —')
    vus, vcb, vub, vud = ckms()
    print("input_vus = " + shown(vus,12))
    print("input_vcb = " + shown(vcb,12))
    print("input_vub = " + shown(vub,12))
    print("unitarity_sum = " + shown(vud*vud+vus*vus+vub*vub,12))
    print("theory_at_cell_precision = " + shown(vud,5))
    compare("full_formula", vud, "0.97367", "0.00032", "0.00032")
    compare("printed_cell", "0.97429", "0.97367", "0.00032", "0.00032")
    print()


if __name__ == "__main__":
    main()

row 8

Actual stdout for this entry; the text blocks in entry order concatenate to N08_stdout.txt.

=== row 8 ===
Scorecard (verbatim): |V ud | first-row unitarity theory 0.97429 experiment 0.97367 ± 0.00032 deviation +0.06% · d = +1.94 Loaded —
input_vus = 0.225256056227
input_vcb = 0.041996052557
input_vub = 0.003861973786
unitarity_sum = 1.000000000000
theory_at_cell_precision = 0.97429
full_formula.theory = 0.974291945
full_formula.reference = 0.973670000
full_formula.signed_percent = +0.063876375%; rounded = +0.06%
full_formula.uncertainty_used = 0.00032 (upper)
full_formula.d = +1.943578445; rounded = +1.94
printed_cell.theory = 0.974290000
printed_cell.reference = 0.973670000
printed_cell.signed_percent = +0.063676605%; rounded = +0.06%
printed_cell.uncertainty_used = 0.00032 (upper)
printed_cell.d = +1.937500000; rounded = +1.94

Comparison

row 8

Theory 0.97429; comparator 0.97367 ±0.00032, PDG 2026 first-row determination, dimensionless (LIB2-217 / SL-14). Signed deviation rounds to +0.06%, naive d to +1.94. No separate running scale is supplied. Exact normalization of the constructed row is not independent evidence for its data-selected inputs.

Tier and what this does not show

Literal tier: Loaded; status: —. Route choice and the hierarchy inputs are consumed. The algebraic unitarity operation does not make those choices physical consequences of the bulk algebra.

Sources

LIB2-063; LIB2-066; LIB2-067; LIB2-065; LIB2-217; SL-14; p3_ckm_pmns_mixing.tex:145-157; p0_framework_foundations.tex:712-719; s1162.

N09 · The data-selected Cabibbo route

Row

row 9

|V us | sin(θ 12 fw )/√6 theory 0.225256 experiment 0.22431 ± 0.00085 deviation +0.42% · d = +1.11 Loaded (data-selected route) (digit from kernel s1162, Rev32.6; the Rev32.5 print 0.225247 was a hand calculation) —

The finer cell agrees with the current kernel-line formula. The historical hand-calculated digit and the separate measured-solar-angle diagnostic are not used to obtain this row.

Theory value

row 9

The framework-angle route is

The superscript “fw” is essential: the measured solar angle is not the input.

Derivation chain

row 9

1. Evaluate the conditional framework tangent and convert it to its sine without rounding the angle. (appendix_x_zero_parameter_input_ledger.tex:68).
2. Apply the stated normalization in Route B. The source gives the precise value and distinguishes a coarsely rounded angle from the framework computation. (p3_ckm_pmns_mixing.tex:155-158).
3. Record why this route is retained: it was selected against kaon data. NOT IN SUITE — a data-independent rule selecting this physical route; the alternative measured-angle diagnostic is a different calculation. (p3_ckm_pmns_mixing.tex:155-162).

Registrar sync

row 9

LIB2-060 — Carries the conditional framework solar-angle input.

LIB2-063 — Carries the data-selected Route-B formula and corrected numeric value.

Comparator LIB2-214 / SL-11 — value 0.22431 (+0.00085/−0.00085) · scheme PDG first-row average · edition 2026 (A1546 lined).

LIB2-064 is the measured-angle diagnostic. LIB2-237, LIB2-238 and LIB2-239 describe superseded digits or routes; they do not carry the retained computation.

Calculation

Run python3 N09_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N09 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 9 ===')
    print('Scorecard (verbatim): |V us | sin(θ 12 fw )/√6 theory 0.225256 experiment 0.22431 ± 0.00085 deviation +0.42% · d = +1.11 Loaded (data-selected route) (digit from kernel s1162, Rev32.6; the Rev32.5 print 0.225247 was a hand calculation) —')
    solar = 3.0/(PHI**4+3.0)
    angle = math.atan(math.sqrt(3.0)/PHI**2)
    vus = math.sin(angle)/math.sqrt(6.0)
    assert abs(vus-math.sqrt(solar)/math.sqrt(6.0)) < 1e-14
    print("framework_angle_deg = " + shown(math.degrees(angle),9))
    print("framework_sine_squared = " + shown(solar,12))
    print("theory_at_cell_precision = " + shown(vus,6))
    compare("full_formula", vus, "0.22431", "0.00085", "0.00085")
    compare("printed_cell", "0.225256", "0.22431", "0.00085", "0.00085")
    print()


if __name__ == "__main__":
    main()

row 9

Actual stdout for this entry; the text blocks in entry order concatenate to N09_stdout.txt.

=== row 9 ===
Scorecard (verbatim): |V us | sin(θ 12 fw )/√6 theory 0.225256 experiment 0.22431 ± 0.00085 deviation +0.42% · d = +1.11 Loaded (data-selected route) (digit from kernel s1162, Rev32.6; the Rev32.5 print 0.225247 was a hand calculation) —
framework_angle_deg = 33.488005129
framework_sine_squared = 0.304441745202
theory_at_cell_precision = 0.225256
full_formula.theory = 0.225256056
full_formula.reference = 0.224310000
full_formula.signed_percent = +0.421762840%; rounded = +0.42%
full_formula.uncertainty_used = 0.00085 (upper)
full_formula.d = +1.113007326; rounded = +1.11
printed_cell.theory = 0.225256000
printed_cell.reference = 0.224310000
printed_cell.signed_percent = +0.421737774%; rounded = +0.42%
printed_cell.uncertainty_used = 0.00085 (upper)
printed_cell.d = +1.112941176; rounded = +1.11

Comparison

row 9

Theory 0.225256; comparator 0.22431 ±0.00085, PDG 2026 first-row average, dimensionless (LIB2-214 / SL-11). Signed deviation +0.42%; naive d +1.11. The agreement was involved in selecting the route, so it is not independent evidence for that selection.

Tier and what this does not show

Literal tier: Loaded (data-selected route) (digit from kernel s1162, Rev32.6; the Rev32.5 print 0.225247 was a hand calculation). Status: —. This retains the route selection and the conditional solar attachment. It does not turn the separately obtained normalization into a physical route-selection law.

Sources

LIB2-060; LIB2-063; LIB2-214; SL-11; appendix_x_zero_parameter_input_ledger.tex:68; p3_ckm_pmns_mixing.tex:155-162; s1162.

N10 · The adjacent quark-mixing magnitude

Row

row 10

|V cb | 1/(9√7) theory 0.0419961 experiment 0.0407 ± 0.0013 deviation +3.18% · d = +1.00 Loaded-correspondence (physical attachment: inherits the octant registration; the integer 9 data-selected) / Structural formula — A1566 —

The formula is distinct from the failed universal orbit-average proposal. Its physical attachment and the selected integer are preserved in the literal tier.

Theory value

row 10

The suite’s retained expression is

Derivation chain

row 10

1. Take the DET-7 quantity as the imposed structural invariant; evaluating it at the working vacuum does not derive its upstream necessity. (appendix_x_zero_parameter_input_ledger.tex:64).
2. Apply the retained adjacent-magnitude expression. The current row names the independently unforced integer and inherited octant registration. (appendix_x_zero_parameter_input_ledger.tex:73; p3_ckm_pmns_mixing.tex:403-404).
3. NOT IN SUITE — a selector for the integer or a common Peirce-block weighting law that frees the loaded quark rows. The conditional formula is evaluated without supplying that missing physical rule. (appendix_x_zero_parameter_input_ledger.tex:73).

Registrar sync

row 10

LIB2-018 — Carries the imposed status of the invariant appearing under the square root.

LIB2-066 — Carries the retained magnitude formula and its loaded physical attachment.

Comparator LIB2-216 / SL-13 — value 0.0407 (+0.0013/−0.0013) · scheme PDG global fit · edition 2026.

LIB2-073 describes a failed universal averaging proposal, not this formula. Historical candidate proposals do not replace the retained expression.

Calculation

Run python3 N10_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N10 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 10 ===')
    print('Scorecard (verbatim): |V cb | 1/(9√7) theory 0.0419961 experiment 0.0407 ± 0.0013 deviation +3.18% · d = +1.00 Loaded-correspondence (physical attachment: inherits the octant registration; the integer 9 data-selected) / Structural formula — A1566 —')
    value = 1.0/(9.0*math.sqrt(7.0))
    print("formula = 1/(9*sqrt(7))")
    print("theory_at_cell_precision = " + shown(value,7))
    compare("full_formula", value, "0.0407", "0.0013", "0.0013")
    compare("printed_cell", "0.0419961", "0.0407", "0.0013", "0.0013")
    print()


if __name__ == "__main__":
    main()

row 10

Actual stdout for this entry; the text blocks in entry order concatenate to N10_stdout.txt.

=== row 10 ===
Scorecard (verbatim): |V cb | 1/(9√7) theory 0.0419961 experiment 0.0407 ± 0.0013 deviation +3.18% · d = +1.00 Loaded-correspondence (physical attachment: inherits the octant registration; the integer 9 data-selected) / Structural formula — A1566 —
formula = 1/(9*sqrt(7))
theory_at_cell_precision = 0.0419961
full_formula.theory = 0.041996053
full_formula.reference = 0.040700000
full_formula.signed_percent = +3.184404316%; rounded = +3.18%
full_formula.uncertainty_used = 0.0013 (upper)
full_formula.d = +0.996963505; rounded = +1.00
printed_cell.theory = 0.041996100
printed_cell.reference = 0.040700000
printed_cell.signed_percent = +3.184520885%; rounded = +3.18%
printed_cell.uncertainty_used = 0.0013 (upper)
printed_cell.d = +0.997000000; rounded = +1.00

Comparison

row 10

Theory 0.0419961; comparator 0.0407 ±0.0013, PDG 2026 global-fit value, dimensionless (LIB2-216 / SL-13). Signed deviation +3.18%; naive d +1.00. The supplied row assigns no separate running scale. Numerical proximity does not establish the unforced integer or the physical registration.

Tier and what this does not show

Literal tier: Loaded-correspondence (physical attachment: inherits the octant registration; the integer 9 data-selected) / Structural formula — A1566. Status: —. Both stated choices are consumed. Agreement does not derive either choice.

Sources

LIB2-018; LIB2-066; LIB2-216; SL-13; appendix_x_zero_parameter_input_ledger.tex:64; appendix_x_zero_parameter_input_ledger.tex:73; p3_ckm_pmns_mixing.tex:403-404.

N11 · The small first-row quark-mixing magnitude

Row

House correction — R77 (S327h). The Scorecard printed d = −0.17. Computed at full precision (|V_ub| = 0.003861973786, from θ₁₂ = 33.4880°, |V_us| = 0.225256, |V_cb| = 0.041996) and rounded once, it is d = −0.18; the percentage stays −0.72%. The Scorecard now prints −0.18. The suite's own −0.17σ (p3:141, p3:404) is queued for Rev32.12 (= Rev33.0, R156). The cell quoted below, and the cell the script echoes, are the text as it was supplied to the drafting lane (the Scorecard through S327g). Scorecard and Registrar are unchanged in every other respect; the sealed papers keep the earlier figure until Rev32.12 (= Rev33.0, R156).

row 11

|V ub | |V us ||V cb |/√6 theory 0.003862 experiment 0.00389 ± 0.00016 deviation −0.72% · d = −0.17 Loaded —

Arithmetic finding: the full formula gives a naive distance rounding to −0.18, whereas the cell prints −0.17. The cell is retained verbatim; the executed calculation uses an explicit decimal half-up display convention.

Theory value

row 11

The retained hierarchy reads

The two prerequisite magnitudes are calculated before display rounding.

Derivation chain

row 11

1. Evaluate the framework-angle Cabibbo route, with its documented data selection. (p3_ckm_pmns_mixing.tex:157).
2. Evaluate the retained adjacent-magnitude expression with its selected integer. (appendix_x_zero_parameter_input_ledger.tex:73).
3. Apply the stated hierarchy factor. The source explicitly retains the loaded status and the current rather than superseded digit. (p3_ckm_pmns_mixing.tex:139-144; appendix_x_zero_parameter_input_ledger.tex:74).

Registrar sync

row 11

LIB2-063 — Carries the selected first-row input.

LIB2-066 — Carries the adjacent-magnitude input.

LIB2-067 — Carries the retained hierarchy and its inherited loading.

Comparator LIB2-215 / SL-12 — value 0.00389 (+0.00016/−0.00016) · scheme PDG global fit · edition 2026.

