N05 · Atmospheric mismatch and selected octant registration

Row

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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

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

Derivation chain

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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

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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

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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.