Scoped negative result: all-support R439 common-frame kernel entrances

[mightyOil]

The fixed PR589 R439 word has only one nonzero binary response-null direction whose entire support admits a common nonzero rational first-contact frame: e_444 + e_470, at the frame79 line. This closes the arbitrary-support version of Adam Gall's PR1179 sparse-support census; it adds no new supplier, gate saving or κ claim.

The proof reduces every support size and every rational common entrance to a complete finite intersection closure, because the 439 helpers' first-contact frames have dimension at most two. All 366 distinct nonzero subspaces are certified: 365 restricted response matrices have zero nullity, and one has nullity one. The full response is bound to the raw A/scatter/B/C word on all 661 dirty columns. A separately written exact Gram-projector/row-elimination checker agrees with the RREF/column-elimination checker on every subspace, eligible set and kernel.

Scope is deliberately narrow: fixed raw word and first-contact frames; binary helper mixing at a common entrance. Later cuts, new helpers, altered raw words or frames, physical hosting, and differently timed basis changes remain outside the classification. Even free entry/exit synthesis cannot produce a second algebraic direction within this boundary. No full multiplication theorem or proof-assistant verification is claimed.

Only research/r439-kernel-entrance-closure/ is added. Base: dd6403f774a0891093a006ae9716c02e371b1fdb; all input/provenance pins remain identical at refreshed main dadfea6e8a78ff6ba901705f87532a71c6f5bbb8. OS seed 5 selected the user-assigned bit-supplier track. The local claim records three alternatives and the declared change from the catalogue card; no pinned coordination issue existed. Final overlap check covered 844 open PR bodies through #1247 and recent discussions; PR1179 remains the nearest distinct predecessor.

Validation completed on macOS:

python3.12 scripts/research_package.py --package research/r439-kernel-entrance-closure

• Registered Python 3.12.14 replay passes both verifiers and all 10 package tests.
• Python 3.14.7 also passes; relocated optimized replay is included.
• Every binary 3×4 response matrix (4,096) is checked against every support mask (16). Controls include a minimal six-helper dependency beyond the former cutoff, changed response bits, incompatible/three-dimensional geometry, three raw boundary mutations, source/receipt corruption and refused receipt overwrite.
• Existing 9 finite-bit-contract and 5 selected-record tests pass; metadata/source pins and staged whitespace check pass.
• Selected cold replay, native/physical admission and remote CI are not claimed.

Credit: Adam Gall's PR1179 (a09f799fdb312e049a81f59b44f1339b5a053bbe) for the sparse first-contact formulation and known pair construction; Dugongue PR254 and Chafik Boukhalfa PR382 for prior kernel-entrance mechanisms; DreamingOfClouds PR589 on eumemic PR555/543 for the source word. Full boundaries and predecessor credit are in README/PROOF. Prepared for mightyOil with substantial OpenAI Codex (GPT-6 Astra) assistance in mathematics, code, verification and writing. Both algorithms belong to the same AI-assisted contribution; no independent human review is implied. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 21dd0227f0c0d1b2a91c01c23cb0a16a3d1934be.

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

Reviewed scope: All-support fixed-first-contact kernel classification using complete366-space intersection closure; only444+470 survives. Completes PR1179 support range without a new supplier.

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.