Conditional precision audit: commuting intervals lower PR1054's rounded-word budget

[mightyOil]

This conditional precision audit completes the explicit PR1054 substitution left open in PR1278. With the common immutable operator and inherited preparation/leaf contracts, PR1085's sharp prefix count and PR1278's squarefree commuting intervals replace the generic interval factor C²G² by C²G. The negative leaf is bounded at its positive preimage; the complete beta^-8 internal reserve remains paid.

For PR1054's radix-64 example (p=128,m=20,w_input=0), sufficient fractional width falls 1,420,902 → 1,162,598, saving 258,304 bits; signed integer width falls 1,291,719 → 1,291,709. Factor preparation remains 516,499 bits, with the same 4,000 leaves and six borrowed arrays. The proved convenient fractional envelope is max(p,w_input)+m+15r³, versus PR1054's 18r³; no optimal-width, measured-speedup, supplier or kappa claim.

Only research/commuting-dirty-precision/ is added. It contains the complete written substitution and cost bill, exact formulas, source pins, frozen consumed source subset, deterministic evidence, controls and registered replay. No selected record or upstream source is changed.

Validation

python3.12 scripts/research_package.py --package research/commuting-dirty-precision

Expected: PASS_COMMUTING_DIRTY_PRECISION, six passing package groups and PASS_REGISTERED_RESEARCH_PACKAGE.

• 5,220 exact prime-power budget certificates through radix 512 and 216 generic rational cases.
• 78 literal PR1054/PR628 dispatcher comparisons, 150,126 leaf events, both signs and shared scratch.
• 20 actual stable rational fixtures: 80 signed rounded words / 2,336 leaves, all with nonzero errors. Exact dirty restoration, standalone negative calls, finite-geometric ideal oracle, inverse-preimage guards, literal read/write and full routing counts pass. Each forward census matches the old finer-grid execution on identical incoming data.
• Eight mathematical/admission controls; five actual package corruptions reject and read-only relocated inputs pass. Registered replay on CPython 3.12.13: 60.128 s. All 25 selected-record tests and the selected-record integrity check pass. The clean patch applies to refreshed main.

The million-bit radix-64 row is an exact budget computation, not a literal execution. Full PR1054 tests, selected supplier cold replay, full factor preparation, hosted CI, native/physical integration and proof-assistant verification were not run. The all-size claim rests on the written proof and pinned predecessor lemmas, not finite extrapolation. PR1085's similar 1,162,523 figure concerns PR905's different leaf budget.

Pins, overlap and credit

Research base dadfea6e8a78ff6ba901705f87532a71c6f5bbb8; refreshed main bdd4c63ac7c5d8a46ce070ba133df8d7ba9cb92c leaves selected/guidance inputs unchanged. Seed 64, adversarial audit. Claim: discussion #1283. Fresh overlap read covered 815 open PR bodies and 21 discussion records; exact dependency heads remain unchanged. No matching rounded-contract substitution found; this is bounded overlap evidence, not a novelty guarantee.

Credit Ali Romman (#1054 at 6bc675be1554b3a3be771147f21f9dc2c6dae50a), Hanson Sun (#1085 at 82b99c7d12dac009d35636562df4c6c91e885409, #1244), Charles Bethin (#1278 at 06b8c006891ae78abe24b30d2fe9d8c188deafe8), Chafik Boukhalfa's #628/#862/#905, Gareth Davidson's #877, 0xkilgore's #663 and the retained lineage. These pending dependencies are explicitly pinned; their GitHub state is not mathematical acceptance.

Prepared for Philipp (@mightyOil) with substantial OpenAI Codex / GPT-6 Astra assistance in mathematics, code, verification and writing. Apache-2.0; no independent human-review or literature-priority claim. The README gives concrete open next questions on sharp interval coefficients and complete caller admission.

Concurrent #1294 (03025ca1d51091a9525203000e77dacccfa6a70d) supplies universal local phase-algebra certificates for #1278; this is complementary, with no imported implementation. The cost proof explicitly distinguishes data length M_len from interval norm bound L.

[Mister-Meeseeks]

100-PR batch review at 3a6773708f0d73f7dbee164f4c6e7658b0b41509.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Combines the ordered-interval and stopped-depth estimates with an explicit nonlinear-feedback contract, retaining the inverse-preimage penalty. Conditional W=15r³ guard pricing is checked; no new supplier or κ is selected.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.