Calculation

Run python3 N11_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N11 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))


def ckms():
    solar = 3.0 / (PHI**4 + 3.0)
    vus = math.sqrt(solar) / math.sqrt(6.0)
    vcb = 1.0 / (9.0 * math.sqrt(7.0))
    vub = vus * vcb / math.sqrt(6.0)
    vud = math.sqrt(1.0 - vus*vus - vub*vub)
    return vus, vcb, vub, vud

def main():
    print('=== row 11 ===')
    print('Scorecard (verbatim): |V ub | |V us ||V cb |/√6 theory 0.003862 experiment 0.00389 ± 0.00016 deviation −0.72% · d = −0.17 Loaded —')
    vus, vcb, value, vud = ckms()
    print("input_vus = " + shown(vus,12))
    print("input_vcb = " + shown(vcb,12))
    print("formula = vus*vcb/sqrt(6)")
    print("theory_at_cell_precision = " + shown(value,6))
    compare("full_formula", value, "0.00389", "0.00016", "0.00016")
    compare("printed_cell", "0.003862", "0.00389", "0.00016", "0.00016")
    print("finding = printed d=-0.17; explicit half-up audit gives d=-0.18")
    print()


if __name__ == "__main__":
    main()

row 11

Actual stdout for this entry; the text blocks in entry order concatenate to N11_stdout.txt.

=== row 11 ===
Scorecard (verbatim): |V ub | |V us ||V cb |/√6 theory 0.003862 experiment 0.00389 ± 0.00016 deviation −0.72% · d = −0.17 Loaded —
input_vus = 0.225256056227
input_vcb = 0.041996052557
formula = vus*vcb/sqrt(6)
theory_at_cell_precision = 0.003862
full_formula.theory = 0.003861974
full_formula.reference = 0.003890000
full_formula.signed_percent = -0.720468223%; rounded = -0.72%
full_formula.uncertainty_used = 0.00016 (lower)
full_formula.d = -0.175163837; rounded = -0.18
printed_cell.theory = 0.003862000
printed_cell.reference = 0.003890000
printed_cell.signed_percent = -0.719794344%; rounded = -0.72%
printed_cell.uncertainty_used = 0.00016 (lower)
printed_cell.d = -0.175000000; rounded = -0.18
finding = printed d=-0.17; explicit half-up audit gives d=-0.18

Comparison

row 11

Theory 0.003862; comparator 0.00389 ±0.00016, PDG 2026 global fit, dimensionless (LIB2-215 / SL-12). The signed deviation rounds to −0.72%. Both the full-formula and printed-cell audits round d to −0.18 under the declared convention; the source’s −0.17 is not silently copied as a recalculated result. No independent running scale is specified.

Tier and what this does not show

Literal tier: Loaded; status: —. The route, adjacent-magnitude choices and hierarchy readout are consumed. This row is not independent evidence selecting its own inputs. The arithmetic finding is not a tier change.

Sources

LIB2-063; LIB2-066; LIB2-067; LIB2-215; SL-12; p3_ckm_pmns_mixing.tex:139-144; p3_ckm_pmns_mixing.tex:157; appendix_x_zero_parameter_input_ledger.tex:73-74; s1162.

N12 · The CKM phase and its uncorrected control

Row

House note — R84 (S328a). Row 12a now prints the PDG global-fit comparator in the unit it is published in, 1.154 ± 0.025 rad, and computes the distance there: d = +1.40 (the degree cells quoted below give +1.41; R84-e extends R77-a — the comparator's published representation is primary). Rows 12a and 12b now carry Paper 3's own sentence in their status cells: “the 5φ⁻⁵ correction (+2.54°) is not supported by current data” (p3_ckm_pmns_mixing.tex:413-414; R84-d). Row 12c is unchanged. The cells quoted below are the Scorecard as it was supplied to the drafting lane; the sealed papers keep their figures until Rev32.12 (= Rev33.0, R156).

House correction — R77 (S327h). Row 12b: +2.60% → +2.61% (δ = 68.129749°, rounded once). Row 12c: −0.80% → −0.81% against the global fit, and the direct distance −0.30 → −0.29. R77 fixes the asymmetric-error convention: a distance uses the error on the side facing the theory value. So 12b keeps +0.64 (above the central value, upper error 2.7), and 12c uses the lower error 2.8. Of the two denominators this note audits below, the directional one is now the Scorecard's, and the "lower errors are used" sentence the note quotes is queued for Rev32.12 (= Rev33.0, R156) as wording. The cell quoted below, and the cell the script echoes, are the text as it was supplied to the drafting lane (the Scorecard through S327g). Scorecard and Registrar are unchanged in every other respect; the sealed papers keep the earlier figure until Rev32.12 (= Rev33.0, R156).

row 12a

δ CKM (°) vs global fit arctan√(3G 7 ) theory 68.13 experiment 66.12 ± 1.43 deviation +3.04% · d = +1.41 Coincidence-class —

row 12b

δ CKM (°) vs direct γ arctan√(3G 7 ) theory 68.13 experiment 66.4 +2.7 −2.8 deviation +2.60% · d = +0.64 Coincidence-class —

row 12c

δ CKM (°) — bare-φ control (no G 7 correction) arctan√(3φ) theory 65.59 experiment 66.12 ± 1.43 (global) / 66.4 +2.7 −2.8 (direct) deviation −0.80% · d = −0.37 / −0.30 Control (printed beside 12a/b) not scored — the uncorrected argument sits closer than G 7 on both comparators; 28 of 64 sibling corrections land within 1σ, so the numeral’s agreement carries no significance (Paper 3, Rev32.2)

The asymmetric direct-angle convention is inconsistent across the printed summaries: the above-centre corrected value uses the upper error, while the below-centre control also matches the upper error. A nearby source note instead says lower errors are used. Both phase-distance conventions are exposed below. The direct corrected percentage also rounds to +2.61%, not the printed +2.60%; no comparator is reselected.

Theory value

row 12a

The suite prints

row 12b

The same \arctan\sqrt{3G_7} value, 68.13°, is compared with direct \gamma. This is a second comparator, not a second theory value.

row 12c

The uncorrected control is

It is printed beside the corrected argument and is not scored.

Derivation chain

row 12a

1. Take the retained corrected golden argument. Its first-principles motivation is explicitly incomplete. (appendix_x_zero_parameter_input_ledger.tex:75-82).
2. Evaluate the arctangent in degrees against the stated global-fit Dirac phase. (p3_ckm_pmns_mixing.tex:405-409).
3. NOT IN SUITE — a selection law for the correction. The printed sibling census and bare control are reasons not to treat agreement as evidence selecting that correction. (p3_ckm_pmns_mixing.tex:410-416).

row 12b

1. Reuse the corrected phase expression without changing its parameters. (appendix_x_zero_parameter_input_ledger.tex:75-82).
2. Keep the global Dirac phase and the direct unitarity-triangle angle as separately named comparison objects. (p3_ckm_pmns_mixing.tex:405-409).

row 12c

1. Remove the stated correction and evaluate the source’s bare-argument control. (p3_ckm_pmns_mixing.tex:410-416).
2. Keep both comparators and the supplied sibling census. The note does not rerun that search or select a replacement correction. (p3_ckm_pmns_mixing.tex:410-416).

Registrar sync

row 12a

LIB2-068 — Carries the corrected argument, degree-valued expression and coincidence classification.

Comparator LIB2-222 / SL-19 — value 66.12 (+1.43/−1.43) deg · scheme PDG global fit (=1.154±0.025 rad) · edition 2026.

row 12b

LIB2-068 — Carries the same corrected phase; this entry changes only the comparator.

Comparator LIB2-223 / SL-20 — value 66.4 (+2.7/−2.8) deg · scheme direct UT measurement · edition 2026.

row 12c

LIB2-075 — Carries the bare-argument control and its non-scored comparison, not a new physical selection law.

Comparator LIB2-222 / SL-19 — value 66.12 (+1.43/−1.43) deg · scheme PDG global fit (=1.154±0.025 rad) · edition 2026.

Comparator LIB2-223 / SL-20 — value 66.4 (+2.7/−2.8) deg · scheme direct UT measurement · edition 2026.

LIB2-069 and LIB2-070 carry comparison summaries, not the correction’s derivation. Historical claims and open questions are not substituted for LIB2-068.

Calculation

Run python3 N12_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N12 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 12a ===')
    print('Scorecard (verbatim): δ CKM (°) vs global fit arctan√(3G 7 ) theory 68.13 experiment 66.12 ± 1.43 deviation +3.04% · d = +1.41 Coincidence-class —')
    g7 = PHI+5.0*PHI**(-5)
    phase = math.degrees(math.atan(math.sqrt(3.0*g7)))
    print("G7 = " + shown(g7,12))
    print("theory_at_cell_precision_deg = " + shown(phase,2))
    compare("full_formula_global_deg", phase, "66.12", "1.43", "1.43")
    compare("printed_cell_global_deg", "68.13", "66.12", "1.43", "1.43")
    print()
    print('=== row 12b ===')
    print('Scorecard (verbatim): δ CKM (°) vs direct γ arctan√(3G 7 ) theory 68.13 experiment 66.4 +2.7 −2.8 deviation +2.60% · d = +0.64 Coincidence-class —')
    phase = math.degrees(math.atan(math.sqrt(3.0*(PHI+5.0*PHI**(-5)))))
    print("theory_at_cell_precision_deg = " + shown(phase,2))
    compare("full_formula_direct_deg", phase, "66.4", "2.8", "2.7")
    compare("printed_cell_direct_deg", "68.13", "66.4", "2.8", "2.7")
    print("alternate_lower_error_d = " + shown((phase-66.4)/2.8,9,True)
          + "; rounded = " + shown((phase-66.4)/2.8,2,True))
    print()
    print('=== row 12c ===')
    print('Scorecard (verbatim): δ CKM (°) — bare-φ control (no G 7 correction) arctan√(3φ) theory 65.59 experiment 66.12 ± 1.43 (global) / 66.4 +2.7 −2.8 (direct) deviation −0.80% · d = −0.37 / −0.30 Control (printed beside 12a/b) not scored — the uncorrected argument sits closer than G 7 on both comparators; 28 of 64 sibling corrections land within 1σ, so the numeral’s agreement carries no significance (Paper 3, Rev32.2)')
    phase = math.degrees(math.atan(math.sqrt(3.0*PHI)))
    print("theory_at_cell_precision_deg = " + shown(phase,2))
    compare("full_control_global_deg", phase, "66.12", "1.43", "1.43")
    compare("printed_control_global_deg", "65.59", "66.12", "1.43", "1.43")
    compare("full_control_direct_deg", phase, "66.4", "2.8", "2.7")
    compare("printed_control_direct_deg", "65.59", "66.4", "2.8", "2.7")
    print("alternate_upper_error_d = " + shown((phase-66.4)/2.7,9,True)
          + "; rounded = " + shown((phase-66.4)/2.7,2,True))
    print("source_census = 28 of 64 siblings within 1 sigma; reported, not rerun")
    print()


if __name__ == "__main__":
    main()

row 12a

Actual stdout for this entry; the text blocks in entry order concatenate to N12_stdout.txt.

=== row 12a ===
Scorecard (verbatim): δ CKM (°) vs global fit arctan√(3G 7 ) theory 68.13 experiment 66.12 ± 1.43 deviation +3.04% · d = +1.41 Coincidence-class —
G7 = 2.068883707497
theory_at_cell_precision_deg = 68.13
full_formula_global_deg.theory = 68.129749089
full_formula_global_deg.reference = 66.120000000
full_formula_global_deg.signed_percent = +3.039547926%; rounded = +3.04%
full_formula_global_deg.uncertainty_used = 1.43 (upper)
full_formula_global_deg.d = +1.405418943; rounded = +1.41
printed_cell_global_deg.theory = 68.130000000
printed_cell_global_deg.reference = 66.120000000
printed_cell_global_deg.signed_percent = +3.039927405%; rounded = +3.04%
printed_cell_global_deg.uncertainty_used = 1.43 (upper)
printed_cell_global_deg.d = +1.405594406; rounded = +1.41

row 12b

Actual stdout for this entry; the text blocks in entry order concatenate to N12_stdout.txt.

=== row 12b ===
Scorecard (verbatim): δ CKM (°) vs direct γ arctan√(3G 7 ) theory 68.13 experiment 66.4 +2.7 −2.8 deviation +2.60% · d = +0.64 Coincidence-class —
theory_at_cell_precision_deg = 68.13
full_formula_direct_deg.theory = 68.129749089
full_formula_direct_deg.reference = 66.400000000
full_formula_direct_deg.signed_percent = +2.605043809%; rounded = +2.61%
full_formula_direct_deg.uncertainty_used = 2.7 (upper)
full_formula_direct_deg.d = +0.640647811; rounded = +0.64
printed_cell_direct_deg.theory = 68.130000000
printed_cell_direct_deg.reference = 66.400000000
printed_cell_direct_deg.signed_percent = +2.605421687%; rounded = +2.61%
printed_cell_direct_deg.uncertainty_used = 2.7 (upper)
printed_cell_direct_deg.d = +0.640740741; rounded = +0.64
alternate_lower_error_d = +0.617767532; rounded = +0.62

row 12c

Actual stdout for this entry; the text blocks in entry order concatenate to N12_stdout.txt.

