[ToikY]

Change and mathematical scope

For the fixed fused256-by256 hexadecimal-digit,512-point bounded Word RAM template, specialize31constant-two inverse-transform butterfly reductions after the existing unit pass. The additional saving is exactly 930 executed instructions per admitted input and1,395static instructions: post-unit length435,650 becomes434,255. This is a source-bound program-refinement proof with finite corroboration. It preserves complete memory, including TEMP, control exits, operands, cleanup and exteriors. No global optimum, all-length optimizer or new multiplication theorem.

The four-instruction replacement retains MUL and the final SUB/BLTZ/copy. For every residue0..65,536, the15higher threshold groups always skip their copies; exact savings are45static/30executed per site. TEMP remains unreduced2b-65537 modulo2^64, not always reduced VALUE minus65537. Complete coefficient write inventories, exact macro/alias/lifetime checks and once-applied old-to-new labels bind the actual source. Setup, literal constants, inverse normalization, carry, clearing and halt remain charged. The original producer's range/setup/executed-initialization/traversal and correctness contracts are cited premises, not independently re-audited.

Task and overlap

Canonical main7c49fe32c55de02c2c873655c804b16e4c3fef0a, revision8, selected6030 unchanged; refreshed at entry and before submission. The formal-interface-lemma card is explicitly CHANGED/partial: one bounded compiler/cost interface, no formalized Lean proposition or selected-interface discharge. Advance claim. Fresh759open bodies/heads, source feedback, live Hub/index and seven bounded all-state queries found no direct equivalent; sparse helper omissions and unseen work remain unknown. A prepublication “constant two” hit #6789 concerns dyadic error-cut envelopes and does not supply this ISA refinement.

Nick Petalas #6802, exact headb792a58669a3bd2372a38db567ba04241b562519, owns the unit transformer/full-state proof/relocation and existing47,523executed saving; its released known-nonunit question is the handoff. David Ganz/Dugongue #5466 supplies the bounded producer/ISA/NTT and cited theorem; #5886liveness and #6435assertion portability remain separate. Only research/wordram-double-twiddles is added.

Validation

First CPython3.12.14 run passed in4.108s/220.625MiB, under120s/256MiB forecast, with all20file hashes unchanged. The emitted census is31inverse sites at widths32/64/128/256/512:16/8/4/2/1, coefficient cell23590. Every site records original/post-unit/new PCs and lifetime. Full local literal comparison covers all65,537residues with independent VALUE/TEMP oracles and exact memory/write frames. Three complete dirty-memory fixtures pass: zero314002→313072, maximum343556→342626, patterns342989→342059. Six exact-reason structural controls and two executed semantic differences pass, including VALUE-correct/TEMP-wrong and an out-of-domain witness. The latter illustrates a premise; it is not rejection of an admitted input.

Final normal/O, both registered commands and read-only Git-free empty-PATH export packets agree byte-for-byte. Official21-member export/input coverage,18early source-corruption rejections,20committed blobs/modes/sizes and exact9-body/51,318Bsource custody pass. Source-aware static proof/code/metadata/delivery reviews found no blocker; no blind, human or proof-kernel acceptance. Original run42279311757, attempt1, passed711helper tests/24skips and both registered finite commands at exact public head2b8509a8170c253c769778d3443f85898d494fec. Both complete11,943-byte hosted packets equal the frozen local packet byte-for-byte. Saved decoded logs retain exact tool-character readback; synthetic checkout8cdc58f1e50850589d1bf50f172ad0a2faad112d has the exact public tree and canonical/public parents. This is a synthetic PR test ref, not a repository merge. Hosted CPython3.12.16 corroborates finite execution, not independent mathematical acceptance.

The authenticated original builder/ISA and credited unit transformer actually executed. The old broad6802verifier was fetched/read inertly and not imported/run. Unit1,533site binding is regenerated; its associated47,523saving is the cited theorem value, not a newly executed P0-versus-P1 whole-program comparison. New whole fixtures execute P1versusP2. No old nine-template suite or all operand/length-pair census.

Reproduce with python3 scripts/research_package.py --package research/wordram-double-twiddles; direct isolated normal/O commands, exact normalized-JSON program hashes and complete evidence are in README. PROOF distinguishes written universal implications from finite fixtures. Original, post-unit and new program hashes are bound separately.

Credit and remaining obligations

Credit Nick Petalas6802/5886/6435, David Ganz/Dugongue5466, Shilun-Allan-Li/tcslib with Anthropic/PBC attribution, Thomas Ahle/FastPoly, Bas Spitters/CatCrypt, Brett Saiki/mpfx and retained compiler/multiplication lineage. Constant specialization/block simulation are classical; original notices retained. Substantial source-aware OpenAI Codex proposal,implementation,proof/code challenge,overlap and metadata assistance; source/provisional exposure and pre-first provenance/import-origin corrections disclosed. First receipts and later metadata hashes remain separate.

Native word-to-bit costs, selected consumer conversion/routing/storage/precision/ownership/restoration, all-size paid compiler and complete supplier invoice remain open. All five selected assumptions remain; no kappa/frontier/supplier/adoption change or merge.

Open next questions

README next questions: first bind one actual selected consumer with its complete matched tariff and conversions. Review/install only this exact scoped refinement; other coefficients, asymmetric lengths, liveness composition or global optimality need separate evidence. The physical/compiler interface remains the blocker.