[petalas]

Summary

A new composition of Rohan Arun's PR6399 clean native merge with Ali Romman's PR6398 mixed root passes the exact raw saving screen 0.0032868. Claim type: scoped accounting proof conditional on the retained native and caller interfaces, with an exact finite certificate. The predecessor constructions are cited premises, not audit deliverables.

 complete recursive invoice, eighteen native copies
-18 H1 + 18 H4
+18 H5
 productive histogram unchanged

The complete new invoice has 13,652 productive fields and 67,132 paid jobs, preserving rank masses 185,740 and 184,980. Its exact signed gain is 18 (1 + 4^t - 5^t) > 0 for every 0<t<1. At t=1-0.0032868, the combined margin is enclosed in (0.013061578546729933727885198969, 0.013061578546729933727885198970). The original PR6398 invoice has negative margin at this same saving. The extra scratch lifetime and 508 scalar units per native call are charged; the declared local ordinary allowance is 5,512,178, below 10,000,000.

The contribution was produced by Nick Petalas. Rohan Arun retains the clean-merge construction, Ali Romman the mixed root and original invoice, DreamingOfClouds the shared-carrier lifts, Cinna Davis and Jacob Alan Sussman the caller/productive interfaces, and zxv the interval arithmetic. Exact predecessor proofs, receipts and notices remain unchanged in retained snapshots.

Evidence and reproduction

On CPython 3.12.15, both warning-strict normal and optimized direct checks pass, taking 0.35 and 0.36 seconds respectively. Both registered commands pass. The verifier constructs every new histogram entry, checks exact interval signs and the ordinary allowance, rejects seven enumerated semantic mutations, and checks 145 exact square-root enclosure controls. RESULT.json is generated and bound to source/verifier hashes.

From the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/clean-native-mixed-root/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -O -W error -B research/clean-native-mixed-root/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/clean-native-mixed-root
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/clean-native-mixed-root --check-source-history --check-modes

Use an equivalent Python 3.12 path elsewhere. Committed bytes, modes and declared source history pass for all 14 package/input files. Official export and declared-input coverage pass. Both normal and optimized Git-free replays pass from read-only exported sources with an empty PATH; all 15 exported files, including the export receipt, retain their hashes. Actual source-byte and generated-receipt corruptions reject.

The main-based arithmetic pin is checked through Git history. Six exact external predecessor snapshots are self-contained, SHA256/Git-blob bound and attributed by commit/path/URL; the source-history preflight does not certify their external publication ancestry. No predecessor mathematical replay was used as the deliverable.

Limitations and unrun obligations

This is a favorable complete recursive invoice and a declared local ordinary-envelope calculation. It does not claim a new whole-algorithm kappa, a combined physical supplier, a selected-frontier update or a complete multiplication theorem. The combined physical/native/caller replay, new completion/compiler parameters, precision/tape validation and outer ledger are unrun. All five inherited framework assumptions remain. Independent human and formal proof-kernel review are unclaimed.

Open next questions

Bind PR6399's concrete constructor and scratch-zero checker to PR6398's eighteen-call controller, then certify the changed physical contacts, choose strict completion/compiler/outer parameters, and run the combined admission ledger below this raw screen. That is a new composition obligation. It does not require extending this raw threshold first.

Related open work

• Conditional κ = 0.003151787: clean donor-transport merge #6399 supplies the clean native replacement, priced there with nineteen native calls; this result composes its unchanged-target contract with eighteen calls.

• Mixed-query root: conditional κ = 0.00328621476572836015146308 (+4.28455% over #6375) #6398 supplies the mixed root and original source invoice; this result changes its native source and certifies one newly funded point.

• Conditional κ = 0.00315120 (+3.3e-7 over #6372): three shared-carrier input lifts #6375 supplies the shared-carrier source used by both predecessors; its construction and original tariff retain their credit.

• Conditional κ = 0.00315087 (+3.0e-7 over #6353) #6372 supplies the two-anchor contact contraction retained in that source; its endpoint is a premise here.