=== row 12c ===
Scorecard (verbatim): δ CKM (°) — bare-φ control (no G 7 correction) arctan√(3φ) theory 65.59 experiment 66.12 ± 1.43 (global) / 66.4 +2.7 −2.8 (direct) deviation −0.80% · d = −0.37 / −0.30 Control (printed beside 12a/b) not scored — the uncorrected argument sits closer than G 7 on both comparators; 28 of 64 sibling corrections land within 1σ, so the numeral’s agreement carries no significance (Paper 3, Rev32.2)
theory_at_cell_precision_deg = 65.59
full_control_global_deg.theory = 65.587428410
full_control_global_deg.reference = 66.120000000
full_control_global_deg.signed_percent = -0.805462176%; rounded = -0.81%
full_control_global_deg.uncertainty_used = 1.43 (lower)
full_control_global_deg.d = -0.372427686; rounded = -0.37
printed_control_global_deg.theory = 65.590000000
printed_control_global_deg.reference = 66.120000000
printed_control_global_deg.signed_percent = -0.801572898%; rounded = -0.80%
printed_control_global_deg.uncertainty_used = 1.43 (lower)
printed_control_global_deg.d = -0.370629371; rounded = -0.37
full_control_direct_deg.theory = 65.587428410
full_control_direct_deg.reference = 66.400000000
full_control_direct_deg.signed_percent = -1.223752395%; rounded = -1.22%
full_control_direct_deg.uncertainty_used = 2.8 (lower)
full_control_direct_deg.d = -0.290204139; rounded = -0.29
printed_control_direct_deg.theory = 65.590000000
printed_control_direct_deg.reference = 66.400000000
printed_control_direct_deg.signed_percent = -1.219879518%; rounded = -1.22%
printed_control_direct_deg.uncertainty_used = 2.8 (lower)
printed_control_direct_deg.d = -0.289285714; rounded = -0.29
alternate_upper_error_d = -0.300952441; rounded = -0.30
source_census = 28 of 64 siblings within 1 sigma; reported, not rerun

Comparison

row 12a

Global comparator: 66.12 ±1.43°, PDG 2026 Dirac-phase global fit (LIB2-222 / SL-19). Theory 68.13°, signed deviation +3.04%, naive d +1.41. No renormalization scale is supplied for this fit parameter.

row 12b

Direct comparator: 66.4 +2.7 −2.8°, PDG 2026 direct \gamma (LIB2-223 / SL-20). The cell prints +2.60%, but either full-formula or rounded-cell arithmetic gives +2.61% at two decimals; directional-upper d +0.64. Always using the lower error instead gives +0.62. The two named angles are not silently identified by their numerical proximity.

row 12c

The printed −0.80% refers to the rounded control against the global comparator; full-precision arithmetic is also shown. Global d rounds to −0.37. For the direct comparator the directional-lower d is −0.29, not the printed −0.30; the latter uses the upper error. The control is closer on both comparisons, but no significance or new selection is assigned.

Tier and what this does not show

Literal tiers: Coincidence-class for rows 12a and 12b; Control (printed beside 12a/b) for 12c. The corrected argument remains unselected from first principles; the control is not a hit. The supplied census is retained as a source report, not independently reproduced.

Sources

LIB2-068; LIB2-069; LIB2-070; LIB2-075; LIB2-222; LIB2-223; SL-19; SL-20; appendix_x_zero_parameter_input_ledger.tex:75-82; p3_ckm_pmns_mixing.tex:405-416.

N13 · The fenced structural weak-angle target

Row

row 13

sin²θ W φ⁻³ = √5 − 2 theory 0.236068 experiment 0.23122 ± 0.00006 (MS-bar, M Z ; PDG 2026) deviation +2.10% · d = no d — fenced Structural (~2% target) —

The generic request to print d does not override this row’s explicit “no d — fenced” rule. A better upstream record, LIB2-200, is supplied among another note’s candidates and carries the named scalar readout.

Theory value

row 13

The suite prints the declared readout

The agreement quoted here is a structural percentage comparison, not a scheme-matched weak-angle measurement.

Derivation chain

row 13

1. Take the independent AX6_{\rm pol} postulate and its stated scalar readout. It is not the retired Det-squared object. (appendix_x_zero_parameter_input_ledger.tex:90; p4_higgs_ewsb.tex:360-369).
2. Evaluate the printed reciprocal-power and radical expressions and check their equality numerically. (p4_higgs_ewsb.tex:367-368).
3. NOT IN SUITE — a derived matching scale and threshold map to the measured scheme. The source explicitly retains the structural target and bars a significance calculation. (p4_higgs_ewsb.tex:361-365; p6_rg_thresholds.tex:198-207).

Registrar sync

row 13

LIB2-200 — Carries the independent AX6-pol scalar readout and its distinction from the retired object.

LIB2-199 — Carries the retained reciprocal-power target and the scheme/scale fence.

Comparator LIB2-209 / SL-06 — value 0.23122 (+0.00006/−0.00006) · scheme MZ MS-bar · edition 2026 (A1546 lined).

LIB2-249 and the historical candidates do not replace the current readout. LIB2-200 is explicitly taken from the supplied cross-note material, not invented as a mapping.

Calculation

Run python3 N13_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N13 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")

def main():
    print('=== row 13 ===')
    print('Scorecard (verbatim): sin²θ W φ⁻³ = √5 − 2 theory 0.236068 experiment 0.23122 ± 0.00006 (MS-bar, M Z ; PDG 2026) deviation +2.10% · d = no d — fenced Structural (~2% target) —')
    readout = 3.0/(4.0+(6.0*PHI-1.0))
    value = PHI**(-3)
    assert abs(readout-value) < 1e-14
    assert abs(value-(math.sqrt(5.0)-2.0)) < 1e-14
    print("readout = " + shown(readout,12))
    print("radical = " + shown(math.sqrt(5.0)-2.0,12))
    print("theory_at_cell_precision = " + shown(value,6))
    for label, theory in (("structural_full_formula", Decimal(str(value))),
                          ("structural_printed_cell", Decimal("0.236068"))):
        offset_percent = 100*(theory-Decimal("0.23122"))/Decimal("0.23122")
        print(label+".theory = "+shown(theory,12))
        print(label+".signed_percent = "+shown(offset_percent,9,True)+"%"
              +"; rounded = "+shown(offset_percent,2,True)+"%")
    print("comparator_uncertainty_as_printed = 0.00006")
    print("d_policy = NOT COMPUTED: explicit suite fence; missing scheme/scale matching")
    print()


if __name__ == "__main__":
    main()

row 13

Actual stdout for this entry; the text blocks in entry order concatenate to N13_stdout.txt.

=== row 13 ===
Scorecard (verbatim): sin²θ W φ⁻³ = √5 − 2 theory 0.236068 experiment 0.23122 ± 0.00006 (MS-bar, M Z ; PDG 2026) deviation +2.10% · d = no d — fenced Structural (~2% target) —
readout = 0.236067977500
radical = 0.236067977500
theory_at_cell_precision = 0.236068
structural_full_formula.theory = 0.236067977500
structural_full_formula.signed_percent = +2.096694706%; rounded = +2.10%
structural_printed_cell.theory = 0.236068000000
structural_printed_cell.signed_percent = +2.096704437%; rounded = +2.10%
comparator_uncertainty_as_printed = 0.00006
d_policy = NOT COMPUTED: explicit suite fence; missing scheme/scale matching

Comparison

row 13

Theory 0.236068; comparator 0.23122 ±0.00006, dimensionless, MS-bar at M_Z, PDG 2026 (LIB2-209 / SL-06). Signed structural offset +2.10%. The theoretical effective target is not supplied in that matched scheme and scale. No d is assigned despite the comparator’s small reported uncertainty.

Tier and what this does not show

Literal tier: Structural (~2% target); status: —. The independent readout postulate is consumed; matching is missing. The percentage agreement neither derives an electroweak matching scale nor licenses a sigma-level comparison.

Sources

LIB2-200; LIB2-199; LIB2-209; SL-06; appendix_x_zero_parameter_input_ledger.tex:90; p4_higgs_ewsb.tex:360-369; p6_rg_thresholds.tex:198-207.

N14 · The supplied one-loop gauge coefficients

Row

House note — R84 (S328a). Row 14's tier cell now reads “SM content — not a test of J₃” instead of “no tier assigned” (R84-d). No number moved. The cells quoted below are the Scorecard as it was supplied to the drafting lane; the sealed papers keep their figures until Rev32.12 (= Rev33.0, R156).

row 14

b 1 , b 2 , b 3 41/10, −19/6, −7 theory exact experiment SM one-loop constants deviation 0 · d = exact no tier assigned —

No supplied candidate record carries this coefficient tuple’s derivation. In particular, LIB2-116 concerns a Yukawa trajectory, not the gauge coefficients. The experiment cell names the adopted SM constants rather than independent measurements.

Theory value

row 14

The suite states

The theory entry “exact” refers to this stated rational tuple.

Derivation chain

row 14

1. Use the printed one-loop equation and coefficient tuple. (p6_rg_thresholds.tex:94-98).
2. Retain the GUT-normalized hypercharge convention. The source explicitly excludes the alternative SM-normalized hypercharge coefficient from this calculation. (p6_rg_thresholds.tex:99-102).
3. NOT IN SUITE — in the supplied excerpts, the term-by-term matter and gauge-loop calculation producing the tuple. The script checks the stated rational coefficients and their equivalent inverse-coupling equation; it does not reconstruct that omitted calculation. (p6_rg_thresholds.tex:94-105).

Registrar sync

row 14

NONE — supplied candidates do not state or derive the gauge-coefficient tuple; Paper 6 supplies the equation and constants, not the omitted loop calculation.

Comparator NONE — the reference is internal, structural or adopted, not a supplied experimental ledger entry.

LIB2-116 concerns a different Yukawa-running predicate. The remaining keyword candidates are historical weak-angle material, not this coefficient derivation.

Calculation

Run python3 N14_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N14 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")

def main():
    print('=== row 14 ===')
    print('Scorecard (verbatim): b 1 , b 2 , b 3 41/10, −19/6, −7 theory exact experiment SM one-loop constants deviation 0 · d = exact no tier assigned —')
    values = (Fraction(41,10), Fraction(-19,6), Fraction(-7,1))
    reference = (Fraction(41,10), Fraction(-19,6), Fraction(-7,1))
    for i,(value,ref) in enumerate(zip(values,reference),1):
        assert value == ref
        print("b" + str(i) + " = " + str(value)
              + "; decimal = " + shown(float(value),12)
              + "; adopted_reference = " + str(ref)
              + "; signed_percent = 0%")
        print("inverse_alpha_slope_"+str(i)+" = "
              + shown(-float(value)/(2.0*math.pi),12))
    print("normalization = GUT hypercharge; alternative b1=41/6 is not used")
    print("d = exact (same adopted constants, not experimental distances)")
    print("loop_derivation = NOT IN SUITE (supplied excerpts do not provide it)")
    print()


if __name__ == "__main__":
    main()

row 14

Actual stdout for this entry; the text blocks in entry order concatenate to N14_stdout.txt.

=== row 14 ===
Scorecard (verbatim): b 1 , b 2 , b 3 41/10, −19/6, −7 theory exact experiment SM one-loop constants deviation 0 · d = exact no tier assigned —
b1 = 41/10; decimal = 4.100000000000; adopted_reference = 41/10; signed_percent = 0%
inverse_alpha_slope_1 = -0.652535266677
b2 = -19/6; decimal = -3.166666666667; adopted_reference = -19/6; signed_percent = 0%
inverse_alpha_slope_2 = 0.503990653124
b3 = -7; decimal = -7.000000000000; adopted_reference = -7; signed_percent = 0%
inverse_alpha_slope_3 = 1.114084601643
normalization = GUT hypercharge; alternative b1=41/6 is not used
d = exact (same adopted constants, not experimental distances)
loop_derivation = NOT IN SUITE (supplied excerpts do not provide it)

Comparison

row 14

Theory and internal reference are the same adopted rational constants, with 0% arithmetic deviation. They are dimensionless one-loop coefficients in the source’s GUT-normalized convention, not measurements at an experimental edition. No uncertainty or statistical d exists; “exact” is an identity label. Their values alone do not certify the framework’s full matter-loop derivation.

Tier and what this does not show

Literal tier: no tier assigned; status: —. The source adopts the ordinary one-loop coefficients and normalization. No tier is supplied by this note, and no derivation from the exceptional algebra is inferred from the printed match.

Sources

p6_rg_thresholds.tex:94-105.

N15 · The declared unit top-Yukawa boundary value

Row

row 15

y t (tree) cubic invariant / Peirce ½ theory 1 experiment y t (M Z ) ≈ 0.967 deviation — Structural (declared) —

The “experiment” cell is a reported running result, not a measured comparator at the boundary scale. The attached excerpts do not supply a complete numerical RGE initial-value specification reproducing that result.

Theory value

row 15

The source’s internal extraction gives the middle carrier weight \lambda_2=1, read as the declared boundary value

The separately reported low-scale result is y_t(M_Z)\approx0.967.

Derivation chain

row 15

1. Take the cubic invariant and the stated carrier Higgs direction in the specified Peirce block; the supplied theorem extracts the middle weight. (appendix_a_lagrangian_derivation.tex:231-236).
2. Read that weight as a physical, scale- and scheme-specific Yukawa only through the declared attachment. NOT IN SUITE — the Higgs-direction, coupling-scheme and Planck-scale identifications; the source explicitly says none is proved. (appendix_a_lagrangian_derivation.tex:237-244).
3. Keep the reported running endpoint separate. NOT IN SUITE — in the supplied excerpts, all boundary couplings, matching choices and numerical integration data needed to reproduce that endpoint. (p0_framework_foundations.tex:1002).

Registrar sync

row 15

LIB2-120 — Carries the internal eigenvalue and the declared rather than derived physical attachment.

LIB2-139 — Carries the reported low-scale endpoint, not an experimental comparator or a reproduced integration.

Comparator NONE — the comparison cell is a reported scale-dependent calculation, not an experimental ledger entry.

