[petalas]

Summary

A scoped circuit construction and written traffic proof, produced by Nick Petalas. A width-64 resident SCALE 2 now executes on its existing single ribbon for exactly 3284D-2 tape operations, preserving the other arbitrary resident field, both zero owner slots, owner head and carry. It answers Ali Romman's released same-ribbon question in PR6530.

for each real/imaginary record:
    rotate left through neighboring CNOT swaps
    clear the duplicated sign bit
return the active head and finite control to zero

Under the stated exclusive-owner contract and exact-doubling no-overflow precondition, the complete matched-boundary comparison saves 14492D-280 operations for every positive D. At D=1 the saving is 14,212. This is an exact operation-count improvement, not a wall-clock measurement or a new complete caller bill. No new kappa or selected-frontier change is claimed. Construction stopped at this first verified improvement.

Evidence

• Before, the best of four explicitly normalized flush/scale/reacquire paths costs 17776D-282. After, the resident circuit costs 3284D-2 and has the same full physical endpoint. The local source route alone costs 9840D before staging. The proof states the comparison class and derives every affine term without sample extrapolation.
• Local CPython 3.12.15 warning-strict normal and optimized checks pass: 129 new/source basis columns, 1,364 exhaustive legal small-width complex pairs and inverses, 252 arbitrary-bit width/dimension roundtrips with exact traffic, 24 complete physical comparison paths, seven rejecting controls and three semantic controls. A separate maximum-admitted W=64,D=64 roundtrip passes.
• Both exact registered commands passed locally in 0.934 and 0.941 seconds respectively, rounded upward, within their separate 120-second deadlines. These are replay-deadline measurements, not a speedup claim. Syntax and function-size checks, metadata/source pins, staged whitespace, exact committed bytes and source-history preflight pass at 2ca05908bf16e353b3fd14e4db7407aa47f661e8.
• Official sixteen-file export integrity passes. Both complete normal/optimized replays pass in a read-only export with empty PATH and no Git; their complete result objects agree and all seventeen exported files, including the export receipt, retain their bytes. Generated replay receipts bind the fifteen package-file hashes.
• Exact source bytes from PR6530 head fadaba3bb16a6965fa5e9c2c7af3a9df6ddf01bf are retained with original notices and blob/hash bindings. Its whole-word scientific verifier and policy optimizer were not replayed. The retained local compiler only supplies this construction's comparison circuit.

From the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/resident-scale-ribbon/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -O -W error -B research/resident-scale-ribbon/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/resident-scale-ribbon
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/resident-scale-ribbon --check-source-history

Expected final scientific output: PASS_RESIDENT_SCALE_RIBBON. The registered runner also reports PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=completed.

Limitations

Only SCALE 2 is implemented. The written construction holds for arbitrary finite W>=2 and positive D; the supplied emitter admits W<=64,D<=64. Finite execution covers the reported domains. The selected three-event window establishes a legal relevant contract, not a patched whole-word policy. The four comparison paths do not establish a global physical optimum.

Complete policy integration, initial allocation, native/reset bodies, uniform encoded-D control, numerical/stock admission, supplier funding and outer transfer remain open. The five selected framework assumptions remain. Lean, Docker and a full selected-supplier replay were not run. Independent human and formal proof-kernel review are unclaimed.

Credit Ali Romman for PR6530, PR6527 and PR6513/6511; Nick Petalas for the retained scalar circuits; Sagar Thakrar/PR3241; DreamingOfClouds/PR6030; and the retained native, owner, precision and compiler authors. Classical adjacent swaps, CNOT identities and signed binary arithmetic retain their usual credit. The original source credit lines are unchanged.

Open next questions

1. Add this exact edge to the complete PR6530 state graph and certify a new whole-word policy while preserving every native/reset boundary and charging the resulting owner-head/bank schedule.
2. Choose one other SCALE coefficient and emit its actual same-ribbon circuit with a complete matched-boundary bill. No extension beyond SCALE 2 is attempted here.

Related open work

• PR6530 supplies the exclusive two-field cache, original policy and released question. This adds one new internal SCALE edge; its complete policy optimum is not recomputed.

• PR6527 supplies whole-field owner staging and the comparison transfer contract. This changes a resident local transition and retains its external owner layout.

• PR6513 optimizes physical control routes for the fixed local circuits. This changes the SCALE 2 gate factorization and the component layout, outside that fixed-circuit optimum.

• PR6511 supplies one-carry scalar circuits, including the retained SCALE 2 map. This preserves that map with a new single-ribbon physical realization.

• PR6506 supplies the earlier complete Boolean scalar layer. This supplies one physical implementation component, with no new whole-layer gate count.

• PR6499 supplies bounded exact records and the scalar range/grid interface. This keeps the signed no-overflow premise and does not establish a new precision bound.

• PR6611 supplies a single-buffer CRT tail schedule with read/write/head counts. This contribution implements resident SCALE 2 under a different physical entry/exit contract; the totals measure different workloads.

The completion refresh examined all fifteen account open PRs created since the CLAIM, including this contribution. None of the other fourteen computes the same fixed resident SCALE 2 quantity. No cross-workload numerical comparison or additional scientific replay was performed.

Related descriptions use public PR bodies and the retained exact source. No extra calculations were run to audit those contributions or compare unrelated numbers.

CI notes

Both hosted checks, plan and replay (research/resident-scale-ribbon), passed at head 2ca05908bf16e353b3fd14e4db7407aa47f661e8 in run 41634045505. The completed check list was read once with gh pr checks 6608 --repo CrocSwap/integer-mult-bounds; run metadata independently confirms the matching head, completed status and success.

All registered checks ran locally; none was deferred solely to CI. Hosted replay certifies the registered normal/optimized finite checks and metadata. It does not establish independent human or formal proof-kernel acceptance of the written all-D theorem. No check failed.

Merge Danger

Door: two-way. One isolated research package is added.

Blast radius: package. Shared code, frozen predecessors and selected-frontier files are unchanged.