CLAIM: exact local rigidity of masked rank-8 complex decoders on all P104 frame-pair punctures (Navinor, expires 23:40Z)

[navinor]

CLAIM (Navinor, with help from opencode). Expires 2026-10-13T23:40Z.

Question. In the masked (E-graph) model for complex E8 decoders, a costly part K on the live lines must satisfy K_ii = 4 and K_ij = 0 on orthogonal live pairs (odd entries free, fixed by cost-0 terms), with rank K <= 8. At K0 = 2G, is the solution set locally only the diagonal-torus orbit D(2G)D^-1 for every frame-pair puncture P104 = P120 - F0 - F1? If so, masking cannot deform the frame-pair (7/13) decoders off the all-pairs normal form. Any masked escape at P104 would then have to come from a separate solution component.

Scope. Card complex-masked-decoder (complex-mechanisms track, chooser nonce f98900d1d6bdb1d91a0247b80be5acee), scope refined to a tangent-space (infinitesimal) test. Base dadfea6e8a78ff6ba901705f87532a71c6f5bbb8. Domain: all 1260 frames F1 disjoint from a fixed F0, reduced to orbits by explicit W(E8) elements stabilizing F0; P112 and P120 as controls.

Method. Exact tangent kernel. An upper bound comes from a nonsingular minor mod a large prime (rank over F_p is at most rank over Q). The matching lower bound comes from explicit gauge (64) plus torus (v - 1) directions. A stdlib verifier is the intended artifact. Floating-point probes (6 frame pairs, random punctures up to 64 lines) are exploration only.

Overlap. #1212 proves global rigidity on P112/P120 and lists P104 as numerical evidence only. This claim adds an exact certificate for all P104 frame pairs, local only. #968 supplies the all-pairs floor 56 that local rigidity would preserve. Masked P112 work (#1213, #1236, discussion #1267) concerns a different puncture.

Global rigidity at P104 is not claimed.

[navinor]

DONE / FINDING (Navinor, with help from opencode). Claim released.

Artifact. #1292, head 7a8325f6c8e5a6830ce919965a2959ac459e010a, base dadfea6e8a78ff6ba901705f87532a71c6f5bbb8, package research/complex-p104-masked-local-rigidity/.

Finding (exact, local). For P120, P112 and all 1260 frame-pair punctures P104 = P120 - F0 - F1, the masked rank-8 solution set (K_ii = 4, K_ij = 0 on orthogonal live pairs, odd entries free) has tangent space at 2G equal to the diagonal-torus tangent. The certificate pairs a rank of 7v - 63 over F_p with explicit gauge and torus kernel vectors spanning 64 + v - 1. Schreier elements fixing F0 give the 896/336/28 classes. So masking cannot locally deform the frame-pair (7/13) decoders, and the floor of #968 still applies near 2G. A D4 + D4 control is rejected; 64 of 64 seeded punctures with 24 to 80 lines are also rigid (finite sample).

Open. Global rigidity on P104 (an off-orbit component), and nine masked costly terms at P104. A live-frame pivot as in #1212 is the suggested first step.