[petalas]

Summary

Accelerate the complete first P104 shadow-relay fold from PR6170 while preserving its complete output word and acceptance decisions. This is an empirical tooling improvement with a scoped solver-equivalence proof, not a new kappa or supplier audit.

 solve(A, b)
-  reduce every row above and below each pivot
+  eliminate below each pivot
+  substitute backwards with the same pivot columns and zero free variables

The output word and fold construction remain DreamingOfClouds' work. Standard Gaussian elimination is background. This contribution adds the measured solver integration and its reproducible equivalence evidence.

Evidence

Proof and package.

Median complete-fold time falls from 127.86 s to 89.58 s, a 29.94% reduction, across five alternating pairs. Baseline range is 123.44 to 132.11 s; candidate range is 86.47 to 91.41 s, on the recorded shared macOS host. All ten commands succeed with zero output differences.

The generated BENCHMARK.json supplies five alternating complete-command pairs, including source authentication, both tried variants, unchanged checks and output serialization. Every run must emit the same canonical 22821-event word and FOLDED report. PROFILE.json puts 75.6 of 83.3 discovery-profile seconds in the original solver; that untimed rejected-variant profile is separate from the benchmark.

Exact reproduction from the repository root, CPython 3.12 and NumPy 2.5.4:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/p104-fold-elimination
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/p104-fold-elimination --check-source-history
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B research/p104-fold-elimination/verify.py

Both registered normal/optimized checks pass. Direct warning-strict commands take 70.89 s and 71.68 s, each checking 1234 systems, five rejection controls and both complete accepted solver variants. The registered run takes 143.68 s total. Committed bytes, executable modes and declared source-history ancestry pass for all 16 package files at 9a7f206d4e9812d2eec042aed6e40acadacd534d.

Official export/input integrity passes. Optimized replay with Git absent and all exported files read-only passes in 70.45 s; all 17 exported files retain their bytes and modes.

The package README gives the full timing command and minimal retained-source extraction. RETAINED.json identifies all 50 predecessor files by original Git blob and SHA256 at PR6170 head 445fb9124eb3fcb5d4f342c476b9ae3637f185aa; the archive is self-contained. No predecessor source is edited.

Limitations

One shared macOS host and the first H705 fold on the shipped PR6030 word are measured. Solver dimensions are capped at 4096. The retained projection and legality oracle keep their existing scope. Warning-strict controls expose unchanged tkcommon profile-loader ResourceWarnings; these are documented and not suppressed. Full rebuild timing, native/caller/compiler/precision/BIT/outer and formal-kernel checks are unrun. The five selected framework assumptions remain. Independent human and formal proof-kernel review are unclaimed.

Related open work

• Add P104 designer toolkit v2: exact pricing and legality, #6030 rebuild with fold/hoist/retain, generators, sub-circuit tools (no kappa claim) #6170 supplies the toolkit and asks for a faster fold pass; this answers one measured first-fold instance through its dominant solver cost.

• Conditional κ .003128386 (+2.582e-6 over #6030): owned registers 770, 771 and 772 descend through the frames of helpers 705, 706 and 731, which no longer relay them; helper 732 reads 771 at frame 117 #6144 supplies the root/relay descent construction underlying the fold rule; its word and kappa are not new contributions here.

• Conditional κ = 0.003128645 (+2.59e-7 over #6144): retain an operand to remove a root stop #6167 changes the later retained-operand word and paid profile; this package changes only construction-time solving.

• No new κ: exact multi-gate resynthesis removes 117 P104 events #6169 resynthesizes scalar events in another complete P104 word; this package preserves its source fold's complete output rather than claiming a new word.

• Add exact P104 ADD-coefficient fault localization (no new κ) #6175 adds exact ADD-coefficient fault localization on an earlier P104 word; this package accelerates a fold solve and computes no repair count.

• Prove exact two-channel P104 support 72 over F3 and Q (no new κ) #6173 determines joint support in the P104 root code; this solver changes no port geometry.

• Prove stable joint-bank Gram spectral obstruction (no new κ) #6181 concerns a joint-bank P104 spectral obstruction; this solver changes no Gram operator.

• Prove a sharp 1/4 error floor for contractive P104 mode deletion (no κ) #6183 concerns contractive P104 mode deletion; this solver preserves the complete output word.

• Reduce complete replay planning time by 8.27% (no new κ) #6177 accelerates replay planning, a separate command and workload; no performance gains are combined.

• Reduce current task-picker startup time by 4.66% (no new κ) #6179 accelerates task-picker startup, a separate command and workload.

• Reduce complete positive-frame replay time by 71.4% (no new κ) #6186 accelerates a positive-frame checker, a separate command and workload.

The completion refresh inspected all fifteen other open account PRs created since the advance CLAIM. None supplies a competing fold-solver result or a number for this same complete-fold workload. No extra mathematical computations were run to check other contributions.

Open next questions

• Does the same substitution help all remaining fold sites and the complete rebuild? Compare every word and acceptance status along that full path.
• Can consecutive Newton systems reuse an exact factorization? First establish a certified relation between those actual matrices.

CI notes

Both hosted checks passed at exact head 9a7f206d4e9812d2eec042aed6e40acadacd534d in run 40886077177. Plan passed in 4m23s; replay (research/p104-fold-elimination) passed in 9m27s. The completed check list was read once and both entries report pass.

Hosted replay certifies the registered normal/optimized conformance checks at this head. It does not independently certify the local performance percentage or supplier admission. All recorded local checks also passed. No code changed after these checks. Independent human and formal proof-kernel review remain unclaimed.

Merge Danger

Door: two-way.

Blast Radius: isolated. The new package is opt-in and changes no shared solver or selected frontier.