Calculation

Run python3 N15_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N15 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")

def main():
    print('=== row 15 ===')
    print('Scorecard (verbatim): y t (tree) cubic invariant / Peirce ½ theory 1 experiment y t (M Z ) ≈ 0.967 deviation — Structural (declared) —')
    carrier_diagonal = (PHI, 1.0, PHI**(-1))
    unit = carrier_diagonal[1]
    assert unit == 1.0
    print("carrier_middle_weight = " + shown(unit,0))
    print("declared_boundary_y_t = 1")
    print("reported_running_y_t_MZ = approximately 0.967 (source report; not rerun)")
    print("running_inputs = NOT IN SUITE (complete initial-value data absent from excerpts)")
    print("signed_percent = NOT ASSIGNED (different scales; no experimental comparator)")
    print("d = NOT ASSIGNED (not an experimental comparison)")
    print()


if __name__ == "__main__":
    main()

row 15

Actual stdout for this entry; the text blocks in entry order concatenate to N15_stdout.txt.

=== row 15 ===
Scorecard (verbatim): y t (tree) cubic invariant / Peirce ½ theory 1 experiment y t (M Z ) ≈ 0.967 deviation — Structural (declared) —
carrier_middle_weight = 1
declared_boundary_y_t = 1
reported_running_y_t_MZ = approximately 0.967 (source report; not rerun)
running_inputs = NOT IN SUITE (complete initial-value data absent from excerpts)
signed_percent = NOT ASSIGNED (different scales; no experimental comparator)
d = NOT ASSIGNED (not an experimental comparison)

Comparison

row 15

Boundary theory 1 versus reported low-scale running ≈0.967. Both are dimensionless, but the first is a declared Planck-scale attachment and the second is labelled M_Z. The supplied row does not identify a common renormalization scheme, measurement uncertainty or experimental edition. A difference between scales is not an experimental deviation; percentage and d remain unassigned.

Tier and what this does not show

Literal tier: Structural (declared); status: —. The physical Higgs, coupling and scale identifications are consumed. The internal unit eigenvalue does not by itself derive the physical top coupling or validate its running.

Sources

LIB2-120; LIB2-139; appendix_a_lagrangian_derivation.tex:231-244; p0_framework_foundations.tex:1002.

N16 · The electroweak tree-level top-mass value

Row

House note — R84 (S328a). Row 16 now prints the suite's own running endpoint beside the tree value: 0.967 · v_EW/√2 = 168.36 GeV (−2.46% against 172.60; the suite reports y_t(M_Z) ≈ 0.967 at p2_mass_hierarchy_resolvent_quintics.tex:339-340). Whether the row keeps a distance is not yet ruled (R84-f). The Scorecard footer now names this comparator as the direct-measurement (MC) mass, as this note does (H199). The cells quoted below are the Scorecard as it was supplied to the drafting lane; the sealed papers keep their figures until Rev32.12 (= Rev33.0, R156).

row 16

m t (GeV) v EW /√2 theory 174.104 experiment 172.60 ± 0.27 deviation +0.87% · d = +5.57 Structural cross-scheme

The tree expression is evaluated with the named electroweak anchor. It is not the same object as either a Planck-scale boundary value or the direct/MC mass comparator; those interfaces are not silently filled.

Theory value

row 16

The retained mass expression is

Derivation chain

row 16

1. Take the external electroweak anchor as given by the named operational-anchor inventory. (Appendix X, Table 4, Named operational anchors, PDF p.334).
2. Evaluate the displayed tree-level mass relation. Its physical interpretation inherits the declared Yukawa attachment, rather than the internal eigenvalue theorem. (appendix_x_zero_parameter_input_ledger.tex:93; appendix_a_lagrangian_derivation.tex:231-244).
3. NOT IN SUITE — the scheme/threshold conversion and its uncertainty needed to compare this tree value with a direct/MC top-mass determination. The ledger types the existing distance as cross-scheme and non-status-setting. (appendix_x_zero_parameter_input_ledger.tex:119).

Registrar sync

row 16

LIB2-124 — Carries the external electroweak anchor and its usage inventory.

LIB2-120 — Carries the declared Yukawa attachment inherited by the mass expression.

LIB2-121 — Carries the structural tree-mass expression and cross-scheme comparison boundary.

Comparator LIB2-220 / SL-17 — value 172.60 (+0.27/−0.27) GeV · scheme direct (MC) mass, not MS-bar · edition 2026.

Calculation

Run python3 N16_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N16 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 16 ===')
    print('Scorecard (verbatim): m t (GeV) v EW /√2 theory 174.104 experiment 172.60 ± 0.27 deviation +0.87% · d = +5.57 Structural cross-scheme')
    vew = 246.22
    value = vew/math.sqrt(2.0)
    print("external_vEW_GeV = " + shown(vew,2))
    print("theory_at_cell_precision_GeV = " + shown(value,3))
    compare("full_tree_GeV", value, "172.60", "0.27", "0.27")
    compare("printed_tree_GeV", "174.104", "172.60", "0.27", "0.27")
    print("comparison_type = cross-scheme naive distance; no theory/matching uncertainty supplied")
    print()


if __name__ == "__main__":
    main()

row 16

Actual stdout for this entry; the text blocks in entry order concatenate to N16_stdout.txt.

=== row 16 ===
Scorecard (verbatim): m t (GeV) v EW /√2 theory 174.104 experiment 172.60 ± 0.27 deviation +0.87% · d = +5.57 Structural cross-scheme
external_vEW_GeV = 246.22
theory_at_cell_precision_GeV = 174.104
full_tree_GeV.theory = 174.103831664
full_tree_GeV.reference = 172.600000000
full_tree_GeV.signed_percent = +0.871281381%; rounded = +0.87%
full_tree_GeV.uncertainty_used = 0.27 (upper)
full_tree_GeV.d = +5.569746903; rounded = +5.57
printed_tree_GeV.theory = 174.104000000
printed_tree_GeV.reference = 172.600000000
printed_tree_GeV.signed_percent = +0.871378911%; rounded = +0.87%
printed_tree_GeV.uncertainty_used = 0.27 (upper)
printed_tree_GeV.d = +5.570370370; rounded = +5.57
comparison_type = cross-scheme naive distance; no theory/matching uncertainty supplied

Comparison

row 16

Theory 174.104 GeV; comparator 172.60 ±0.27 GeV, PDG 2026 direct/MC mass determination (LIB2-220 / SL-17), not an MS-bar running mass. Signed deviation +0.87%; naive cross-scheme d +5.57. The source supplies neither a matched scale/scheme conversion nor theory uncertainty, so d is not a tension or a status rule.

Tier and what this does not show

Literal tier: Structural; status: cross-scheme. The electroweak anchor and physical attachment are consumed. This arithmetic does not transport a high-scale coupling to the electroweak scale or derive a direct/MC pole proxy.

Sources

LIB2-124; LIB2-120; LIB2-121; LIB2-220; SL-17; Appendix X, Table 4, Named operational anchors, PDF p.334; appendix_x_zero_parameter_input_ledger.tex:93; appendix_x_zero_parameter_input_ledger.tex:119; appendix_a_lagrangian_derivation.tex:231-244.

N17 · The muon tree value and the supplied QED correction

Row

row 17a

m μ tree (MeV) (φ/√5) 8/3 ·√2/10·m τ theory 106.05 experiment 105.6583755 deviation +0.37% Structural / loaded fit gap

row 17b

m μ phys (MeV) tree / (1+δ QED ) theory 105.72 experiment 105.6583755 deviation +0.06% same —

No comparator uncertainty, Registrar comparator ID or SL ID accompanies the precise muon cell. The QED percentage is supplied as a matching input; the script does not claim to derive it from an unspecified electromagnetic coupling.

Theory value

row 17a

The retained tree relation is

row 17b

The suite prints

The script uses the displayed correction, not a newly chosen value of \alpha.

Derivation chain

row 17a

1. Take the tau anchor and retained mass-ratio formula. The source identifies the exponent and geometric normalization but explicitly distinguishes those exact facts from a derivation selecting them as mass coefficients. (appendix_a_lagrangian_derivation.tex:699-704; appendix_x_zero_parameter_input_ledger.tex:419-420).
2. Multiply without first rounding the mass ratio. The residual is the source’s coefficient gap, not an automatically generated radiative correction. (p2_mass_hierarchy_resolvent_quintics.tex:226-233).
3. NOT IN SUITE — the physical exponent/normalization selector. The supplied provenance paragraph expressly retains its target-first origin and blocking formal derivation. (appendix_a_lagrangian_derivation.tex:704).

row 17b

1. Reuse the unrounded structural tree mass; do not absorb its coefficient gap into the matching correction. (p2_mass_hierarchy_resolvent_quintics.tex:226-235).
2. Apply the positive supplied correction by division, as printed. (p2_mass_hierarchy_resolvent_quintics.tex:234-236).
3. NOT IN SUITE — in the supplied excerpts, the fully specified electromagnetic-coupling and matching prescription that reproduces the quoted correction independently. Its numerical value is therefore a declared calculation input here. (appendix_x_zero_parameter_input_ledger.tex:97).

Registrar sync

row 17a

LIB2-122 — Carries the retained ratio and its loaded provenance.

LIB2-123 — Carries the coefficient-gap interpretation of the tree residual.

LIB2-125 — Carries the tau-anchored tree mass.

Comparator NONE — no matching comparator record is supplied for this exact entry; the stated cell is retained without inventing an ID.

row 17b

LIB2-122 — Carries the inherited structural ratio.

LIB2-125 — Carries its anchored tree mass.

LIB2-126 — Carries the separate QED division and supplied correction.

Comparator NONE — no matching comparator record is supplied for this exact entry; the stated cell is retained without inventing an ID.

LIB2-127 concerns the downstream electron construction. Superseded empirical mass proposals are not used.

Calculation

Run python3 N17_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N17 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))


def lepton_chain():
    # The printed matching correction is an input, not re-derived here.
    tau = 1776.93
    ratio = (PHI / math.sqrt(5.0))**(8.0/3.0) * math.sqrt(2.0)/10.0
    tree = tau * ratio
    delta = 0.003125
    return tau, ratio, tree, delta, tree / (1.0 + delta)

def main():
    print('=== row 17a ===')
    print('Scorecard (verbatim): m μ tree (MeV) (φ/√5) 8/3 ·√2/10·m τ theory 106.05 experiment 105.6583755 deviation +0.37% Structural / loaded fit gap')
    tau, ratio, tree, delta, physical = lepton_chain()
    print("tau_anchor_MeV = " + shown(tau,2))
    print("mass_ratio = " + shown(ratio,12))
    print("exponent = 8/3; normalization = sqrt(2)/10")
    print("normalization_value = " + shown(math.sqrt(2.0)/10.0,9))
    print("theory_at_cell_precision_MeV = " + shown(tree,2))
    compare("full_tree_MeV", tree, "105.6583755")
    compare("printed_tree_MeV", "106.05", "105.6583755")
    print()
    print('=== row 17b ===')
    print('Scorecard (verbatim): m μ phys (MeV) tree / (1+δ QED ) theory 105.72 experiment 105.6583755 deviation +0.06% same —')
    tau, ratio, tree, delta, physical = lepton_chain()
    print("supplied_delta_QED = " + shown(delta,6) + "; percent = " + shown(100*delta,4)+"%")
    print("full_tree_input_MeV = " + shown(tree,12))
    print("theory_at_cell_precision_MeV = " + shown(physical,2))
    print("alternative_from_rounded_tree_MeV = " + shown(106.05/(1+delta),12))
    compare("full_matching_chain_MeV", physical, "105.6583755")
    compare("printed_physical_cell_MeV", "105.72", "105.6583755")
    print("source_finer_percent_display = +0.058%; rounded-cell rather than full-chain convention")
    print()


if __name__ == "__main__":
    main()

row 17a

Actual stdout for this entry; the text blocks in entry order concatenate to N17_stdout.txt.

=== row 17a ===
Scorecard (verbatim): m μ tree (MeV) (φ/√5) 8/3 ·√2/10·m τ theory 106.05 experiment 105.6583755 deviation +0.37% Structural / loaded fit gap
tau_anchor_MeV = 1776.93
mass_ratio = 0.059683648785
exponent = 8/3; normalization = sqrt(2)/10
normalization_value = 0.141421356
theory_at_cell_precision_MeV = 106.05
full_tree_MeV.theory = 106.053666035
full_tree_MeV.reference = 105.658375500
full_tree_MeV.signed_percent = +0.374121345%; rounded = +0.37%
full_tree_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
printed_tree_MeV.theory = 106.050000000
printed_tree_MeV.reference = 105.658375500
printed_tree_MeV.signed_percent = +0.370651638%; rounded = +0.37%
printed_tree_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)

row 17b

Actual stdout for this entry; the text blocks in entry order concatenate to N17_stdout.txt.

