Moduli screen: G1-uniform at height ≤ 4, two G2 classes, candidate completeness pairs - #21
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family_screen.py enumerates the degree-4 endpoint-identity moduli
(rational parametrization: e2 = e1 - 1, so c = (1-a)(1-b)/((1-a)(1-b)
- ab)) and screens members pairwise with the CI-pinned census
instrument. Engine-assumption violations are recorded as SKIPPED with
the reason, never silently dropped.
Result at parameter height <= 4 (14 distinct members, 0 skipped): the
moduli is G1-UNIFORM -- every member has the identical component census
(the one A and B share) -- and splits into exactly two G2 isomorphism
classes: B's class (10 members, wall-attached Sigma-branch ending
{cusp, cusp}) and A's class (4 members: (-1,3,4), (-2,4,9), (-1/2,2,3),
(-3/5,2,4)). 51 G0-G2-tied pairs total.
family_equiv.py generalized to take any pair (--pair 'a,b,c;d,e,f');
the default remains the original (A, B) so the CI gate is unchanged.
Candidate completeness pairs, both decided NOT affinely equivalent in
either direction:
alpha: (-1,3,4) ~ (-1/2,2,3) [contains A; n2 sets tie at
[0..10] on a shared 240-target
stream]
beta: (-2,-1,3/2) ~ (-3,-2,2) [contains B; 240-target n2 shows a
tail gap at 12 -- consistent with
undersampling, needs depth]
Screening results are measurements with the validated instrument, not
adoptions: the chosen pair still needs its own gate run and the tame
caveat before becoming the completeness test case.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Found while validating the alpha-pair n2 sweep: a direct n2_numeric call in a fresh process disagreed with the banked pipeline run by one marginal target (4:190 vs 4:189). Root cause: n2_numeric called _mp_kit(M) BEFORE entering workdps(60), so the cached mpf constants were built at the ambient precision -- 15 digits in a fresh process -- and every subsequent 60-digit computation ran on 15-digit constants. The published runs were unaffected only because phase2()'s calibration gate happened to build the cache inside workdps(60) first. Fix: _mp_kit takes the target precision, builds inside its own workdps, and caches with the precision recorded (rebuilds if a higher precision is requested). Verified: the direct-call sweep now reproduces the banked histograms exactly, including the exclusion count (5 member-cases across both members). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Screens the degree-4 endpoint-identity moduli for the landscape-matched pair the completeness hunt needs (#14), using the CI-pinned census instrument from PR #20.
Findings (14 distinct members at parameter height ≤ 4, zero engine skips):
Candidate completeness pairs, both decided NOT affinely equivalent (generalized
family_equiv.py --pair, Gröbner {1} both directions):Screening results are measurements, not adoptions: the recommended pair (α) still needs its own gate run and carries the tame caveat before becoming the completeness test case.
🤖 Generated with Claude Code