Research consolidation: exact rational numerator and residue contracts

[bitplane]

Change and mathematical scope

Add research/rational-residue-scope/, an executable comparison of PR1057 exact additive borrowing, Ali Romman's PR1135 common-numerator/rounded contracts, and PR1159 binary residues. Exact rational factors with odd reduced denominators can use the same residue kernel when the completed map is integral and the signed endpoint has a strict recovery bound. This does not contradict PR1135 or implement rounded leaves.

On the frozen 52-factor, 1,376-call word, alternating central scales 1/3 and 3 preserve the complete integer product. The least common denominator of every formal rational prefix is exactly 9, with an explicit -2584/9 witness. The common-numerator data bound is 94 bits using denominator 9 (194 using the conservative 3^65); residue data need 56 bits. The numerator widths are sufficient bounds, not minima.

Residues incur 2,406 additional preparation commands, including inverses and all 208 coefficient conversions: 54,698 kernel-plus-preparation commands, using 283 private bits. The package prices the original descriptors, inverse table and external routing. Admission/normalization, generic product-check workspace and coefficient-height costs, input/output conversion, controller dispatch and physical implementation remain separately charged obligations. No runtime, supplier-adoption or κ improvement is claimed.

Task and overlap

Discussion/claim: #1202. Consolidation seed 99 was drawn before detecting the revised donation prompt; the existing assignment was retained. Card scope-navigation, scope changed: PR1159 already links PR1135, so a navigation-only edit would add little; the useful result is the source-bound representation comparison and finite construction. Its connection is a possible precision representation at exact additive boundaries, with no changed paid supplier profile.

Experimental base: 1b59b624d21924f8e3537cdc1ac52d3be6eda2fe; submission base: 49b3157d1d89adcef16df8be98445451672be5ba. Exact dependencies:

• PR1057: 78a062df1dcab2bffea5ff4d8243f3da6e465414.
• PR1135: 4c35687d7c0da8e6cf33f17e418ecf31c95ff3ad.
• PR1159: f38bfe5da0bed21f42ce5251d23491a56519d7c4.

Twenty scientific source files are frozen byte for byte, with Git/SHA-256 pins. The final helper snapshot covers 836 open PRs through #1228, all six Discussion threads/comments and 324 local records, with complete pagination and no refresh warnings. Literal-search coverage and limits are in VALIDATION.md. No matching borrowed-word unit-denominator comparison was identified. PR1164 changes echo arity; PR1199/1203/1205 concern deferred readers; PR1211 prices a different factor layout. Those mechanisms are not imported.

Validation

python3 -I -B research/rational-residue-scope/verify.py
python3 -I -O -B research/rational-residue-scope/test_package.py
python3.12 scripts/research_package.py --package research/rational-residue-scope

All pass. CPython 3.14.4 and an isolated optimized Python 3.12.3 replay of the complete read-only package produce the identical receipt:
2c63ba9c68e4537a49815af076b9097ae49c3f5a7ca66229710455b9d3aed6e2.

Evidence: all ten formal columns at 2,752 prefixes; four primary executions/5,504 literal boundaries; 144 small cases/2,862 prefixes; 128 unit inverses, 120 nonunit exclusions and 65,520 quotient-addition cases. Twelve mathematical/admission/price failure controls and three exact rounded/nonintegral counterexamples delimit the contract. Eight package tests exercise actual subprocess corruption and artifact recompression. Twenty-five selected-record/inventory/proof-binding tests pass. The registered metadata check and both replay commands pass.

The all-size/physical compiler, selected hosted cold replay, historical global suite, native supplier admission and proof-assistant build were not run. Hosted PR CI is reported separately.

Credit

Gareth Davidson (@bitplane), with substantial OpenAI Codex assistance. Credit Ali Romman (PR1135), the retained PR1057/1159 source lineage, and classical localization/Newton inversion. Source notices/licenses are preserved; no new algebraic priority or independent human/subagent review is claimed. Apache-2.0.

Open next questions

README.md and TASK.json give two bounded follow-ups: test the unit-denominator/integral-boundary contract on a named selected supplier segment, and price a structured integrality certificate without forming the entire rational product. Their algebraic, physical and online-cost blockers are explicit.

[Mister-Meeseeks]

100-PR batch review at 3e76ef5d86561e100f8812714eb316cfe5939fc6.

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

Reviewed scope: Odd-denominator exact rational residue contract: unchanged1376-call word restores all dirty residues; example has actual denominator9, sufficient94-bit numerators versus56-bit residues. Conversions, inverses and routing remain paid; no rounded-leaf substitution.

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.