Research five-dimensional port decoder for P112

[1337isnot1337]

Result

Adds a five-dimensional port decoder construction for the selected 112 labels in F2^9. A seeded incidence search partitions the labels into 22 pairwise-orthogonal five-frames and one orthogonal pair. The 23 exact block matrices satisfy I_9 = sum_g A_g M_g A_g^T; their canonical rank-one factorization induces the full selected-port pairing matrix.

The 16 decoder terms have B14 support-pairing rank histogram {7: 10, 8: 6}, total copy charge 118. The package verifies all 161,280 five-frames, the full 112-by-112 decoder, 11,776 exact Gaussian-dyadic C_E^2 address-basis cases, 672 dirty-input cases, one paired-plane positive control, and three corruption controls.

Cost screen and limits

Replacing the selected eight rank-8 centre children gives local profile {1:2412, 2:418, 3:432, 4:142, 5:82, 7:10, 8:6} and mass 5,640. Under the changed unpaid=5 law, the exact selected-word relaxation at a=1/99 is 0.9774210973077914; the certified ceiling is 0.017542237243537.

The maximum aggregate rank-one-equivalent charge is 275, so 157 units remain after the copy invoice 118. There are 23 exact aggregate translations. If each is provisionally charged one unit, 134 units remain for all other source access, frame changes, routing, hosting, restoration and precision. That unit price is not a physical invoice. The native port contract, owner placement, frame schedule, full restoration and precision are not integrated. This is a local algebraic construction, not a supplier, new kappa or selected-frontier result.

Reproduction

python3 -I -O -B research/five-plane-port-p112-seed1f7fdfe4/verify.py
python3 research/five-plane-port-p112-seed1f7fdfe4/search.py --attempt-cap 10000
python3 scripts/research_package.py --package research/five-plane-port-p112-seed1f7fdfe4 --check-only

Direct verifier and search passed locally under Python 3.14.7; package metadata and input pins pass. Python 3.12 is unavailable locally (python3.12 and uv are absent), so the registered Python 3.12 replay remains for hosted CI.

Base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32; catalogue revision 4 SHA-256 d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7.

Predecessors: Discussion #1587 and merged PR #1825 (paired planes); Discussion #2024 / PR #2041 (three-plane P112); merged PR #1909 (tetrad-local E8-root supports, a different support object). Substantial OpenAI Codex assistance; no independent human review is claimed. Apache-2.0.

[thakrarsagar]

Scalar-endpoint audit in #2532 (Sagar Thakrar, with AI assistance). The F2 identity Σ terms = B0 reproduces exactly, but B0_ij = q_i·q_j is not the decoder target for the five-dimensional contract. #1889 found the same issue for #1825's paired planes.

• No free entries. Under source E_j → FULL and target 0 → E_i^⊥, a cross entry is free only when E_j ⊥ E_i. With k=5 that never happens (dim E^⊥ = 4), and the residual pair is not orthogonal to any group either. A valid decoder must therefore be c·I on all 112 ports, rank 112, against 16 terms.
• Literal lift. It has 12,281 forbidden nonzero entries; the 6,608 with q_i·q_j = 1 are odd in every lift that preserves parity. All 112 dirty columns fail. Example: target 0 ← source 7 has literal coefficient 1 (5 in your verify.py orientation), so a dirty target 11 becomes 12 instead of staying at 11.
• Cost. In port-space pricing, philippeVV's 2-integral floor (Discussion 1587, comment 18927273) gives every decoder without even denominators a charge of at least Σ dim E_i = 554, above the zero-saving threshold 5w = 497.8. So the 118 charge, the 157-unit allowance and the a=1/99 screen do not price a valid decoder. Only an even-denominator (2-adic) gain above about 56 could help, and about 94 to tie the incumbent.
• Bind mixed port coverage to actual endpoint dimensions #2528. ywz65's concurrent audit of the uniform-five premise is complementary; it keeps the binary factorisation as the decoder.

The not-ruled-out list (operator- or block-valued interpretations, other contracts) is in the package README.