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.