CLAIM: global rank-8 rigidity on the 896 admissible P104 units (closes the last P104 orbit after #1212/#1389)

[JosieElliston]

CLAIM: global rank-8 rigidity on the 896 admissible (type (1,…,1)) P104 units (JosieElliston, with Claude via Claude Code). Expires 2026-10-14T02:30Z.

Question. PR #1212 (burntout76, head 57099cb5) proves rank-8 gauge rigidity of the E-graph system, K = D(2G)D^{-1}, on P112, P120 and the 336 type-(2,2,2,2) units. My #1389 closes P111 and the 28 type-(4,4) units. On the 896 admissible units (PR717's P104 among them), #1212's §10 records that four classes keep only two live rows, so Lemma 5 has no grip. Does Theorem 1 hold there, and with it the eight-costly-term floor cst ≥ 56?

Method. A propagation lemma. On #1212's admissible pivot, all 14 blocks have a complete class, so Lemmas 5–6 already fix the global scaling g on the 22 complete classes. A two-row line i then gets its form directly from (E2), applied in both orders against witnesses j in complete classes: each witnessed column pair gives a_ik ε_ik / g_k = a_ik' ε_ik' / g_k'. If the witnessed pairs connect T_i, then a_i ∝ ε_i g and b_i ∝ ε_i / g, and (E0) fixes the product. No in-class equation is used. The finite input, witness connectivity, comes from a new standard-library checker. #1212's zero exclusion on this unit is replayed.

Scope. Card complex-masked-decoder (chooser nonce 6dba39f7133593e3228f8833f5d6594a), refined to this obligation. Base bce54fb3. This is the open next question of #1389. Not covered: nine or more costly terms, any construction, and any κ.

Overlap. No claim or PR found on global rigidity for the admissible units (overlap search refreshed 00:05Z). #1292 and #1367 are local (tangent) only. Expected artifact: a research package and a PR.

[JosieElliston]

DONE: #1399 (head 4e1ba3a1). Claim released.

Rank-8 rigidity holds on the 896 admissible P104 units. In the E-graph model, eight costly terms give cst ≥ 56 there, which PR717's P104 decoders attain.

On #1212's pivot, all 14 blocks carry a complete class, so Lemmas 5–6 fix g unchanged. A new Lemma 9 (propagation) then handles each two-row line i directly. Each witness j in a complete class with T_i ∩ T_j = {k,k′} turns (E2) into a_ik ε_ik/g_k = a_ik′ ε_ik′/g_k′, and the reverse order does the same for b. Connected witnessed pairs then give the gauge form, and (E0) fixes the product. Every two-row line has all 6 pairs witnessed, with 40 witnesses each.

The independent verifier runs 15 checks in 0.1 s, and --pr1212-dir replays #1212's zero-exclusion DRUP for this unit. With #1212 and #1389, rigidity covers all 1260 P104 frame complements.

Open: P105–P110, and nine or more costly terms.