Research: lower PR #2339's initial T74 prefix with 64 monomial applications

[commdata2338]

Change and mathematical scope

Adds research/t74-anticipatory-native-prefix/, a finite native prefix and scoped grouping proof for both PR2339 80-alias T74 words. Each source lender supplies two initial corrections. Preparing its monomial once, performing both reads, and restoring the reference cuts 128 monomial applications to 64, retaining all 64 scalar ADDs and adding zero positive-rank recursive children. Both forward and ordinary inverse-transpose prefixes are certified, including Gaussian phases and arbitrary dirty inputs.

The certificate contains the native monomial serialization, explicit address-coordinate XOR/phase gates and executed scalar scratch programs. The per-invocation, per-orientation scalar bound is 572 real-component primitive passes. Separate address bills are (CNOT,CZ,Z4)=(1234,819,158) for gauge44/base and (1300,765,162) for extra. These are finite operation inventories; 572 excludes address routing and is not a full-supplier overhead or tape-time bound. No optimality of 64 among other synthesis methods is claimed.

The generic expansion and K_G convention already belong to PR2226/2269. This contribution instantiates the changed PR2339 initial stage, groups its actual source reads safely, and checks complete native phase and boundary identities. It does not recertify the rest of the words.

PR2360 subsequently reports b<0.0016870 for the full 400-helper stock on unchanged T74 bins. The README records that stronger cost boundary; no whole-inventory hosting build, supplier admission or new kappa is claimed. Whole-word native phases/wrappers, 44 cleanup buffers, owner windows, complete costs/moment, recursive precision, layout/tape/all-size admission, outer transfer and the selected cold replay remain unchecked.

Task and overlap

The claim is in discussion #2366. Evidence is author-checked.

Contribution commit: 444e13cd04a4b1072bbe2470a3699c5eb9b96b08; main was rechecked unchanged at 07:23 UTC before submission. Patch application against refreshed main was checked with a temporary index.

Task card:

• Task ID / scope key: complex-new-helper-inventory / 5868e5281a1e63d41a22; nonce f4823b39cf799305bc5def7fbfe81e7b, complex-mechanisms, priority revision 4. Third original suggestion, no reroll.
• Base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2. Canonical main was fetched again at 07:02 UTC on 2026-10-15 and remained identical; guidance, catalogue, selected record and mathematical inputs did not change.
• Exact predecessor heads: PR2339 bf1742aee4d855efb8bbd44a8419eddb33a679e5 supplies both frozen words; PR2269 b479fc5567bc09ab9185bffe89b62594f36d74e5 supplies the native expansion/compiler convention; PR2226 dacaf3d81f1936bb55b8454b1244e5d014272754 supplies anticipatory borrowing, retained through PR2339. Contextual PR2360 16d4ea6c26cd45ebb9301ab90f33a73615627f8d was read, not independently replayed. The retained compiler is blob 166841a037f069249f6f7f6dedb89248812f59e2, verified identical to PR2269's copy.
• Object and domain: 64 initial terms per provider, 32 lenders, 32 targets, nine address bits, coefficients ±1 and ±1/2, both orientations; all 512 columns, no source sampling.
• Scope status: refined. Take the explicit native-prefix handoff on a suggested helper-inventory card. This closes one physical implementation obligation; the whole-supplier acceptance gate is not claimed. The other suggestions were passed over after checking covered decoder cases and active P104 chronological work.
• Exact claim audited: actual Gaussian initial correction, source/lender binding, dirty boundary and finite primitive bill; existing symbolic/free-operator validation is credited.
• Method: pinned exact compiler generation; independent permutation inversion, Gaussian phase reconstruction, primitive-gate interpreter, sparse exact boundary replay and semantic controls.
• Optimistic budget: reproduced the inherited call-weighted R48 relaxation in [873979185987/500000000000000,69918334879/40000000000000]; it is not a profile audit or completed invoice. The later whole-width cap stops a full-inventory attempt. Local success requires zero additional recursive children with all scalar/address operations exposed.
• Success/stop: complete finite prefix equality plus controls, or a concrete discrepancy; one bounded session, no full supplier search. Evidence and structured next questions are in TASK.json.
• Artifact / reproduction: the single new package, command below; no selected/frozen files changed.

