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.