=== row 17b ===
Scorecard (verbatim): m μ phys (MeV) tree / (1+δ QED ) theory 105.72 experiment 105.6583755 deviation +0.06% same —
supplied_delta_QED = 0.003125; percent = 0.3125%
full_tree_input_MeV = 106.053666035117
theory_at_cell_precision_MeV = 105.72
alternative_from_rounded_tree_MeV = 105.719626168224
full_matching_chain_MeV.theory = 105.723280783
full_matching_chain_MeV.reference = 105.658375500
full_matching_chain_MeV.signed_percent = +0.061429378%; rounded = +0.06%
full_matching_chain_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
printed_physical_cell_MeV.theory = 105.720000000
printed_physical_cell_MeV.reference = 105.658375500
printed_physical_cell_MeV.signed_percent = +0.058324293%; rounded = +0.06%
printed_physical_cell_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
source_finer_percent_display = +0.058%; rounded-cell rather than full-chain convention

Comparison

row 17a

Theory 106.05 MeV; the supplied experimental cell is 105.6583755 MeV, a charged-lepton mass comparator. Signed deviation +0.37%. The precise comparator’s uncertainty and edition/ledger binding are not supplied, so no d is calculated. This is the retained structural fit gap, not a subtraction justified by the next variant.

row 17b

Theory 105.72 MeV against the same 105.6583755 MeV comparator; signed deviation rounds to +0.06%. The source’s finer +0.058% display depends on the rounded-value convention; both paths are printed. No uncertainty or exact edition binding accompanies the comparator, and d is unavailable. No additional renormalization scale is inferred from the label “physical.”

Tier and what this does not show

Row 17a literal tier: Structural / loaded, status fit gap. Row 17b literal tier: same, status —; “same” refers to the preceding tier. The tau anchor, exponent, normalization and quoted correction are consumed. Improved agreement does not derive the physical coefficient selector or erase the original tree gap.

Sources

LIB2-122; LIB2-123; LIB2-125; LIB2-126; appendix_a_lagrangian_derivation.tex:699-704; appendix_x_zero_parameter_input_ledger.tex:97; appendix_x_zero_parameter_input_ledger.tex:419-420; p2_mass_hierarchy_resolvent_quintics.tex:226-236.

N18 · The external Koide rule and its light electron root

Row

House correction — R77 (S327h). The Scorecard printed −0.67%. With the electron mass kept at full precision (0.507607 MeV) it is −0.66%, which is also what the suite prints (p2:239). The Scorecard now prints −0.66%; the theory cell still displays 0.5076. The "forces the Koide sum rule" wording this note flags (p2:237–238) is queued for Rev32.12 (= Rev33.0, R156). The cell quoted below, and the cell the script echoes, are the text as it was supplied to the drafting lane (the Scorecard through S327g). Scorecard and Registrar are unchanged in every other respect; the sealed papers keep the earlier figure until Rev32.12 (= Rev33.0, R156).

row 18

m e (MeV) QED-Koide, K = 2/3 theory 0.5076 experiment 0.51099895069 deviation −0.67% Koide-consistent ext. selector

The cell is reproduced from the unrounded corrected muon chain. Substituting its displayed rounded muon mass changes the last digits. The cell’s percentage uses the rounded electron value; the full-chain percentage is separately printed. The comparator has no supplied uncertainty or ledger ID.

Theory value

row 18

The supplied Koide equation is

With the unrounded QED-corrected muon chain and the tau anchor, its selected light root is 0.5076 MeV at cell precision.

Derivation chain

row 18

1. Obtain the tau-anchored tree muon value from the retained structural formula, keeping intermediate precision. (appendix_a_lagrangian_derivation.tex:701-704).
2. Divide by the supplied QED factor and insert the result into the printed Koide equation. (p0_framework_foundations.tex:968-977).
3. Solve that equation as a quadratic in the electron square-root mass and take the light positive branch; the source explicitly says a second positive branch exists. (p2_mass_hierarchy_resolvent_quintics.tex:240-243).
4. NOT IN SUITE — a derivation selecting the empirical Koide value or physical light branch. The current attachment is external; older “forces” wording in the intermediate chain does not supply this missing derivation. (appendix_a_lagrangian_derivation.tex:704; appendix_o_restmass_program.tex:117-118; p2_mass_hierarchy_resolvent_quintics.tex:237-243).

Registrar sync

row 18

LIB2-122 — Carries the inherited muon ratio.

LIB2-125 — Carries its tau-anchored tree value.

LIB2-126 — Carries the supplied QED correction.

LIB2-127 — Carries the external Koide constraint, light-root choice and electron value.

Comparator NONE — no matching comparator record is supplied for this exact entry; the stated cell is retained without inventing an ID.

LIB2-267 is historical wording, not a replacement for the current external-selector record.

Calculation

Run python3 N18_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N18 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))


def lepton_chain():
    # The printed matching correction is an input, not re-derived here.
    tau = 1776.93
    ratio = (PHI / math.sqrt(5.0))**(8.0/3.0) * math.sqrt(2.0)/10.0
    tree = tau * ratio
    delta = 0.003125
    return tau, ratio, tree, delta, tree / (1.0 + delta)


def koide_roots(muon, tau):
    # Solve the supplied K=2/3 equation in x=sqrt(m_e), without a mass fit.
    s = math.sqrt(muon) + math.sqrt(tau)
    c = muon + tau - 4.0 * math.sqrt(muon*tau)
    disc = 4.0*s*s - c
    if disc < 0:
        raise ValueError("The supplied Koide inputs have no real roots.")
    lo, hi = 2.0*s - math.sqrt(disc), 2.0*s + math.sqrt(disc)
    if lo < 0:
        raise ValueError("The light square-root solution is not physical.")
    return lo*lo, hi*hi

def main():
    print('=== row 18 ===')
    print('Scorecard (verbatim): m e (MeV) QED-Koide, K = 2/3 theory 0.5076 experiment 0.51099895069 deviation −0.67% Koide-consistent ext. selector')
    tau, ratio, tree, delta, physical = lepton_chain()
    light, heavy = koide_roots(physical,tau)
    rounded_mu_light, unused = koide_roots(105.72,tau)
    rounded_tree_light, unused = koide_roots(106.05/(1+delta),tau)
    k = (light+physical+tau)/(math.sqrt(light)+math.sqrt(physical)+math.sqrt(tau))**2
    assert abs(k-2.0/3.0) < 1e-13
    print("tau_anchor_MeV = " + shown(tau,2))
    print("unrounded_mu_tree_MeV = " + shown(tree,12))
    print("supplied_delta_QED = " + shown(delta,6))
    print("unrounded_mu_physical_MeV = " + shown(physical,12))
    print("selected_light_root_MeV = " + shown(light,12))
    print("other_positive_root_MeV = " + shown(heavy,9))
    print("Koide_K_check = " + shown(k,12))
    print("theory_at_cell_precision_MeV = " + shown(light,4))
    print("light_root_from_rounded_mu_MeV = " + shown(rounded_mu_light,12)
          + "; rounded = " + shown(rounded_mu_light,4))
    print("light_root_from_rounded_tree_MeV = " + shown(rounded_tree_light,12)
          + "; rounded = " + shown(rounded_tree_light,4))
    compare("full_chain_MeV", light, "0.51099895069")
    compare("printed_cell_MeV", "0.5076", "0.51099895069")
    print()


if __name__ == "__main__":
    main()

row 18

Actual stdout for this entry; the text blocks in entry order concatenate to N18_stdout.txt.

=== row 18 ===
Scorecard (verbatim): m e (MeV) QED-Koide, K = 2/3 theory 0.5076 experiment 0.51099895069 deviation −0.67% Koide-consistent ext. selector
tau_anchor_MeV = 1776.93
unrounded_mu_tree_MeV = 106.053666035117
supplied_delta_QED = 0.003125
unrounded_mu_physical_MeV = 105.723280782672
selected_light_root_MeV = 0.507607012435
other_positive_root_MeV = 43693.898514467
Koide_K_check = 0.666666666667
theory_at_cell_precision_MeV = 0.5076
light_root_from_rounded_mu_MeV = 0.507771699106; rounded = 0.5078
light_root_from_rounded_tree_MeV = 0.507790466434; rounded = 0.5078
full_chain_MeV.theory = 0.507607012
full_chain_MeV.reference = 0.510998951
full_chain_MeV.signed_percent = -0.663785757%; rounded = -0.66%
full_chain_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
printed_cell_MeV.theory = 0.507600000
printed_cell_MeV.reference = 0.510998951
printed_cell_MeV.signed_percent = -0.665158057%; rounded = -0.67%
printed_cell_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)

Comparison

row 18

Theory cell 0.5076 MeV, comparator cell 0.51099895069 MeV. Rounded-cell deviation is −0.67%; the unrounded chain rounds to −0.66%. The precise comparator’s uncertainty, edition and scheme/scale binding are not supplied, so d is unavailable. This is an externally constrained charged-lepton calculation, not three independently derived masses.

Tier and what this does not show

Literal tier: Koide-consistent; status: ext. selector. The tau anchor, structural muon ratio, supplied correction, empirical Koide value and light branch are consumed. Reproducing the equation and the cell does not derive those attachments. In particular, the older forcing sentence is not adopted as a tier upgrade.

Sources

LIB2-122; LIB2-125; LIB2-126; LIB2-127; appendix_a_lagrangian_derivation.tex:701-704; p0_framework_foundations.tex:968-977; p2_mass_hierarchy_resolvent_quintics.tex:237-243; appendix_o_restmass_program.tex:117-118.

N19 · The bottom bridge and its tau anchor

Row

House correction — R77 (S327h). Row 19: the Scorecard printed −0.96% · d = −6.67, computed from the displayed 4146 MeV. At full precision (m_b = 4146.17 MeV) it is −0.95% · d = −6.64; the theory cell still displays 4146. It is a naive cross-scheme comparator distance, not a tension, as before. The τ row is unchanged. The cell quoted below, and the cell the script echoes, are the text as it was supplied to the drafting lane (the Scorecard through S327g). Scorecard and Registrar are unchanged in every other respect; the sealed papers keep the earlier figure until Rev32.12 (= Rev33.0, R156).

row 19

m b (MeV) (7/3)·m τ theory 4146 experiment 4186 ± 6 (m b (m b ), MS-bar) deviation −0.96% · d = −6.67 Structural cross-scheme

row τ

— m τ (MeV) anchor theory 1776.93 experiment 1776.93 ± 0.09 deviation 0 Input anchor

The bottom cell and its quoted distance use the integer-MeV display, not the unrounded bridge value. Both are shown. The tau entry is an input anchor and has no derivation record mapped as though it were a prediction.

Theory value

row 19

The suite prints

at cell precision. The unrounded product is 4146.17 MeV.

row τ

The entry is the external anchor

Its equality with the central comparator is by adoption, not an independent theory result.

Derivation chain

row 19

1. Take DET-7 and the stated Jordan rank ratio as the retained bridge coefficient, while preserving the invariant’s imposed status. (appendix_x_zero_parameter_input_ledger.tex:64; appendix_x_zero_parameter_input_ledger.tex:96).
2. Multiply the external tau anchor by the bridge coefficient without intermediate rounding. (appendix_x_zero_parameter_input_ledger.tex:419; appendix_x_zero_parameter_input_ledger.tex:427).
3. NOT IN SUITE — the on-shell/renormalization matching that makes this algebraic ratio a scheme-matched physical mass relation. The supplied source explicitly retains the physical attachment gap. (p2_mass_hierarchy_resolvent_quintics.tex:437-441; appendix_i_dynamics_bounce.tex:643-651).

row τ

1. Load the tau mass from the named operational-anchor inventory and use it unchanged in the formula chains. (Appendix X, Table 4, Named operational anchors, PDF p.334; appendix_x_zero_parameter_input_ledger.tex:419).
2. No derivation step is claimed for this input. The source distinguishes named empirical anchors from a derived relation tying their values together. (Appendix X, Ledger consequence: physical one-input reading, PDF p.331).

Registrar sync

row 19

LIB2-018 — Carries the imposed status of the invariant in the bridge coefficient.

LIB2-124 — Carries the operational tau anchor.

LIB2-130 — Carries the bottom bridge and its cross-scheme boundary.

Comparator LIB2-219 / SL-16 — value 4186 (+6/−6) MeV · scheme MS-bar at m_b · edition 2026.

row τ

NONE — this entry is the externally adopted tau anchor, not a derivation; LIB2-124 documents its use but does not derive its value.

Comparator LIB2-221 / SL-18 — value 1776.93 (+0.09/−0.09) MeV · scheme pole · edition 2026.

LIB2-132 is a scoped negative running test, not a conversion or a derivation of this bridge.

Calculation

Run python3 N19_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N19 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 19 ===')
    print('Scorecard (verbatim): m b (MeV) (7/3)·m τ theory 4146 experiment 4186 ± 6 (m b (m b ), MS-bar) deviation −0.96% · d = −6.67 Structural cross-scheme')
    tau = Decimal("1776.93")
    value = Decimal(7)*tau/Decimal(3)
    print("tau_anchor_MeV = " + shown(tau,2))
    print("bridge_coefficient = 7/3")
    print("unrounded_bottom_MeV = " + shown(value,2))
    print("theory_at_cell_precision_MeV = " + shown(value,0))
    compare("unrounded_bridge_MeV", value, "4186", "6", "6")
    compare("printed_cell_MeV", "4146", "4186", "6", "6")
    print("comparison_type = cross-scheme; tau/matching uncertainty not propagated")
    print()
    print('=== row τ ===')
    print('Scorecard (verbatim): — m τ (MeV) anchor theory 1776.93 experiment 1776.93 ± 0.09 deviation 0 Input anchor')
    compare("adopted_tau_anchor_MeV", "1776.93", "1776.93", "0.09", "0.09")
    print("interpretation = input equality, not independent agreement")
    print()


if __name__ == "__main__":
    main()

row 19

Actual stdout for this entry; the text blocks in entry order concatenate to N19_stdout.txt.

