[Completed] Prospective N=185/265 full-curve test

[LightChainr]

Final audited outcome

The 500M-per-size N=185/265 target is complete and canonical under PR #108. A later contract audit materially changes how the matching-even part must be interpreted.

Matching-odd DeltaM — prospective pass

N=185 DeltaM = +1.36830e-4 +/- 3.42352e-5
N=265 DeltaM = +1.27110e-4 +/- 3.46783e-5

x=21/4 H4: chi2 = 3.04598 / 2
zero:       chi2 = 29.40938 / 2
x=17/4:     chi2 = 30.24613 / 2

The matching-odd H4-like radial law survives genuinely new geometries and clearly beats zero and the predeclared x=17/4 adversary.

Registered DeltaS score — artifact contract failure

The immutable pre-target artifact used the P31 either/even source amplitude and predicted positive N^-1 target means. The threshold-rank production metadata and scorer, however, reconstruct rank-2 cross/even:

source in prediction artifact: either/even
target production channel:     rank-2 cross wrapping
target scorer:                  S_cross=(R_G^cross+R_hat^cross)/2

The original registered positive score therefore fails numerically:

registered positive DeltaS: chi2 = 240.24721 / 2
zero:                       chi2 = 112.53891 / 2

That historical score remains frozen and must not be rewritten.

But P31 already contains both channels and verifies the exact orientation-difference channel map

DeltaS_cross = -DeltaS_either.

Applying only that pre-existing exact map to the frozen source means, with zero target refits, gives

corrected cross means:
N=185 -6.7521637459e-5
N=265 -6.8919446970e-5

observed cross DeltaS:
N=185 -6.0815376233e-5
N=265 -7.0249507845e-5

protocol-repair chi2 = 0.57003 / 2
marginal residual z = +0.667, -0.119

This is recorded in analysis/channel_map_corrected_DeltaS.json. It is a post-reveal protocol correction, not a retroactive preregistered pass. The right conclusion is that the registered source/target channel contract was mismatched; the 240/2 failure is not evidence that the physical cross/even N^-1 sector is falsified.

Intrinsic-center P48 score from the same new geometries

A separate no-refit score uses the original N=65/85/130 P48 amplitudes and the independent N=185/265 intrinsic-center targets:

P4[S]   ~ N^-1:     chi2 =  1.139 / 2
P4[D]   ~ N^-13/8:  chi2 =  0.281 / 2
P4[D']  ~ N^-5/8:   chi2 =  0.088 / 2
P4[S']  ~ N^-5/4:   chi2 = 52.716 / 2

Thus S, D and D-prime pure laws survive prospectively; S-prime is the unique clear pure-law failure and requires the already-frozen correction program.

Consequence

Do not rerun N=185/265. The useful conclusions are already sharp:

• strong prospective support for the matching-odd H4-like law;
• matching-even registered DeltaS artifact had a source/target channel bug, with a successful lower-status exact-map repair diagnostic;
• intrinsic-center P48 parity pattern survives in S, D and D-prime;
• S-prime is nonzero but needs finite-size correction.

Next high-information data remain #57 norm-5 and #50 third full-curve lineage. #48 owns the S-prime correction / channel-coordinate reconciliation, using existing data first.

[LightChainr]

Secondary N=290 has an additional angular-design advantage

The frozen N=290 pair (17,1) vs (13,11) has

cos4 = +0.9725089 versus -0.9452081,

so DeltaCos4 = 1.9177170 is near maximal. Because cos8(theta)=2 cos^2(4theta)-1, the corresponding DeltaCos8 is only about 0.10471; the contamination ratio |DeltaCos8/DeltaCos4| is ~0.0546.

Thus N=290 is not only a secondary radial confirmation but also a nearly H8-orthogonal orientation design. Keep it strictly secondary as preregistered: score N185/265 first, then use N290 to test whether the H4 result persists where H8 angular leverage is strongly suppressed.

[LightChainr]

Pre-target harmonic audit: the already frozen primary sizes also provide useful H12 leverage, so no new geometry is needed for the first H4-vs-H12 check.

Exact/derived ratios:

N=185  (13,4)-(11,8): DeltaCos12/DeltaCos4 = -1.0255132676434948
N=265  (16,3)-(12,11): DeltaCos12/DeltaCos4 = +0.1505079050060446

For context, the prespecified later rows are

N=221: +0.2373720362626388
N=290: +0.6798745121104623

Thus an H12 admixture would push N185 and N265 in materially different relative directions.

Do not change the existing primary H4-only frozen predictions. Scoring order should remain:

1. original two-sector H4-only frozen score;
2. zero effect;
3. then a predeclared shared H4+H12 model using exact harmonic columns;
4. only later free radial/log models.

