Research: verified pure44/q518/506 composition and latest-source comparison

[mdumitrean]

Change and mathematical scope

Preserve a distinct, superseded finite conditional construction composing Dugongue's #2309 pure44 alias619→530 and exact owner fill with Jeremy Kothe's #2302 q518/506 helper-donor kernels (mdumitrean/#1625 shape). The modern κ is exactly 0.00169659996105181924736999999999979966068000768963615052600000000004, about 8.48368e-8 above the pinned #2309 claim.

The contribution is the actual chronological gate/warp composition, portable reconstruction with recovered predecessor controls, complete inverse cleanup, and source-bound supplier/owner/outer admission. Local profile: {1:2341,2:505,3:420,4:124,5:42,8:8}, mass 5381; 436 helpers, 76 private FULL buffers; all 666 hosted calls use the extra provider. Global profile: {1:1582416,2:336330,3:288393,4:82584,5:29451,7:148,8:5328,14:1,48:24479}; mass 4,816,512, live 66,304, physical 66,826, roles 290,376, row 19,545<20,161. The exact paid-profile delta is +1332 C1 -2664 C2 +1332 C3, strictly cheaper for C(r)=r^p, 0<p<1.

This is not a new leading bound and does not stack as an extra saving on #2474. Its actual words already contain the same two kernels; #2322 has already removed619, while530 serves651. Minimal source-pinned comparison inputs and executable checks establish these facts in both orientations. A future rescheduling could be a different investigation; we claim no universal non-composability theorem.

The modern fixed-profile packing cap is κ < 0.001728266380383; about 98.167735% is realized. The existing cap engine is used for native saving a; this modern outer has κ<a, rather than the engine README's historical balanced a/(1+a) conversion.

Inherited all-size compiler, physical fixed-tape hosting, precision, recovery, analytic transfer, bit-supplier and modern-outer interfaces remain conditions. No unconditional multiplication theorem, full Lean reflection or independent human review is claimed. The selected record is unchanged.

Task and overlap

User-assigned T01 composition and publication; nearest catalogue card complex-rank-shape-decoder, changed scope: this is an incremental composition and reproducibility result, not the card's five-percent acceptance gate.

Base main: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.

• Improve conditional κ to 0.0016965151242727336 with a pure 44th dirty alias #2309: 95aea1e24dede937f00545a4d8250caa02f60339.
• Conditional κ = 0.001696395766736081: exact pivot-518 and 506 helper-donor kernel(s) (PR1625 shape, KernelsOnBorrow) on the borrowed words, exact frame refit (WildIdeas), 1e-3000 certified supplier endpoint, fixed-grid-maximum kappa C - 1/… #2302: d520b92d7bf18efcb7d84f12757face6fe9541f1.
• Nearest superseding lineage: Conditional κ = 0.001696891067241618: helper width exchange on the borrowed T74 words #2312 → Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322 → Conditional κ = 0.001697194950901770: exact owner fill on #2322's handoff construction #2374/Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435/Conditional κ = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words #2447 → Conditional κ = 0.001703552312979594: optimal owner fill for #2436's aliases on the entrance-raised T74 words #2462 → Conditional κ = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words #2474.
• Conditional κ = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words #2474 comparison source: 5298f86c5193db65f869121eab3cac16d557196c; its reported κ≈0.001703676387993676489034 exceeds ours. Comparison is structural, not complete adoption/audit of that claim.

OVERLAP.json records complete pagination of 679 open PRs (12:19 UTC) and 1,197 discussion records (12:22 UTC), plus its search limitations. No exact duplicate of this composition was identified; absence of a match is not a novelty proof. The 479-file supplier is the actual complete runnable derived construction, preserved unchanged under its original manifest e1bcf65a27e52767e2f7f4c28b284ff21b4e4f991ba2a1a803617abe49ef3a9a. New publication metadata and execution receipts live outside that frozen source.

Validation

python3 scripts/research_package.py --package research/t74-pure44-kernel-composition --check-only
python3.12 scripts/research_package.py --package research/t74-pure44-kernel-composition
OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python -I -B \
  research/t74-pure44-kernel-composition/supplier/verify_package.py \
  --out /absolute/new/composition-cold

The bounded hook also adopts the additive centre-to-target cut guard from our concurrent #2478 (dc83994c2dda28064c902ee970ce47db602224ae, Claude-assisted), with two rejected cut mutations per provider. Both unchanged composed words pass that guard and the complete native chain.

The registered standard-library hook freshly reconstructs and independently audits both composed words, checks eight targeted kernel/alias/cleanup mutations, verifies source and receipt/value bindings, reproduces the latest-source comparison and certifies the packing-cap bracket. It does not replace the separately documented complete cold replay.

A fresh complete cold replay passed in 757.17 seconds under CPython 3.14.4 with no native cache; the registered hook also passed under CPython 3.12.15 (standard library). Complete cold evidence and the precise interpreter/dependency environment are retained under evidence/, including native, supplier, modern outer, actual hosted-owner binding and ordinary-bootstrap receipts. All660 arbitrary dirty columns in both orientations, all 88 native warp classes on 512 columns, strict supplier/owner controls and 62 modern outer inequalities with 17 rejecting controls are covered. Hosted CI is a separate gate. The unchanged selected-record cold suite and a full Lean theorem were not run.

Credit

Dugongue/#2309: pure44 alias, repacking and private-buffer accounting. Jeremy Kothe/#2302: q518/506 kernels and exact frame refit; mdumitrean/#1625: kernel shape. Cinna Davis (1337isnot1337)/#2226: anticipatory dirty borrowing. Retained source notices preserve the supplier, verifier, native/outer and analytic lineage. Comparison excerpts credit Jeremy Kothe/#2474, Vlado Vojdanovski/#2322 and tekuuu/#2436.

Prepared for Marius-Paul Dumitrean (mdumitrean) with substantial OpenAI Codex assistance in research, code, validation and writing. Original research included separate agent checks; no independent human review is claimed. New work is Apache-2.0; retained source licenses and notices remain intact.

Open next questions

The README and structured TASK metadata point to independent review of chronological transport and inherited physical/outer premises. A useful first step is replaying both words and inspecting exact gate/warp transport and native receipts. Any further improvement of a current leading supplier must start from its actual handoffs and a new complete invoice; these two kernels and helper619 cannot be counted again.