=== row 19 ===
Scorecard (verbatim): m b (MeV) (7/3)·m τ theory 4146 experiment 4186 ± 6 (m b (m b ), MS-bar) deviation −0.96% · d = −6.67 Structural cross-scheme
tau_anchor_MeV = 1776.93
bridge_coefficient = 7/3
unrounded_bottom_MeV = 4146.17
theory_at_cell_precision_MeV = 4146
unrounded_bridge_MeV.theory = 4146.170000000
unrounded_bridge_MeV.reference = 4186.000000000
unrounded_bridge_MeV.signed_percent = -0.951505017%; rounded = -0.95%
unrounded_bridge_MeV.uncertainty_used = 6 (lower)
unrounded_bridge_MeV.d = -6.638333333; rounded = -6.64
printed_cell_MeV.theory = 4146.000000000
printed_cell_MeV.reference = 4186.000000000
printed_cell_MeV.signed_percent = -0.955566173%; rounded = -0.96%
printed_cell_MeV.uncertainty_used = 6 (lower)
printed_cell_MeV.d = -6.666666667; rounded = -6.67
comparison_type = cross-scheme; tau/matching uncertainty not propagated

row τ

Actual stdout for this entry; the text blocks in entry order concatenate to N19_stdout.txt.

=== row τ ===
Scorecard (verbatim): — m τ (MeV) anchor theory 1776.93 experiment 1776.93 ± 0.09 deviation 0 Input anchor
adopted_tau_anchor_MeV.theory = 1776.930000000
adopted_tau_anchor_MeV.reference = 1776.930000000
adopted_tau_anchor_MeV.signed_percent = +0.000000000%; rounded = +0.00%
adopted_tau_anchor_MeV.uncertainty_used = 0.09 (upper)
adopted_tau_anchor_MeV.d = +0.000000000; rounded = +0.00
interpretation = input equality, not independent agreement

Comparison

row 19

Theory cell 4146 MeV; comparator 4186 ±6 MeV, PDG 2026, m_b(m_b) in MS-bar (LIB2-219 / SL-16). The cell gives −0.96%, naive d −6.67. The unrounded product gives −0.95%, naive d −6.64 at the same display precision. These are cross-scheme comparator distances, not tensions; no conversion or theory uncertainty is supplied.

row τ

Adopted value 1776.93 MeV; comparator 1776.93 ±0.09 MeV, PDG 2026 tau pole mass (LIB2-221 / SL-18). Arithmetic deviation and naive d are 0 because the central value was used as input. A running scale is not applicable to this pole-mass anchor. Its uncertainty is not propagated into the bottom row’s naive experimental-error distance.

Tier and what this does not show

Row 19 literal tier: Structural; status cross-scheme. The tau anchor and structural bridge are consumed. The τ entry has literal tier Input, status anchor. Agreement at the anchor adds no evidence for the bridge and does not derive a shared dimensional calibration.

Sources

LIB2-018; LIB2-124; LIB2-130; LIB2-219; LIB2-221; SL-16; SL-18; appendix_x_zero_parameter_input_ledger.tex:64; appendix_x_zero_parameter_input_ledger.tex:96; appendix_x_zero_parameter_input_ledger.tex:419; appendix_x_zero_parameter_input_ledger.tex:427; p2_mass_hierarchy_resolvent_quintics.tex:437-441; appendix_i_dynamics_bounce.tex:643-651; Appendix X, Table 4, Named operational anchors, PDF p.334; Appendix X, Ledger consequence: physical one-input reading, PDF p.331.

N20 · The constituent-anchored charm bridge

Row

row 20

m c (MeV) (7/3)·m s const theory 1291.9 experiment 1272.9 ± 4.5 (m c (m c ), MS-bar) deviation +1.49% · d = +4.22 Structural cross-scheme

The printed charm cell is obtained by retaining the full strange-constituent formula before applying the bridge. Multiplying the displayed rounded strange value instead changes the final decimal. The approximate hadronic anchor has no supplied uncertainty.

Theory value

row 20

The source prints

The supplied explicit form is m_s^{\rm const}=260\phi\,3^{1/4} MeV. Keeping its intermediate precision gives 1291.9 MeV at cell precision.

Derivation chain

row 20

1. Take the approximate external hadronic anchor and the source’s constituent prescription. The explicit formula supplies the fourth-root factor numerically. (p0_framework_foundations.tex:529; appendix_x_zero_parameter_input_ledger.tex:428).
2. Apply the retained invariant/rank bridge to the unrounded constituent proxy. (appendix_x_zero_parameter_input_ledger.tex:96; appendix_x_zero_parameter_input_ledger.tex:424).
3. NOT IN SUITE — a constituent-to-MS-bar conversion with uncertainty or a physical matching theorem for this bridge. The source explicitly retains that gap. (appendix_x_zero_parameter_input_ledger.tex:96; p2_mass_hierarchy_resolvent_quintics.tex:437-441).

Registrar sync

row 20

LIB2-018 — Carries the imposed invariant used by the bridge.

LIB2-124 — Carries the named external hadronic anchor.

LIB2-129 — Carries the strange-constituent proxy and its modifier.

LIB2-131 — Carries the retained charm bridge and missing-conversion boundary.

Comparator LIB2-218 / SL-15 — value 1272.9 (+4.5/−4.5) MeV · scheme MS-bar at m_c · edition 2026.

LIB2-132 does not supply the missing conversion. Historical mass offsets do not replace the current comparator.

Calculation

Run python3 N20_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N20 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 20 ===')
    print('Scorecard (verbatim): m c (MeV) (7/3)·m s const theory 1291.9 experiment 1272.9 ± 4.5 (m c (m c ), MS-bar) deviation +1.49% · d = +4.22 Structural cross-scheme')
    anchor = 260.0
    strange = anchor*PHI*3.0**0.25
    charm = (7.0/3.0)*strange
    rounded_strange_bridge = Decimal(7)*Decimal("553.7")/Decimal(3)
    print("external_hadronic_anchor_MeV = approximately 260 (used as 260.0)")
    print("strange_full_formula_MeV = " + shown(strange,12))
    print("strange_display_MeV = " + shown(strange,1))
    print("bridge_coefficient = 7/3")
    print("theory_at_cell_precision_MeV = " + shown(charm,1))
    print("bridge_from_rounded_strange_MeV = " + shown(rounded_strange_bridge,9)
          + "; rounded = " + shown(rounded_strange_bridge,1))
    compare("full_constituent_bridge_MeV", charm, "1272.9", "4.5", "4.5")
    compare("printed_cell_MeV", "1291.9", "1272.9", "4.5", "4.5")
    print("comparison_type = constituent-anchored versus MS-bar; no conversion uncertainty")
    print()


if __name__ == "__main__":
    main()

row 20

Actual stdout for this entry; the text blocks in entry order concatenate to N20_stdout.txt.

=== row 20 ===
Scorecard (verbatim): m c (MeV) (7/3)·m s const theory 1291.9 experiment 1272.9 ± 4.5 (m c (m c ), MS-bar) deviation +1.49% · d = +4.22 Structural cross-scheme
external_hadronic_anchor_MeV = approximately 260 (used as 260.0)
strange_full_formula_MeV = 553.657646013577
strange_display_MeV = 553.7
bridge_coefficient = 7/3
theory_at_cell_precision_MeV = 1291.9
bridge_from_rounded_strange_MeV = 1291.966666667; rounded = 1292.0
full_constituent_bridge_MeV.theory = 1291.867840698
full_constituent_bridge_MeV.reference = 1272.900000000
full_constituent_bridge_MeV.signed_percent = +1.490128109%; rounded = +1.49%
full_constituent_bridge_MeV.uncertainty_used = 4.5 (upper)
full_constituent_bridge_MeV.d = +4.215075711; rounded = +4.22
printed_cell_MeV.theory = 1291.900000000
printed_cell_MeV.reference = 1272.900000000
printed_cell_MeV.signed_percent = +1.492654568%; rounded = +1.49%
printed_cell_MeV.uncertainty_used = 4.5 (upper)
printed_cell_MeV.d = +4.222222222; rounded = +4.22
comparison_type = constituent-anchored versus MS-bar; no conversion uncertainty

Comparison

row 20

Theory 1291.9 MeV; comparator 1272.9 ±4.5 MeV, PDG 2026, m_c(m_c) in MS-bar (LIB2-218 / SL-15). Signed offset +1.49%, naive d +4.22. The theory is constituent-anchored and has no supplied conversion uncertainty; the offset is not a physics tension. The approximate anchor is not secretly adjusted to the comparator.

Tier and what this does not show

Literal tier: Structural; status: cross-scheme. The hadronic anchor, constituent prescription and bridge attachment are consumed. Numerical agreement does not derive a current-quark mass from a constituent proxy or establish the absent matching relation.

Sources

LIB2-018; LIB2-124; LIB2-129; LIB2-131; LIB2-218; SL-15; p0_framework_foundations.tex:529; appendix_x_zero_parameter_input_ledger.tex:96; appendix_x_zero_parameter_input_ledger.tex:424; appendix_x_zero_parameter_input_ledger.tex:428; p2_mass_hierarchy_resolvent_quintics.tex:437-441; s194.

N21 · The light constituent-mass proxy

Row

House correction — R77 (S327h). The Scorecard printed −1.49%, computed from the displayed 331 MeV. At full precision (Λ_G2·√φ = 330.725 MeV against the ~336 MeV constituent target) it is −1.57%; the theory cell still displays 331. The suite's Appendix X table prints −1.4% with no stated convention; that is queued for Rev32.12 (= Rev33.0, R156). The cell quoted below, and the cell the script echoes, are the text as it was supplied to the drafting lane (the Scorecard through S327g). Scorecard and Registrar are unchanged in every other respect; the sealed papers keep the earlier figure until Rev32.12 (= Rev33.0, R156).

row 21

m u const (MeV) Λ G2 ·√φ theory 331 experiment ~336 (constituent target) deviation −1.49% Structural constituent

The quoted percentage is calculated from the displayed integer-MeV theory value. The full proxy gives a different rounded percentage. The supplied suite table also prints a coarser percentage that does not equal either audit at the same precision.

Theory value

row 21

The suite prints

The script uses the stated central anchor without treating its approximate value as exact physical knowledge.

Derivation chain

row 21

1. Load the named approximate hadronic anchor, not an algebraically derived scale. (appendix_x_zero_parameter_input_ledger.tex:89; Appendix X, Table 4, Named operational anchors, PDF p.334).
2. Apply the printed constituent proxy and round only for the cell display. (appendix_x_zero_parameter_input_ledger.tex:94; appendix_x_zero_parameter_input_ledger.tex:425).
3. Keep the constituent/current-mass distinction. NOT IN SUITE — a supplied uncertainty and unique scheme/scale definition for the approximate constituent comparison, or a conversion to a current-quark mass. (Appendix X, Table 4, Constituent/current-mass boundary, PDF p.334).

Registrar sync

row 21

LIB2-124 — Carries the externally supplied hadronic anchor.

LIB2-128 — Carries the light constituent proxy and its distinction from a current-quark mass.

Comparator NONE — no matching comparator record is supplied for this exact entry; the stated cell is retained without inventing an ID.

LIB2-129 concerns the strange proxy; its quoted constituent/current-mass boundary is relevant, but its formula does not derive the up-constituent row.

Calculation

Run python3 N21_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N21 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 21 ===')
    print('Scorecard (verbatim): m u const (MeV) Λ G2 ·√φ theory 331 experiment ~336 (constituent target) deviation −1.49% Structural constituent')
    anchor = 260.0
    value = anchor*math.sqrt(PHI)
    print("external_hadronic_anchor_MeV = approximately 260 (used as 260.0)")
    print("full_constituent_proxy_MeV = " + shown(value,12))
    print("theory_at_cell_precision_MeV = " + shown(value,0))
    print("reference_type = approximate constituent target; 336 used for arithmetic only")
    compare("full_proxy_MeV", value, "336")
    compare("printed_cell_MeV", "331", "336")
    print("suite_table_percent_as_printed = -1.4%; precision convention not specified")
    print()


if __name__ == "__main__":
    main()

row 21

Actual stdout for this entry; the text blocks in entry order concatenate to N21_stdout.txt.

=== row 21 ===
Scorecard (verbatim): m u const (MeV) Λ G2 ·√φ theory 331 experiment ~336 (constituent target) deviation −1.49% Structural constituent
external_hadronic_anchor_MeV = approximately 260 (used as 260.0)
full_constituent_proxy_MeV = 330.725108873658
theory_at_cell_precision_MeV = 331
reference_type = approximate constituent target; 336 used for arithmetic only
full_proxy_MeV.theory = 330.725108874
full_proxy_MeV.reference = 336.000000000
full_proxy_MeV.signed_percent = -1.569908073%; rounded = -1.57%
full_proxy_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
printed_cell_MeV.theory = 331.000000000
printed_cell_MeV.reference = 336.000000000
printed_cell_MeV.signed_percent = -1.488095238%; rounded = -1.49%
printed_cell_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
suite_table_percent_as_printed = -1.4%; precision convention not specified

Comparison

row 21

Theory cell 331 MeV, approximate constituent target ~336 MeV. Rounded-cell offset −1.49%; full-formula offset −1.57%. The suite table’s −1.4% is retained as a separate print discrepancy. No comparator uncertainty, experimental edition, unique constituent scheme/scale, or comparator record is supplied. No d is available; this is not a current-quark PDG comparison.

Tier and what this does not show

Literal tier: Structural; status: constituent. The approximate hadronic anchor and constituent reading are consumed. Agreement with an approximate constituent target neither determines the anchor independently nor derives a current-quark mass or matching prescription.

