Certify cold-host cancellation and fixed-word restoration obstructions

[mdumitrean]

Change and mathematical scope

The J-dim1 hosting lead predicts a gain only if the merged host can be restored below full width. This package resolves its free-operator cancellation and certifies why direct contiguous restoration fails on the pinned words. No new κ or admitted supplier is claimed.

• An explicit inverse prelude and terminal undo restore 473→277 in both orientations under the unchanged algebra/frame auditor. The resulting FULL9 buffer is rejected by the pinned native transport; this is a constructive local component.
• For 184 words (92 pairs, both orientations), all 131,788 direct insertion slots require rank at least eight. All 8,208 rank-eight gate orders in 720 commuting classes have explicit target-port end-frame witnesses. Enlarging other helper ends alone cannot remove those witnesses.
• A separate 992-variant entry-hyperplane census checks 368,218 slots; every variant requires rank nine.
• Exact rational duals over 1,163 patterns reject the conditional width-nine/−H3 ledger, including batches of one, two and four. Ideal restored width-seven/eight ledgers leave less than 0.017959/0.005786 H1-equivalent extra net cost per call at the pinned comparison point. These budgets do not establish realizable words or chronological owners.

Staged recovery, changed bases, changed scalar words and changed interfaces remain outside the obstruction. No complete native supplier, stock/precision, literal-owner or outer admission is provided.

Task and overlap

Task complex-new-helper-inventory, refined to the user-assigned cold-host restoration obligation. The full cost ledger, stopping decision, source pins and overlap coverage are in research/t74-cold-host-restoration/TASK.json.

Publication base: cfddb8581e7e96d4f4cd9bfd279037014c8b296d, priority revision 5. Scientific inputs remain pinned to the J leads branch, based on #2802 at 17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd. Related borrowing sources: #2745 and #2767.

The submission refresh covered all 705 open PR records and 1,466 Discussion records. New #2818 at 175822aee7a1858ec653f7f92d7a750aec2c2795 has identical complete words and allocation data to #2802 and claims a finer endpoint. Its endpoint certificate was not rerun here; it adds no cold-host mechanism. The present obstruction remains applicable to those words. No matches in titles/bodies/discussion records is not a universal novelty claim.

Validation

Python 3.12, standard library only:

python3 -B scripts/research_package.py --package research/t74-cold-host-restoration

The replay authenticates the package and consumed sources, reconstructs all 184 words, checks the full finite censuses, executes the unchanged operator auditor, and checks 20 rational duals plus ten integer-pattern root brackets. It includes positive fixtures, semantic/frame/cost mutants, and expected native rejection. Imported bytecode uses a fresh cache namespace. Frozen predecessor evidence is unchanged. The registered replay and a second full replay from a read-only Git export both passed; the latter also planted valid stale bytecode and confirmed the package entrypoint ignores it. All 53 staged files preserve their checked bytes. Only README/TASK freshness metadata changed afterward; source and certificate bytes are identical.

Credit

Marius-Paul Dumitrean's J lead, #2802 and #1186 toolkit, with the assistance disclosed in those sources; tekuuu/#2751, DavidAriasC/#2766, mason-hale/#2696, Cinna Davis/#2226, philippeVV/#2679, Jeremy Kothe and the retained borrowing/native/owner/outer lineage. Original notices and exact source bytes are retained. This package was prepared with substantial OpenAI Codex assistance, including three parallel agents and a separate integration replay; no independent human or proof-assistant review is claimed.

Open next questions

See the package README: the smallest useful follow-up is staged or precomputed recovery for 473→277 that avoids the target-port collision and supplies an actual paid profile within the width-eight budget. A profitable sub-full word must then pass native, stock/precision, literal-owner and outer checks.