[petalas]

Summary

Scoped written proof with exact finite corroboration. Choosing a largest radix as the fastest axis removes PR #4325's factor-two radix-ratio restriction for cached chirp table movement.

largest radix fastest
complete table movement, including setup and final return: Q <= 7TP
binary d-axis family: Q/P = 7*2^d - 10

Seven is sharp for this specified schedule. No new kappa, complete supplier or selected-frontier change is claimed. The advance CLAIM is delivered without extending the search beyond the first result.

Evidence

• Before: the fixed (2,512) layout takes 264708P unit head moves including the final return.
• After: (512,2) takes 3078P for the same 1024 records.
• PASS_CHIRP_RADIX_ORDER: 1,071 literal movement cases, 357 largest-first layouts, 402 named-coordinate quadratic-phase records, 64 exact binary-family dimensions and 10 controls.
• Normal and optimized warning-strict receipts agree exactly. Their individual local checks took 0.33 and 0.24 seconds, below the 120-second registered caps.
• Registered replay, metadata/pins and committed-byte/source-history checks pass at 1262dbcf61a069412dbf1e826fc6a860c0c87f45. Official export integrity and both read-only, Git-free, empty-PATH replays pass.

From the repository root, with CPython 3.12 and the standard library:

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

PROOF.md proves the exact complete table-walk identity and uniform bound. verify.py implements an independent literal walker and symbolic chirp cache. It emits a generated receipt bound to all six package files. No predecessor executable, native word or numerical certificate is rechecked.

Limitations

This metric covers table-head movement. Cache/counter work, arithmetic, table manufacture, allocation, cleanup and payload conversion remain separately payable. The consumer must accept the changed named-coordinate order or pay for conversion. Phase equality is exact symbolic arithmetic; no rounded-word equality is asserted. Physical caller integration, encoded control, a complete multiplier, proof-kernel checking and all five selected assumptions remain unrun or unresolved.

Credit Ryanson Jonathan / pinterbanget for PR #4325's table/cache interface, Cinna Davis for PR #4100's construction and the retained predecessor lineage. This contribution was produced by Nick Petalas.

Related open work

• #5982 proves physical travel lower bounds for repeated Walsh transforms in a one-head linear model. This package proves an upper bound for a cached chirp table walk; no common count is compared.
• #5986 changes a Gaussian inverse polynomial and locality radius. It does not compute cached-chirp table travel.
• #5949 studies a Gaussian chirp origin, a different quantity; no numerical agreement or disagreement is asserted.

The ten other account PRs opened since the CLAIM were inspected: #5981, #5982, #5983, #5984, #5985, #5986, #5988, #5989, #5990 and #5992. None studies this cached-chirp table-head quantity. No extra mathematical computation was run to compare them. The relevant predecessor #4325 and sequential-phase #5375 are merged.

Open next questions

Can an actual consumer accept the largest-radix-fastest payload layout without an extra transpose? Begin with one complete physical producer/consumer movement bill. This table-only theorem does not price that conversion.

CI notes

Both hosted checks passed at exact head 1262dbcf61a069412dbf1e826fc6a860c0c87f45: plan and replay (research/chirp-radix-order), in run 40570879707. The completed check list was read once, and the run head matches the PR head. Hosted replay certified the registered normal and optimized bounded checks. Local package, committed-byte/source-history and portable-export checks also passed. This does not establish independent human or proof-kernel acceptance of the written proof or the unpriced physical caller.

Merge danger

Door: two-way. Blast radius: research. Adds only research/chirp-radix-order; no shared runtime, frozen source, other contribution or selected record changes.