Sources

LIB2-124; LIB2-128; LIB2-129; appendix_x_zero_parameter_input_ledger.tex:89; appendix_x_zero_parameter_input_ledger.tex:94; appendix_x_zero_parameter_input_ledger.tex:425; Appendix X, Table 4, Named operational anchors, PDF p.334; Appendix X, Table 4, Constituent/current-mass boundary, PDF p.334.

N22 · > ★★ **House correction — PI ruling R144 (S356), landed in the note S357.** **Row 22b is no longer typed an

★★ House correction — PI ruling R144 (S356), landed in the note S357. Row 22b is no longer typed an EDGE TARGET. The Scorecard now types it a Δm² RATIO PREDICTION, asserting m₁ = 0: m₁ drops out of the ratio, so R₂² = 0.029180 is a direct, JUNO-decidable statement of Δm²₂₁/Δm²₃ₗ. Against the comparators built from the printed rows it stands at −1.44σ (JUNO, 59.1 d) and +2.67σ (NuFIT 6.1) — the two disagree in sign and both are named — and the 1σ band of the ratio holds 10 members of the declared M1 monomial menu, density 186 per unit relative width. At JUNO design reach a −2.8% miss becomes −7.73σ, so the row is a falsifier and is printed as one. m₁ = 0 is an ASSERTION of this framework, not a derivation, and d(ν) = 2 remains selected, not derived (H202). JUNO's design-reach projection is a declared external input: verify before relying on it. Every figure in this box is read from Kernels/current/s1184_sibling_density_and_juno_calendar_results.json, none typed by hand.

>

What that means for the text below, and why it is still here. Everything under this box is the note as the drafting lane wrote it and the house verified it at R77, when row 22b was an edge target — including its title, its two "EDGE TARGET, not a hit" sentences, the Scorecard cell quoted verbatim in the code block, and N22_calc.py with its stdout, which echo that same cell and print status = EDGE TARGET, not a hit. None of it is rolled. It is the record of what was said then and of what was supplied to the lane, kept under H239 exactly as R77 kept the lane's own "not s1162" label. Read the typing from this box and from the Scorecard row; the sentences below are superseded on that one point and correct on every other.

>

Found because the R144 landing was checked per-file, passed, and then failed a corpus-wide check: the Scorecard row said PREDICTION while this note, one click away, still said EDGE TARGET (queue row S356.33). Nothing in the house measured whether a Scorecard row and its own note agree; scripts/scorecard_row_note_agreement_S357.py now does.

(title as written at R77; row 22b's typing is superseded — see the R144 box above)

Row 22 is a RECORDED NEGATIVE and row 22b an EDGE TARGET, not a hit. ★ SUPERSEDED on row 22b by PI ruling R144 — it is now a Δm² ratio prediction asserting m₁ = 0. The sentence is kept as written (H239); read the typing from the box above.

Row

House correction — R77 (S327h). Row 22: +820% → +821% (0.276393 / 0.030016, rounded once; the factor 9.21 is unchanged; still the RECORDED NEGATIVE). Row 22b (R77-c): the house re-ran s1162 (Kernels/current/s1162_vus_closed_form_r2_asymmetric_audit.py) twice on 2026-09-11. Both runs are byte-identical to its filed output, with z = 1.436 / 1.789. Its lines 70–73 compute the floor error by the same first-order propagation this note uses (Δm²₂₁ at its lower error, Δm²₃ₗ at its upper error). The −1.44 / −1.79 below are therefore s1162's certified distances, reproduced by the house. The drafting lane did not have s1162, and its script's label "not s1162" is kept verbatim as written. The suite calls this "exact asymmetric errors", but the method is first-order propagation, not a profile likelihood; that wording is queued for Rev32.12 (= Rev33.0, R156). Row 22b is still an EDGE TARGET, not a hit. ★ That sentence was true at R77 and is SUPERSEDED by R144 (see the box at the head of this note); R77's words are kept verbatim, H239. The cell quoted below, and the cell the script echoes, are the text as it was supplied to the drafting lane (the Scorecard through S327g). Scorecard and Registrar are unchanged in every other respect; the sealed papers keep the earlier figure until Rev32.12 (= Rev33.0, R156).

row 22

Δm² 21 /Δm² 3l φ⁻¹/√5 theory 0.27639 experiment 0.03002 (7.537e−5 / 2.511e−3, NuFIT 6.1) deviation +820% Refuted falsified 9.21× — this is the d = 1 reading; see 22b

row 22b

m ν2 /m ν3 = R 2 (d = 2 rung) 1/(φ⁴−1); R 2 ² vs Δm² 21 /Δm² 3l theory 0.02918 experiment 0.03002 (NuFIT 6.1); m 1 =0 NO floor √ratio = 0.17325 vs R 2 = 0.17082 deviation −2.8% · d = −1.44 / −1.79 (below floor) Structural (ladder tier) EDGE TARGET, not a hit — R 2 lies below the m 1 =0 floor and equality is impossible for any m 1 ≥ 0 — i.e. a 1.4–1.8σ tension with the m 1 =0 normal-ordering floor, printed as a tension (Rev32.5); stands only with normal ordering and m 1 ≲ 1 meV; d(ν)=2 is selected, not derived (Paper 5, Rev32.2)

Row 22 is a RECORDED NEGATIVE and row 22b an EDGE TARGET, not a hit. ★ SUPERSEDED on row 22b by R144 — see the box at the head of this note. The supplied excerpts report the asymmetric-distance certificate but do not include its kernel. The optional marginal-error arithmetic below is expressly not that certificate.

Theory value

row 22

The rejected literal reading gives

Its measured-ratio comparator is 0.03002 at the displayed precision.

row 22b

The selected ladder rung is

The physical boundary comparison instead uses R_2 against the normal-ordering floor \sqrt{\Delta m_{21}^2/\Delta m_{3\ell}^2}; these two comparison coordinates must not be mixed.

Derivation chain

row 22

1. Identify the literal Jordan-adjoint mass reading as the rejected interpretation, rather than a statement about the retained mixing carrier. The supplied record names the interpretation and its failure. (Paper 5, section 2, Literal mass reading and ratio mismatch, PDF p.80).
2. Evaluate the formula quoted in the Scorecard and the supplied measured splitting ratio; the excerpt prints their mismatch and factor. The equation antecedent is not present in the shipped LaTeX window. (p5_neutrino_cp_violation.tex:110-116).
3. NOT IN SUITE — a successful physical mass attachment for this literal reading. The source explicitly retains it as the falsified row, not a repairable hit within the note. (p5_neutrino_cp_violation.tex:125-126).

row 22b

1. Use the stated resolvent family and the selected neutrino rung; the source calls the assignment selected, not derived. (p2_mass_hierarchy_resolvent_quintics.tex:83-97; p5_neutrino_cp_violation.tex:116-126).
2. Square the rung for the splitting-ratio display, but compare the unsquared rung to the stated zero-lightest-mass floor. The source says equality is impossible at the central splittings for nonnegative lightest mass. (p5_neutrino_cp_violation.tex:118-124).
3. NOT IN SUITE — in the supplied material, the executable asymmetric-distance kernel or its full joint-error prescription. Its reported certificate is not reproduced merely by matching its rounded output. (p5_neutrino_cp_violation.tex:115-124). House note (R77-c): the kernel is s1162, in the release machinery. The house re-ran it and it reproduces; see the house correction under ## Row.

Registrar sync

row 22

LIB2-134 — Carries the literal mass interpretation, the failed splitting-ratio test and the mixing-carrier boundary.

Comparator LIB2-204 / SL-01 — value 7.537e-5 (+0.094e-5/−0.100e-5) eV^2 · scheme with/without SK · edition 2026 (A1546 lined).

Comparator LIB2-205 / SL-02 — value 2.511e-3 (+0.021e-3/−0.020e-3) eV^2 · scheme with SK-ATM · edition 2026 (A1546 lined).

row 22b

LIB2-140 — Carries the selected rung, below-floor boundary and explicit non-hit status.

Comparator LIB2-204 / SL-01 — value 7.537e-5 (+0.094e-5/−0.100e-5) eV^2 · scheme with/without SK · edition 2026 (A1546 lined).

Comparator LIB2-205 / SL-02 — value 2.511e-3 (+0.021e-3/−0.020e-3) eV^2 · scheme with SK-ATM · edition 2026 (A1546 lined).

Comparator LIB2-206 / SL-03 — value 2.521e-3 (+0.026e-3/−0.018e-3) eV^2 · scheme without SK-ATM · edition 2026 (A1546 lined).

LIB2-142 concerns a separate boundary mass summary, not selection of the rung. The supplied cosmological limits are not inputs to these ratios.

Calculation

Run python3 N22_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N22 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 22 ===')
    print('Scorecard (verbatim): Δm² 21 /Δm² 3l φ⁻¹/√5 theory 0.27639 experiment 0.03002 (7.537e−5 / 2.511e−3, NuFIT 6.1) deviation +820% Refuted falsified 9.21× — this is the d = 1 reading; see 22b')
    value = PHI**(-1)/math.sqrt(5.0)
    solar, atmospheric = 7.537e-5, 2.511e-3
    ratio = solar/atmospheric
    print("solar_splitting_eV2 = " + str(solar))
    print("atmospheric_splitting_with_SK_eV2 = " + str(atmospheric))
    print("theory_at_cell_precision = " + shown(value,5))
    print("splitting_ratio = " + shown(ratio,12))
    print("comparator_at_cell_precision = " + shown(ratio,5))
    compare("literal_full_formula", value, ratio)
    compare("printed_cells", "0.27639", "0.03002")
    print("full_ratio_factor = " + shown(value/ratio,9)
          + "; rounded = " + shown(value/ratio,2))
    print("deviation_at_cell_precision = " + shown(100*(value-ratio)/ratio,0,True)+"%")
    print("d_policy = unavailable: no ratio-level uncertainty or joint likelihood supplied")
    print("status = RECORDED NEGATIVE; d=1 is a rung label, not a statistical distance")
    print()
    print('=== row 22b ===')
    print('Scorecard (verbatim): m ν2 /m ν3 = R 2 (d = 2 rung) 1/(φ⁴−1); R 2 ² vs Δm² 21 /Δm² 3l theory 0.02918 experiment 0.03002 (NuFIT 6.1); m 1 =0 NO floor √ratio = 0.17325 vs R 2 = 0.17082 deviation −2.8% · d = −1.44 / −1.79 (below floor) Structural (ladder tier) EDGE TARGET, not a hit — R 2 lies below the m 1 =0 floor and equality is impossible for any m 1 ≥ 0 — i.e. a 1.4–1.8σ tension with the m 1 =0 normal-ordering floor, printed as a tension (Rev32.5); stands only with normal ordering and m 1 ≲ 1 meV; d(ν)=2 is selected, not derived (Paper 5, Rev32.2)')
    rung = 1.0/(PHI**4-1.0)
    solar, u_solar_lower = 7.537e-5, 0.100e-5
    print("selected_rung = " + shown(rung,12))
    print("rung_at_display_precision = " + shown(rung,5))
    print("squared_rung_at_cell_precision = " + shown(rung*rung,5))
    print("solar_splitting_eV2 = " + str(solar))
    print("naive_floor_audit_assumption = independent marginal errors; first-order propagation")
    print("assumption_provenance = NOT IN SUITE; arithmetic diagnostic only, not s1162")
    for name, atmospheric, u_atm_upper in (
            ("without_SK",2.521e-3,0.026e-3),
            ("with_SK",2.511e-3,0.021e-3)):
        ratio = solar/atmospheric
        floor = math.sqrt(ratio)
        sigma = floor/2.0*math.hypot(u_solar_lower/solar,u_atm_upper/atmospheric)
        naive_d = (rung-floor)/sigma
        print(name+".atmospheric_splitting_eV2 = "+str(atmospheric))
        print(name+".solar_lower_error_eV2 = "+str(u_solar_lower))
        print(name+".atmospheric_upper_error_eV2 = "+str(u_atm_upper))
        print(name+".ratio = "+shown(ratio,12))
        print(name+".floor = "+shown(floor,12))
        print(name+".floor_at_display_precision = "+shown(floor,5))
        print(name+".naive_floor_sigma = "+shown(sigma,12))
        print(name+".naive_floor_d = "+shown(naive_d,9,True)
              +"; rounded = "+shown(naive_d,2,True))
        print(name+".squared_rung_signed_percent = "
              +shown(100*(rung*rung-ratio)/ratio,9,True)+"%"
              +"; rounded_1dp = "+shown(100*(rung*rung-ratio)/ratio,1,True)+"%")
        assert rung < floor
    print("printed_squared_cells_percent = "
          +shown(100*(Decimal('0.02918')-Decimal('0.03002'))/Decimal('0.03002'),9,True)+"%")
    print("source_floor_distances = -1.44 / -1.79 (without / with SK); reported s1162")
    print("source_conditions = normal ordering; lightest mass approximately at most 1 meV")
    print("status = EDGE TARGET, not a hit; rung assignment selected, not derived")
    print()


if __name__ == "__main__":
    main()

row 22

Actual stdout for this entry; the text blocks in entry order concatenate to N22_stdout.txt.

