Research: masked rank-8 complex decoders are locally rigid on all P104 frame-pair punctures (no new kappa)

[navinor]

Status: scoped structural result (exact infinitesimal certificate) plus a seeded finite sample. No new κ, no supplier change. Only research/complex-p104-masked-local-rigidity/ is added; the selected record (κ = 0.001672660197076918), upstream/ and every existing file are unchanged.

Question

The masked (E-graph) decoder model of #717 fixes a costly part K only on the diagonal (K_ii = 4) and on orthogonal live pairs (K_ij = 0); odd entries are free and are repaired by cost-0 terms. Can masking deform the frame-pair decoders of #968, which attain the 7/13 copy ratio on P104 = P120 − F0 − F1, away from the all-pairs normal form? #1212 proves global rank-8 rigidity on P112/P120 and lists P104 as numerical evidence only.

Result

For P120, P112 and every one of the 1260 frame-pair punctures, the tangent space at K0 = 2G of {rank K ≤ 8, masked entries fixed} is exactly the tangent of the diagonal-torus orbit D(2G)D⁻¹. The solution set therefore coincides with that orbit near 2G. A masked eight-costly-term decoder close enough to 2G has the normal-form supports, so the PR 968 floor (cost ≥ 56, ratio ≥ 7/13 for p ≤ 24) still applies.

The certificate is exact:

• After eliminating N, the M-system has rank 7v − 63 over F_p (p = 2³¹ − 1). Since rank over F_p is at most rank over Q, the kernel is at most v + 63.
• The explicit gauge (64) and torus (v − 1) directions lie in the kernel and span 64 + v − 1.
• 66 Schreier elements fixing F0 (products of root reflections, checked) merge the 1260 frames into the 896/336/28 classes of PR 968; one certified representative covers each class, with full row insertion giving rank exactly 665.

Controls and sample:

• The decomposable live set D4 ⊕ D4 is rejected (its torus splits).
• 64 of 64 seeded random punctures with 24 to 80 lines pass. This is a finite sample only.
• The P112 tangent rigidity recorded in PR 717 D1 is reproduced by a separate exact method.

Scope and obligations

• Local only. Components away from the torus orbit on P104 are not excluded (open question 1 in the README).
• Not covered. Nine or more costly terms (open question 2), other punctures beyond the sample, and physical copy trees, frames, restoration and hosting.
• Inherited. The decoder consequence uses PR 968's floor and its cited flat classification. All selected-record obligations remain. This is not a formal proof of multiplication, and there has been no independent human review.

Reproduce

python3 -I -B research/complex-p104-masked-local-rigidity/verify.py        # ~70 s, stdlib only
python3 scripts/research_package.py --package research/complex-p104-masked-local-rigidity --check-only
python3.12 scripts/research_package.py --package research/complex-p104-masked-local-rigidity

Expected final line: PASS_P104_MASKED_LOCAL_RIGIDITY: P120, P112 and all 1260 frame-pair punctures (3 classes) infinitesimally rigid at 2G; D4+D4 control rejected; seeded sample p=24..80 rigid 64/64; local only, no new kappa.

Local runs:

• verify.py passes (9/9 checks) on CPython 3.13.15 and on 3.12 from a git archive export of the committed head.
• research_package.py check-only and the full 3.12 replay pass (PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=negative-result).
• scripts/verify_selected_result.py passes.
• test_research_*.py has 5 errors on this Windows host, all inside the onboarding tests' temporary repositories and unrelated to this package. Four come from the host's system core.autocrlf=true, and disappear with core.autocrlf=false for the process. The fifth uses os.killpg, which does not exist on Windows. Linux CI was not run.

Task card and credit

• Card. complex-masked-decoder (complex-mechanisms track), chooser nonce f98900d1d6bdb1d91a0247b80be5acee, base dadfea6e8a78ff6ba901705f87532a71c6f5bbb8. Scope refined to the changed hypothesis (masked instead of all-pairs exactness) at the ratio-optimal punctures; the full card is in TASK.json.
• Claim. CLAIM: exact local rigidity of masked rank-8 complex decoders on all P104 frame-pair punctures (Navinor, expires 23:40Z) #1275
• Credit.
  • DreamingOfClouds: masked model, cost-0 repair and the P112 tangent rigidity (Format limits part 2 (no κ claim): erratum to #595, exact invoice prices, frontier-word censuses, decoder floors, spec requirements, centre and fragmentation walls #717).
  • themilkman216: frame-pair decoders, the 7/13 floor and the three relative positions (Research: frame-pair decoders and the exact 8-term complex copy-cost floor (no new kappa) #968).
  • burntout76: global P112/P120 rigidity and the P104 question (Research: rank-8 complex decoders are gauge-rigid; E-graph eight-term floor (no new kappa) #1212).
  • Related masked P112 work (Research: classify the P112 masked decoder coordinate component (no new kappa) #1213, Research: masked root-star trimmed-star census on P112; exact covering bound 784/13, 64 falsified for beta-7 atoms (no new kappa) #1226, Research: close the masked root-star assembly gap with sharp cost 64 (no new kappa) #1236) and frame-pair delivery bounds (Research: delivery lower bounds for #968's frame-pair centers (no new κ) #1071) are separate questions.
• Prepared by Navinor with help from opencode. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 7a8325f6c8e5a6830ce919965a2959ac459e010a.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: P104 infinitesimal frame-rigidity audit over all 1,260 frame pairs and three orbits. Modular rank upper bounds meet explicit characteristic-zero tangent families; local rigidity and inherited cost scope do not establish global rigidity.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.