[aliromman]

This proves the sharp seven-deletion all-pivot boundary in the E8 decoder-incidence handoff. For every X subset of P112 with |X|<=7, every function on the surviving lines whose sum on each surviving frame is zero extends uniquely to an ambient trace-zero quadratic. It follows that diagonal incidence D holds at every live pivot, without W, G or nonempty-block assumptions. The known eight-deletion counterexample makes that threshold sharp. This is an enabling proof with a complete finite certificate; no new kappa is claimed.

Proof, complete evidence, verifier, source pins, and validation limits. Exact head: a6ae9be34f8db157f285e1bb77e23452f7338c5d. P112 means the 120 E8 root lines with the fixed eight-line FRAME0 removed; the theorem permits at most seven further deletions and uses all live frames. It holds over every characteristic-zero field.

The missing extension is established by a new global incidence-rank certificate on all 263,922 deletion representatives of sizes zero through seven. A reverified predecessor orbit cover transports those ranks to all 38,760,897,157 deletion subsets in scope. Uniform quadratic and projected-root frame bounds supply injectivity and the seven independent canonical directions. The E7 support-twelve theorem then proves D simultaneously for all pivots. The proof does not replace that universal step with a sample of pivots.

This completes JoyboyBrian's precise extension handoff. Josie Elliston PR #1650 supplies the orbit cover, geometry and row ordering; its existence of one good pivot per deletion class remains a distinct predecessor theorem. Nick Petalas PR #5238 supplies the E7 support proof and complete support verifier. Andrey Mas PR #1560 supplies the structural criterion. Josie Elliston PR #1668 supplies the eight-deletion witnesses, whose discovery and sharpness credit remain unchanged. Aaron Wang and the retained Brett Halligan, themilkman216 and DreamingOfClouds lineage are credited in the proof.

python3.12 -B scripts/research_package.py --package research/seven-deletion-quadratic-extension

Expected: PASS_SEVEN_DELETION_QUADRATIC_EXTENSION for each phase and PASS_REGISTERED_RESEARCH_PACKAGE. Python 3.12 and the standard library suffice. The registered replay passes. It rebuilds the 172,032-element group, verifies every cover transporter, checks all global ranks in two disjoint exhaustive parts, and replays all 134,217,727 nonzero E7 codewords. Separate dense arithmetic checks 512 packed-elimination cases and all nine scalar additions. Both exact eight-deletion witnesses, 128 restored-coordinate ranks, damaged-witness/deficient-family controls and all 92 E7 source controls pass.

The global extension rank is still 69 on both 104-line boundary fixtures, while D fails. Thus extending the global lemma beyond seven does not by itself improve the all-pivot threshold. The result adds no rigidity floor: PR1650 already proved P105 rigidity using a suitable pivot. G/W for every pivot, nine or more costly terms, a changed decoder construction, native realization, preparation, ownership, storage, precision, routes, restoration and a complete recursive invoice remain outside this claim.

Normal and optimized replays pass. The optimized replay runs every registered phase in a sealed read-only Git-free export with empty PATH; all eighteen exported files retain their bytes and modes. Actual source corruption is rejected. Exact committed-byte and official final export checks pass. Full-history preflight is omitted in the shallow checkout; immediate base ancestry and exact local/remote source objects are checked. Hosted CI, independent human review and proof-kernel acceptance remain separate.

Base and final canonical refresh: df0137efd35e11b4445734bf612bdd4c7ebc330c, priority7, selected .00310045. The current main-transform bottleneck is unchanged. Canonical claim. Complete live overlap checks found no competing extension reservation. All nine consumed source files and notices remain byte-exact. New proof, rank certificate and checks: Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. No global literature priority is claimed.