This uses no target information and makes #43 the first prospective H12 constraint. #55 remains a later stronger orthogonal confirmation (r12≈-1.714,+1.813) rather than a prerequisite.

[LightChainr]

Pre-target x=17/4 competing radial prediction frozen

A representation-theory audit found a formal lower spin-4 non-diagonal Kac state W(2,2) with x=17/4. At generic Q it carries Xi(2,2)=Xi(2,0)=[2], so it is not the ordinary S_Q-singlet lattice perturbation; however Q=1 logarithmic mixing means it is worth retaining as a numerical competitor rather than dismissing it by symmetry alone.

Separate artifact committed without changing the original #43 primary:

predictions/x17_spin4_competitor_20260828.yaml

Frozen competitor law:

DeltaM = A17 * DeltaCos4 * N^(-9/8)

with source fit from already-known P31 pooled sizes only:

A17 = 0.08650341474278707 +/- 0.003912649330481595.

Prospective targets:

N=185: x=17/4 -> +2.868415917648024e-4
       x=21/4 original -> +1.9223156676869253e-4

N=265: x=17/4 -> +2.799185461225267e-4
       x=21/4 original -> +1.567390401230751e-4

The separation is deliberately large. Target Monte Carlo error will determine discrimination power.

Frozen scoring order:

1. score the original [Completed] Prospective N=185/265 full-curve test #43 x=21/4 / N^-13/8 prediction first;
2. score the fixed x=17/4 / N^-9/8 competitor;
3. zero effect;
4. only then H4+H12, mixed powers, log or free-exponent models.

Do not refit either source amplitude on N185/N265 before the corresponding fixed score is reported.

[LightChainr]

Second pre-target adversarial radial model: V_<1,3> level-4 spin4, N^-4/3

A more serious singlet competitor than W(2,2) was identified in the diagonal Potts sector. R_<1,3>⊗[] is a generic-Q singlet with h=hbar=1/3; an exact Virasoro check shows a non-null level-4 spin-4 quasiprimary survives, giving x=14/3 and—if it leaked into central D—

DeltaM ~ DeltaCos4 * N^-4/3.

Under the proposed matching/interchiral OPE automorphism it should actually be matching-even, because V_<1,3> occurs in V_<1,2> x V_<1,2> and the self-OPE has parity tau^2=+1. Thus the N^-4/3 law is frozen as a deliberate parity-failure competitor, not the preferred mechanism.

Files:

• notes/interchiral-v13-matching-parity.md
• scripts/v13_level4_spin4_candidate.py
• predictions/v13_spin4_parity_failure_competitor_20260828.yaml

Fixed retrospective source amplitude from P31 only:

A_V13=0.21908248310960696 +/- 0.009828197789383443.

Prospective target predictions:

N=185: V13 N^-4/3 -> +2.448437843402022e-4
       x21 N^-13/8 -> +1.9223156676869253e-4

N=265: V13 N^-4/3 -> +2.2169872033579832e-4
       x21 N^-13/8 -> +1.567390401230751e-4

Updated fixed scoring order, without altering the original artifact:

1. original x=21/4 N^-13/8 prediction;
2. V_<1,3> N^-4/3 parity-failure competitor;
3. W(2,2) x=17/4 N^-9/8 adversarial competitor;
4. zero effect;
5. only then H12/mixed/log/free models.

If N^-4/3 wins prospectively, interpret it primarily as a failure/complication of the matching-interchiral parity mechanism—not merely as a better fitted exponent.

[LightChainr]

Interpretation guard for the frozen V_<1,3> parity-failure competitor

Issue #61 now isolates the theoretical assumption behind calling V_<1,3> matching-even.

The exact matching identity only gives an observable pair relation between G and G*. The argument that

V_<1,2> x V_<1,2> ~ 1 + V_<1,3>

forces V_<1,3> even additionally assumes that the scaling-limit matching exchange is an OPE/interchiral automorphism and does not rotate a degenerate/logarithmic block. That has not been constructed.

Therefore the current #43 scoring order is exactly right: keep the original x=21/4 target first, but treat the frozen x=14/3, N^-4/3 model as a serious parity-failure adversary, not as a model already excluded by theory.

Interpretation if the prospective target chooses among them:

• 13/8 wins: supports the current thermal-family mechanism but does not by itself prove the OPE parity map;
• 4/3 wins: primarily falsifies/complicates the matching/interchiral parity construction;
• 9/8 wins: points toward the special Q=1 non-singlet/logarithmic leakage route;
• none stable: retain multi-sector/preasymptotic status rather than refitting a free exponent immediately.

The norm-5 artifact added on PR #56 now supplies an independent no-fit parent/child ratio test of the same three H4 radial competitors, so #43 and #57 can cross-check the operator interpretation without sharing target data.