[codyw912]

Change and mathematical scope

Add research/halo-copy-enumeration/, a scoped successor to Nick Petalas's #4217 open question about Cinna Davis's #4100 source-driven halo copies. It gives an explicit first-face interval partition, source-first prefix/DFS enumerator, independent destination-first oracle, exact copy-volume identity, and the correct O(gV)+O(gC) operation account. Rare corner fanout is charged as actual copies.

No new κ, supplier admission, Gaussian locality theorem or complete fixed-tape cost theorem. The physical stack/key/radix schedule, coefficient setup and application costs remain explicit obligations. Frozen predecessors and the selected frontier are unchanged.

Task and overlap

Card uniform-transfer-audit, refined to enumeration; scientific base b58ad9ef4d4e861b0eaa5dba41742bdc072dca51, revision 7. Exact base/blob/SHA256 pins in SOURCES.json. Predecessors: #4100 337d04939571a637aeab54a0f58f54fde811663a; #4217 d2479b3606beeb745c19210219acdd96967bf8eb.

Canonical main remains 624de9dc66858af0945e5f8a0942488d62280d43; guidance, selected record and scientific inputs are unchanged. Publication-time overlap refresh at 2026-10-22 22:27 UTC covered 392 open PRs, 3,875 Discussion records and all 5,862 tracked local notes including this package. Exact-term results were predecessors and our own notes; neither publication branch had an existing PR in an all-state head lookup. Separate all-state title/body searches checked differently named contributions. This is not a novelty guarantee. Discussion posting failed; no successful public claim is asserted.

New nearby #4786 (5e0609cb2f313a217ee355a2da148e2562536462) audits rounded raw Gaussian forward/stored-inverse caller composition and explicitly leaves global core/halo work separate. This contribution concerns source-copy enumeration, not its precision contract. The previously merged tensor-error/core-row packages do not supply this enumeration adapter.

Validation

CPython 3.12.13, standard library. Registered replay runs normal and optimized modes:

python3.12 -B scripts/research_package.py --package research/halo-copy-enumeration --check-only
python3.12 -B scripts/research_package.py --package research/halo-copy-enumeration

Three exact 2D/3D fixtures cover periodic wrap, multiple copies, unique returned keys, zero-copy centers and corner fanout. All twenty failure controls pass in normal and optimized modes, including six mutations of the real source-enumeration algorithm checked against the independent oracle. Six live source pins, metadata, refreshed-launcher replay, committed-byte/source-history preflight and deterministic export integrity checks pass. Independent read-only AI review re-derived the scoped proof; it is not independent human or formal certification. Full selected replay and physical-tape implementation were not run.

Credit

Cinna Davis's #4100 caller and Nick Petalas's #4217 locality audit retain attribution and licenses. Prepared for codyw912 with substantial OpenAI Astra assistance and separate AI review, Apache-2.0.

Open next questions

README and TASK.json give concrete next steps: a paid fixed-tape stack/radix schedule and binding coefficient setup/axis exposures to the same copy layout. No devenv or agent configuration is included.