DONE: native rounded butterfly contract

[JoyboyBrian]

DONE — contribution submitted: 5485. Maintainer review remains pending.

Exact head 47c4e95f2aad7b33637aca3ac0dde0a0a2a9ebfe; 3 substantive commits. Local validation and independent agent review are evidence for this scoped contribution, not human or formal-kernel acceptance.

A concrete fixed-grid nearest-even butterfly backend now supplies the completed-call tolerance assumed by the actual PR4743 C0/C2 port analysis. For rho=2^-q, g=q+ceil(f/2)+1 grid bits suffice uniformly. The proof includes internal numerator ranges, actual stored inputs, adjoints, every two/three-call forward/reverse schedule and w=H+g+2f+ceil(f/2)+9 signed component bits. Deterministic nonzero rounding is executed rather than injected.

The exact source pins, all-width proof, executable controls and open next questions are in research/native-rounded-butterfly-contract/. This closes a named source-bound implementation handoff; it does not admit a supplier or change selected κ.

Validation: 20,003 signed half-rounding cases;36 completed-call cases at widths1/2/3 across C0/C2 and adjoints;12 actual forward/reverse port cases with nonzero rounding and off-grid input quantization; every actual completed-call input/output; overflow/axis/adjoint controls;625 one-butterfly residue fixtures. Registered Python3.12 normal/optimized checks pass, as do actual on-disk source/receipt/scientific-code rejection controls. Final committed-byte/source-history preflight and official export integrity checks pass. Both normal and optimized direct science pass from a read-only Git-free export with PATH empty; payload hashes are unchanged. Separate AI peer review found no blocking issue.

python3.12 -B scripts/research_package.py --package research/native-rounded-butterfly-contract
python3 -B scripts/check_research_commit.py --package research/native-rounded-butterfly-contract --check-source-history

Limits: The direct backend costs O(fN), N=8^f, and does not inherit an accelerated recursive rank-one tariff. The source-ordered external channel bounds are reused with attribution, not claimed as a new norm calculation. Concrete fault patterns obey additional parity constraints; no attainability of the earlier independent-ball sharp constant is claimed. Accelerated recursion, fixed tapes, native supplier/outer admission and selected-frontier replay remain open.

Prepared by JoyboyBrian with substantial OpenAI Codex assistance; Apache-2.0. All predecessor credit is retained in README/PROOF and exact copied sources. Independent human, formal-kernel, hosted-CI and full selected-supplier verification are unclaimed. Canonical investigation: #5475.

Claim base 32890bc5de034ab8fc93ac88ead7279a6a416d04. Selected frontier unchanged.