=== row 22 ===
Scorecard (verbatim): Δm² 21 /Δm² 3l φ⁻¹/√5 theory 0.27639 experiment 0.03002 (7.537e−5 / 2.511e−3, NuFIT 6.1) deviation +820% Refuted falsified 9.21× — this is the d = 1 reading; see 22b
solar_splitting_eV2 = 7.537e-05
atmospheric_splitting_with_SK_eV2 = 0.002511
theory_at_cell_precision = 0.27639
splitting_ratio = 0.030015929908
comparator_at_cell_precision = 0.03002
literal_full_formula.theory = 0.276393202
literal_full_formula.reference = 0.030015930
literal_full_formula.signed_percent = +820.821720645%; rounded = +820.82%
literal_full_formula.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
printed_cells.theory = 0.276390000
printed_cells.reference = 0.030020000
printed_cells.signed_percent = +820.686209194%; rounded = +820.69%
printed_cells.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
full_ratio_factor = 9.208217206; rounded = 9.21
deviation_at_cell_precision = +821%
d_policy = unavailable: no ratio-level uncertainty or joint likelihood supplied
status = RECORDED NEGATIVE; d=1 is a rung label, not a statistical distance

row 22b

Actual stdout for this entry; the text blocks in entry order concatenate to N22_stdout.txt.

=== row 22b ===
Scorecard (verbatim): m ν2 /m ν3 = R 2 (d = 2 rung) 1/(φ⁴−1); R 2 ² vs Δm² 21 /Δm² 3l theory 0.02918 experiment 0.03002 (NuFIT 6.1); m 1 =0 NO floor √ratio = 0.17325 vs R 2 = 0.17082 deviation −2.8% · d = −1.44 / −1.79 (below floor) Structural (ladder tier) EDGE TARGET, not a hit — R 2 lies below the m 1 =0 floor and equality is impossible for any m 1 ≥ 0 — i.e. a 1.4–1.8σ tension with the m 1 =0 normal-ordering floor, printed as a tension (Rev32.5); stands only with normal ordering and m 1 ≲ 1 meV; d(ν)=2 is selected, not derived (Paper 5, Rev32.2)
selected_rung = 0.170820393250
rung_at_display_precision = 0.17082
squared_rung_at_cell_precision = 0.02918
solar_splitting_eV2 = 7.537e-05
naive_floor_audit_assumption = independent marginal errors; first-order propagation
assumption_provenance = NOT IN SUITE; arithmetic diagnostic only, not s1162
without_SK.atmospheric_splitting_eV2 = 0.002521
without_SK.solar_lower_error_eV2 = 1e-06
without_SK.atmospheric_upper_error_eV2 = 2.6e-05
without_SK.ratio = 0.029896866323
without_SK.floor = 0.172907103159
without_SK.floor_at_display_precision = 0.17291
without_SK.naive_floor_sigma = 0.001452836829
without_SK.naive_floor_d = -1.436300256; rounded = -1.44
without_SK.squared_rung_signed_percent = -2.399112887%; rounded_1dp = -2.4%
with_SK.atmospheric_splitting_eV2 = 0.002511
with_SK.solar_lower_error_eV2 = 1e-06
with_SK.atmospheric_upper_error_eV2 = 2.1e-05
with_SK.ratio = 0.030015929908
with_SK.floor = 0.173251060338
with_SK.floor_at_display_precision = 0.17325
with_SK.naive_floor_sigma = 0.001358612416
with_SK.naive_floor_d = -1.789080579; rounded = -1.79
with_SK.squared_rung_signed_percent = -2.786264363%; rounded_1dp = -2.8%
printed_squared_cells_percent = -2.798134577%
source_floor_distances = -1.44 / -1.79 (without / with SK); reported s1162
source_conditions = normal ordering; lightest mass approximately at most 1 meV
status = EDGE TARGET, not a hit; rung assignment selected, not derived

Comparison

row 22

Theory 0.27639, comparator 0.03002, dimensionless, from NuFIT 6.1 NO with SK: the supplied solar and atmospheric splittings are in eV² (LIB2-204 / SL-01; LIB2-205 / SL-02). Signed deviation rounds to +821% at unit-percent precision; the printed +820% is coarser. The factor rounds to 9.21. No ratio-level uncertainty is supplied, so no statistical d is assigned.

row 22b

Use LIB2-204 / SL-01 with LIB2-206 / SL-03 without SK, or LIB2-205 / SL-02 with SK, NuFIT 6.1 NO. The with-SK squared-rung deviation rounds to −2.8%. The source reports −1.44 / −1.79 below-floor distances and retains its stated floor tension. A separately labelled independence-based marginal diagnostic matches those rounded distances, but neither establishes the source’s exact-asymmetric protocol nor a profile likelihood.

Tier and what this does not show

Literal tiers: Refuted for row 22; Structural (ladder tier) for 22b. The former is the recorded failed reading. The latter consumes a selected rung, normal ordering and the printed lightest-mass restriction; it is not a physical mass-ratio equality, a derived ordering or a new absolute mass scale.

Sources

LIB2-134; LIB2-140; LIB2-204; LIB2-205; LIB2-206; SL-01; SL-02; SL-03; Paper 5, section 2, Literal mass reading and ratio mismatch, PDF p.80; p2_mass_hierarchy_resolvent_quintics.tex:83-97; p5_neutrino_cp_violation.tex:110-126; s1104; s1162.

N23 · > ★ **House note — added S363 under PI ruling R174-b (queue row S349.R147a).** This row is **DIAGNOSTIC** and is counted in **no tally** of independent results: it is a function of Scorecard rows the table already scores. It was written by the house, not by the D1287 drafting lane that wrote N01–N22, and follows the same contract (SCORECARD_NOTE_CONTRACT_v1_S327). Every number below is the stdout of `N23_calc.py`, pasted verbatim.

★ House note — added S363 under PI ruling R174-b (queue row S349.R147a). This row is DIAGNOSTIC and is counted in no tally of independent results: it is a function of Scorecard rows the table already scores. It was written by the house, not by the D1287 drafting lane that wrote N01–N22, and follows the same contract (SCORECARD_NOTE_CONTRACT_v1_S327). Every number below is the stdout of N23_calc.py, pasted verbatim.

Row 23 is DIAGNOSTIC: J_CKM is assembled from rows 9, 10, 11 and 12a, so it adds no evidence of its own.

Row

row 23

J_CKM   s12 s23 s13 c12 c23 c13² sin δ from |V_us|, |V_cb|, |V_ub|, δ_CKM   theory 3.300e-5   experiment 3.16 (+0.13/−0.11) e-5 (PDG 2026, SL-10)   deviation +4.44 %   d_cmp +1.08   DIAGNOSTIC — counted in no tally

Theory value

row 23

= 3.300 × 10⁻⁵ (the suite prints J_{\rm read}=3.30\times10^{-5}).

Derivation chain

row 23

1. Take the four CKM entries exactly as the Scorecard scores them: |V_us| (row 9, Route B), |V_cb| = 1/(9√7) (row 10), |V_ub| = |V_us||V_cb|/√6 (row 11), δ_CKM = arctan√(3G₇) (row 12a). (p3_ckm_pmns_mixing.tex:438-448).
2. Assemble J in the standard parameterisation. The suite states this is done post-insertion of the loaded magnitudes and is "not an independent prediction". (p3_ckm_pmns_mixing.tex:443-448).
3. NOT IN SUITE — any derivation of J independent of the four rows; none is claimed.

Registrar sync

row 23

NONE — no LIB2 derivation record carries the J assembly; it is an arithmetic function of rows already carried (their notes are N09–N12).

Comparator LIB2-213 / SL-10 — value 3.16e-5 (+0.13e-5/−0.11e-5) · PDG 2026 global fit, Eq. 12.27 · edition 2026 (A1546 lined).

Calculation

N23_calc.py (standard library only). Actual stdout:

=== row 23: J_CKM (DIAGNOSTIC) ===
inputs: |V_us| = 0.225256056 · |V_cb| = 0.041996053 · |V_ub| = 0.003861974 · delta_CKM_deg = 68.129749
J_theory = 3.300390e-05  (s12 s23 s13 c12 c23 c13^2 sin delta)
J_comparator = 3.16e-05 +1.3e-06 / -1.1e-06  (SL-10, PDG 2026 Eq. 12.27)
signed_percent = +4.44%
uncertainty_used = 1.3e-06 (upper)
d_cmp = +1.08
status = DIAGNOSTIC — a function of rows 9, 10, 11, 12a; counted in no tally

Comparison

row 23

Theory 3.300 × 10⁻⁵ · experiment 3.16 (+0.13/−0.11) × 10⁻⁵ (PDG 2026 global fit, SL-10) · +4.44 % · naive comparator distance d_cmp = +1.08 (upper error). The comparison is internal-consistency only: the four inputs are already compared on their own rows, and the PDG value is itself a global-fit output.

Tier and what this does not show

DIAGNOSTIC. It consumes the tiers of rows 9–12a (row 9 Loaded, row 10 Loaded-correspondence, row 11 Loaded, row 12a Coincidence-class) and adds none. It does not show that the framework predicts CP violation in the quark sector; it shows that the four scored entries assemble to a Jarlskog area about one comparator unit from PDG's. No row here may be cited as zero-parameter.

Sources

LIB2-213; SL-10; p3_ckm_pmns_mixing.tex:438-448; kernel s1185 (J_CKM 3.3004e-5, d_cmp +1.08); ruling R147; ruling R174-b.

N24 · > ★ **House note — added S363 under PI ruling R174-b (queue row S349.R147b).** This row is **DIAGNOSTIC** and is counted in **no tally** of independent results: it is a function of Scorecard rows the table already scores. It was written by the house, not by the D1287 drafting lane that wrote N01–N22, and follows the same contract (SCORECARD_NOTE_CONTRACT_v1_S327). Every number below is the stdout of `N24_calc.py`, pasted verbatim.

★ House note — added S363 under PI ruling R174-b (queue row S349.R147b). This row is DIAGNOSTIC and is counted in no tally of independent results: it is a function of Scorecard rows the table already scores. It was written by the house, not by the D1287 drafting lane that wrote N01–N22, and follows the same contract (SCORECARD_NOTE_CONTRACT_v1_S327). Every number below is the stdout of N24_calc.py, pasted verbatim.

Row 24 is DIAGNOSTIC and is not yet a constraint: the comparator's 16–84 % band includes zero, so the data do not yet establish leptonic CP violation at all.

Row

row 24

J_PMNS   √(s12²c12² s23²c23² s13²) c13² sin δ_CP from rows 4, 5, 6, 7   theory −0.0107   experiment −0.0140 ± 0.0149 (house MC over NuFIT 6.1 NH, SL-31; band [−0.0286, +0.0022] includes zero)   d_cmp +0.22 — consistent with the data and with CP conservation   DIAGNOSTIC — counted in no tally

Theory value

row 24

= −0.0107 (the suite prints J_{CP}\approx-0.011 and -0.0107).

Derivation chain

row 24

1. Take the four PMNS entries as the Scorecard scores them: sin²θ₁₂ (row 4), sin²θ₂₃ = 7/16 (row 5), sin²θ₁₃ (row 6), δ_CP = −2π/√5 (row 7). (p5_neutrino_cp_violation.tex:284).
2. Assemble J. The suite states the invariant is "not yet a constraint" and names the band and its zero-crossing. (p5_neutrino_cp_violation.tex:284).
3. NOT IN SUITE — a published NuFIT J with its correlations; the comparator is a house Monte Carlo with correlations ignored, and says so.

Registrar sync

row 24

NONE — no LIB2 derivation record carries the J assembly; it is a function of rows already carried (notes N04–N07).

Comparator SL-31 — −0.0140 ± 0.0149 · house MC (2×10⁵) over the NuFIT 6.1 NH split-normal marginals, correlations ignored · 16–84 band [−0.0286, +0.0022] · house (s1185, S349; ruling R147). No LIB2 comparator record exists yet for SL-31 (it post-dates the Rev32.11 master).

Calculation

N24_calc.py (standard library only). Actual stdout:

=== row 24: J_PMNS (DIAGNOSTIC; comparator band includes zero) ===
inputs: sin2_12 = 0.304441745 · sin2_13 = 0.021446609 · sin2_23 = 0.437500000 · delta_CP_deg = -160.996894
J_theory = -0.010652
J_comparator = -0.0140 +/- 0.0149  (SL-31, house MC over NuFIT 6.1 NH, correlations ignored)
comparator_band_16_84 = [-0.0286, +0.0022]  includes_zero = True
comparator_distance_from_zero = 0.94 sigma
d_cmp = +0.22  — consistent with the data AND with CP conservation; not a constraint
status = DIAGNOSTIC — a function of rows 4, 5, 6, 7; counted in no tally; becomes a constraint only when the band excludes zero

Comparison

row 24

Theory −0.0107 · comparator −0.0140 ± 0.0149 (SL-31) · naive comparator distance d_cmp = +0.22, which must not be read alone: the comparator is only 0.94 σ from zero, so the same data are equally consistent with J = 0. The distance says the theory value is not excluded; it does not say it is supported over CP conservation.

Tier and what this does not show

DIAGNOSTIC. It consumes the tiers of rows 4–7 (θ₁₂ and δ_CP Derived-conditional; the physical θ₂₃ row Loaded-correspondence; θ₁₃ Structural) and adds none. It does not show leptonic CP violation, and it becomes a constraint only when the experimental band excludes zero. No row here may be cited as zero-parameter.

Sources

SL-31; p5_neutrino_cp_violation.tex:284; kernel s1185 (J_PMNS −0.010652, NuFIT MC −0.01397, band [−0.02858, +0.00219]); ruling R147; ruling R174-b.