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 The source explicitly retains the loaded status and the current rather than superseded digit.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.