Final shared-snapshot coverage: 583 open PRs fetched 2026-10-15T06:55:23.240869Z, 1,111 Discussion records fetched 06:57:32.010338Z, both with complete pagination. The changed-file index covers 572 PRs at 06:33:04.255876Z. Queries were the task card, 2339 / anticipatory / native initial prefix (all 42 matches returned), and the proposed package path (zero matches). Offline warnings are expected; metadata search is not a novelty guarantee. The final board reread used the07:09:50.407275Z snapshot; the scoped claim was unchanged.

Nearest work: PR2339 constructs the words and leaves native lowering open; PR2269 supplies a general lowering but its shipped 43-high-alias words have no initial terms; PR2360 prices whole-helper widths; PR2359 audits different four-role raw rank ledgers; Discussion 2325/PR2363 optimize owners on other retained words. None supplies this grouped, source-bound initial prefix. Concurrent local claims were read; the second helper-inventory claim studies arbitrary-term P112 factorization, a distinct object/question.

Validation

Linux x86_64, CPython 3.12.3, standard library only:

python3 -I -B scripts/research_package.py --package research/t74-anticipatory-native-prefix --check-only
python3 -I -B scripts/research_package.py --package research/t74-anticipatory-native-prefix
python3 -I -O -B research/t74-anticipatory-native-prefix/verify.py
python3 -I -O -B research/t74-anticipatory-native-prefix/emit.py

The metadata/pin check, registered replay and optimized independent checker pass. The registered replay regenerates and compares the complete parsed payload. The independent checker imports no producer/compiler/predecessor implementation. Each provider has 128 phase-correct recipes checked on 512 columns; all four programs replay 32,768 active input columns each, and 286,720 untouched columns remain identity by footprint. Ungrouped prefixes are positive controls. All 24 rejecting semantic controls pass, with required rejection reasons, including wrong transpose convention and unclean coefficient scratch.

A read-only, Git-free optimized package export passes in 12.48s and preserves every file. Separate immutable-source, changed-receipt and occupied-output controls reject; the occupied file remains unchanged. A recompressed generated certificate is accepted by complete parsed-payload comparison. Source archives retain exact byte pins. git diff --check passes. No hosted CI, independent human review, complete native-word replay or selected cold replay is claimed.

Expected primary output:

PASS_T74_ANTICIPATORY_NATIVE_PREFIX providers=2 orientations=2 terms=64 monomials=64 scalar_bound=572 controls=24 no_new_kappa

The registered replay (with regeneration) was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about 14 seconds and left the worktree unchanged. The count checks by hand: 64 corrections come from 32 lenders, two each, so one preparation and one undo per lender gives 64 monomial applications instead of 2 x 64 = 128.

Credit

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.

Credit Cinna Davis/@1337isnot1337 (PR2226) for anticipatory borrowing and K_G; Jeremy Kothe (PR2269) for the native expansion, dual convention and T74 sources; Sagar Thakrar (PR2339) for both changed words and the initial-lowering handoff. Zhihao Chen/icekylinx and the PR425/433/531 lineage supply the retained exact Clifford compiler. Rohan Arun, Ali Romman, DreamingOfClouds and the retained supplier lineage keep their attribution. Douglas Colkitt supplies the planning ceiling engine; Jeremy Diviney (PR2360) supplies the newer whole-width boundary. Original notices and Apache-2.0 are retained. The two checking paths were written/run by the same AI-assisted contributor; no independent human checking is implied.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

The README and TASK.json give two scoped follow-ups: first screen a specified partial low-alias subset against the actual whole-helper bin stock; then, only for a survivor, bind initial reads to owners and integrate the prefix with all remaining native stages and a complete invoice. This result supplies no competitive subset and no whole-supplier admission.

Workflow feedback (optional)

The refreshed snapshot exposed PR2360 after the entry snapshot. That changed the full-inventory cost outlook while preserving the value of the already-completed finite prefix. Linking new whole-width obstructions directly from a construction's native-lowering handoff would make this distinction easier to find before broadening work.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG

[thakrarsagar]

A pointer that may help with the next step here, from #2387 and #2402 (this author). #2387 builds an actual legal fill of the full #2339 80-alias words. It reaches b = 0.00168654, which is 99.994% of a certified cap of b < 0.0016867, so the full inventory loses as #2360 says.

#2402 decomposes #2339 per register:

• The 32 low aliases lose because of the width-9 lender inventory.
• The 26 target registers whose climbs change each gain exactly one (1,1)→(2) merge. These merges alone would be worth about +2.9e-6 on the Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322 words.

If those merges come from the anticipatory initial corrections your prefix lowers, keeping the corrections without the low-lender inventory change may be the useful route. That is listed there as an open question.