One-sided P112 fitting rigidity from the support census

[jmbarrancoml]

DONE: PR1815, head c4f1e3ace88ecc69cd1ea959ecf4f2e0930d015e.

The final statement is a one-sided corollary of Adam Gall's PR1098 support-spectrum certificate, based on Mihir Srivastava's PR845 geometry. For N=R W over Q and B=U L over F2, unit diagonals and the directed fitting zeros force N=R R^T and B=U U^T. Only the two column spaces are fixed; neither row space needs a restriction. I retain the predecessors' credit for the support geometry and spectra.

The package makes the joint-fitting corollary explicit and checks it by a separate deletion-rank method. Each column needs its own root to be a coloop of a binary character support. The only such pairs are the 112 original character/port pairs. The checker also binds the current prototype to the predecessor's literal X rows.

The registered Python 3.12 replay and optimized Python 3.14 replay passed: 511 supports, 4,080 basis-row deletions, 4,591 positive integer Gram minors, positive fixtures and nine rejected corruptions. Transcript SHA256: ecd7a758baff7dc84b11dd238fe2bb9b09ad0d2761d5b68f6355132c67e38720. Reproduce with python3.12 scripts/research_package.py --package research/polarized-p112-code-bound.

This replaces the more restricted polarized statement with a stronger credited corollary; it does not claim new underlying geometry. Philipp's PR1191 already treats related fixed-mask one-sided rational rigidity. Thiago Goulart's PR1744 retains credit for the separate fixed-mask rank/broadcast theorem. Source inputs, ancestry and substantial AI assistance remain explicit in the package.

Outside-code factors, changed ports, block-valued replacements and complete native supplier costs remain open. No exponent improvement or selected-frontier change follows. Jose Manuel (@jmbarrancoml), with substantial OpenAI Codex assistance. This contribution claim is complete; the broader constructive research objective remains open.

[jmbarrancoml]

RELEASED: bounded outside-code synthesis did not produce a fitting candidate

The exact model runs produced checked rank-nine obstructions and then ended with solver unknown after their timeouts. I also tested a bounded half-integral grid and two cancellation cases obtained from the verified signed-coordinate symmetry. None produced an unrejected fitting candidate or an UNSAT certificate. These timeouts establish no impossibility theorem, and I make no exhaustive claim for arbitrary rational A.

The two symmetry classes contain 224 same-support root pairs and 2,688 intersecting-support pairs. They give two normalized cancellation cases, but the resulting continuous searches remain unresolved. The earlier matching and octonionic screens retain only their stated finite domains.

PR1815 now states a stronger, credited one-sided corollary of PR1098's support spectra. It implies that a lower-rank pairing must change both binary factor codes when the decoder retains both rational root-code spaces. This still leaves the outside-code search open. I release this bounded search claim without a new search PR. Jose Manuel (@jmbarrancoml), with substantial OpenAI Codex assistance.

Original claim:

FOLLOW-UP CLAIM: directed P112 decoder synthesis outside the retained binary code

This changes the scope of PR1815. I retain N=R(I+A)R^T with rational skew A on the eight root coordinates, but allow binary source and receiver factors outside the retained nine-dimensional code. The target is an explicit rank-eight binary B with unit diagonal and N_ij=0 whenever off-diagonal B_ij=1. A fitting pair alone would not establish a native supplier or exponent.

I am using exact rational SMT to search the 28 skew coefficients. Each rejected model supplies a checked nine-clique or ordered triangular principal witness; I add the corresponding necessary zero condition to the solver. The initial condition requires breaking the 76 edges of PR1744's four-clique certificate, including its odd-incidence four-clique. A candidate must later pass an explicit binary factorization, physical-frame admission and a complete cost budget.

Initial cap: 500 model rounds or 600 seconds, with a ten-second timeout per solver check. An unrejected model is only a candidate. An UNSAT response would need an independent certificate before I state a universal theorem. No solver search or failed bounded run supplies an improved exponent.

Preflight: 14,840 uniformly scaled signed coordinate-matching variants and 2,051 rational octonionic variants each have a checked mutual nine-clique. The E8 quiver Euler family also fails a reduction-modulo-two rank bound. These scoped rejections do not cover arbitrary A and are not separate PRs.

Base main remains 0b1cccf. PR1815 head198f4e7ba8560b2837693dabfd97f23c2b2a21cb covers the previous fixed-code family. I retain @Tuafo's credit for PR1744's fixed-mask theorem and clique certificate. The refreshed overlap snapshot covers 486 open PRs and 466 Discussion records at 11:05–11:06 UTC, with no matching outside-code synthesis claim in those records.

Claim expires 2026-10-14T13:20:00Z. Jose Manuel (@jmbarrancoml), with substantial OpenAI Codex assistance. No selected-frontier change.