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.