• Contract nine native helper outputs at conditional κ 0.00315057 #6353 supplies the earlier nine-output contraction retained in the native lineage.

• Compose native input lifts with the query tree at conditional κ 0.00314980 #6350 composes an earlier source with the old query tree; this result uses the different mixed root and later clean merge.

• Certify PR6375 matched profiles and unique relative-tariff threshold #6378 studies the PR6375 relative tariff and matched profiles; it does not deliver this combined source/root invoice.

• Independently audit PR6372 two-anchor scalar boundary and endpoint #6376 audits PR6372's earlier scalar boundary; this result makes no independent scalar-audit claim.

• Independently recount PR6353 recursive invoices and fixed-saving margin #6359 recounts the earlier PR6353 invoice; it is separate from this changed-source composition.

• Independently audit PR6353 rational joint basis and public boundary #6355 audits PR6353's rational basis and boundary; those source claims remain premises here.

• Independently check four frame1094 native matrices #6360 studies frame1094 native matrices; this package makes no new native-matrix claim.

• Prove the exact nineteen-leaf query-tree topology optimum (no κ) #6380 proves the old nineteen-leaf topology optimum; this uses PR6398's different root and does not extend that optimum.

• Prove a fixed-schedule obstruction for PR6345 helper respanning #6381 studies fixed-schedule helper respanning on PR6345; this uses PR6399's changed native word.

• Prove a paid-rank floor of 22 for three-carrier rank-two tails #6386 studies a three-carrier rank-two tail; no such merge model is used here.

• Prove exact tariffs for carriers visiting distinct entrance lines (no κ) #6388 studies tariffs for multiple required carrier lines; this composition has a different native replacement.

• Prove fixed-prefix P104 tails are optimal for every concave tariff #6394 optimizes the older fixed-prefix P104 schedule; this composition leaves that scheduling question separate.

• Reduce the concrete nonunit handoff allowance to 232 (no κ) #6392 changes a concrete nonunit helper handoff; its boundary programs are not imported here.

• Prove exact signed idle completion for overlapping stage outputs (no κ) #6391 prices a different overlapping-stage demand; this retains the published mixed-root demand.

• Reduce complete query-controller replay time by 37.88% (no κ) #6395 changes a complete historical query-controller replay's arithmetic; this uses the unchanged retained interval functions.

• Conditional κ 0.00309871 from a prepared P104 split helper #5606 studies an earlier prepared P104 split helper; it is outside this exact source/root combination.

• Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553 studies earlier P104 successor handoffs; their lineage is retained rather than repriced here.

• Add P104 flag 0 coefficient transport audit #3915 studies P104 flag-zero coefficient transport; this package does not claim that native admission coverage.

• Isolate explicit historical receipt adapters from P104 research #4103 isolates historical P104 receipt adapters; this package retains snapshots and changes no shared adapter.

• Prove the fixed five-call border needs two repair cuts (no κ) #6400 proves a repair-cut obstruction for PR6398's different five-call approximate border; it does not compute this exact mixed-root/native invoice.

• Prove exact square-zero tensor error and sharp precision (no κ) #6402 gives a square-zero ordinary tensor-error theorem; it does not establish a changed price or physical admission for this exact composition.

No additional predecessor calculations were run to compare unrelated numbers.

CI notes

Hosted run 41527070469 completed successfully at exact head 0645ec2c14669558861e8e9a1281b59643dce4ed. Both plan and replay (research/clean-native-mixed-root) passed. The completed checks were read once; run metadata confirms the successful conclusion and matching head.

The hosted replay certifies execution of the declared normal and optimized package checks. Local metadata, committed bytes/source history/modes, official export/input coverage and Git-free read-only replay also pass. This does not certify the unrun combined physical/caller/compiler/outer obligations or independent scientific acceptance.

Merge danger

Two-way door. Scope is one isolated research package; shared code and the selected result are unchanged.