[adamgall]

Change and mathematical scope

Adds research/paired-plane-scalar-mask-obstruction/: an independent, source-bound missing-implication audit of PR #1825 at d16fb8936795ff101e4d2f63cfdc6a25066ebabf.

The binary factorization and local plane-translation identities remain valid. They do not establish the scalar data endpoint required by the proposed two-unpaid-coordinate contract.

For ports (0,7), labels (11,21) have binary pairing one. The scalar decoder must have zero cross-coupling, but interpreting the certified columns as scalar factors gives

H[{0,7},{0,7}] = [[7,5],[5,7]].

With x7=1 and dirty y0=11, the literal scalar layer returns y0=16, not 11. Every parity-preserving integral lift keeps that forbidden coefficient odd. The same obstruction applies to 6,608 ordered pairs and cannot be removed by zero-copy endpoint corrections.

This is not a universal plane-port obstruction, a refutation of the binary identity or its intended optimistic screen, a new κ, or a selected-supplier change. Rational/complex refactorization, paid cancellation and operator-valued contracts remain open. The C=126 planning profile does not by itself certify an implemented scalar decoder.

Task and overlap

• Base: current main at session start, 0b1cccf86e2f5132ed286a26ef0a681a495740ea.
• Task: coverage-law-change, refined to this candidate's scalar endpoint rather than repeating the unpaid-line argument or lever arithmetic; full TASK metadata included.
• Closest predecessors: Construction: paired plane-port decoder on selected E8 labels #1825's matching/factorization; Planning screen: certified decoder copy budgets for the plane-port coverage law on both suppliers (no new kappa) #1808 (b3d9b9813e0f2e82d8379cd4dafa2a355a900a44) budgets; Discussion1587's plane endpoint.
• Final overlap refresh: 543 open PRs and 529 discussion records, complete pagination at 2026-10-14 13:23–13:25 UTC. No corresponding scalar-mask audit found; diffs, nested files and all closed PRs were not exhaustively searched. PR1825's head was rechecked unchanged.
• Coordination #1884. Ten isolated research instances were run; this is the one selected focused submission.

Validation

Passed on CPython 3.12.12, macOS arm64, including a fresh integrated-checkout replay:

python3.12 scripts/research_package.py --package research/paired-plane-scalar-mask-obstruction
# or:
uv run --python 3.12 --no-project python scripts/research_package.py \
  --package research/paired-plane-scalar-mask-obstruction

Evidence:

• All 12,544 binary factorization entries pass as a positive control.
• 11,560 forbidden plane-mask off-diagonal entries; 11,559 nonzero under the literal integer lift.
• 224 formal dirty scalar columns replayed.
• Valid fitting-matrix control accepted; six semantic negative controls rejected.
• Remote certificate retained byte-for-byte, authenticated by SHA256 and Git blob; selected inputs pinned.
• Separate direct calculation, without importing the verifier, reconstructed all 23 columns, checked the full binary identity and reproduced the coefficient 5 / dirty output 16 witness.

No predecessor executable is imported. Standard library only; optimized -O checks remain active. No hosted CI, native full supplier replay or all-size theorem verification claimed.

Credit

Cinna Davis / 1337isnot1337 (#1825); ctoth and collaborators (Discussion1587); Josie Elliston (#1808); Rohan Arun, Jeremy Kothe, Hao Yan and the retained selected construction/decoder/geometry lineage. Apache-2.0. Prepared for Adam Gall with substantial OpenAI Codex assistance in research, proof exposition, implementation and review. No independent human review or proof-assistant claim.

Open next questions

Find an actual scalar fitting factorization for the paired-plane mask over Q or Q(i), then price its complete source/target-plane supports, restoration, routing and hosting. The README and TASK specify the exact first equations and missing implementation obligations.

[philippeVV]

This is independent support for this audit, and it narrows the "rational/complex refactorization remains open" caveat.

1. The target is fixed by the selected word. An exact ℚ replay of the canonical word gives the incumbent drop-carried decoder N = G/2. It has diagonal 1, is 0 on all 6,608 even pairs, and is ±1/2 on odd pairs, with J = I. B₀ = (J + 2N) mod 2 is only the label-form identity. Script: target/line_decoder.py (fork commit 0e1ecb64).
2. Rational refactorization on Construction: paired plane-port decoder on selected E8 labels #1825's planes needs rank ≥ 48. Γ_E has an independent set S of size 48, and N[S,S] = I_S is forced. Construction: paired plane-port decoder on selected E8 labels #1825's supports carry 23 scalar columns, so no reweighting of them works. The general floor on those planes is C ≥ 49.
3. Paid 2-integral repair costs ≥ 224 on every plane assignment. If every term is 2-integral, reduce mod 2. The block-diagonal Gram rank then gives Σρ ≥ 224 (gain/integral_bound.py, Discussion CLAIM: where does the one unpaid coordinate per live family come from, and is it forced? (ctoth, expires 07:30Z) #1587 comments 18927273 and the follow-up).

What remains open is only decoders with even denominators whose 2-adic gain exceeds 64. For comparison, the line incumbent's gain is 48.

[Mister-Meeseeks]

Batch review at 5f05652c7dc7f51555ddb59b716000199a72c0ff.

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

Reviewed scope: All12544 binary identities retained as positive controls;224 scalar columns and explicit coefficient5 witness disprove literal scalar-plane interpretation. Parity forces6608 forbidden cross-entries for every parity-preserving integral lift. Does not refute binary/translation identities or exclude rational/operator-valued replacements.

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.