[petalas]

Summary

Finite exact circuit certificate and scoped substitution proof, produced by Nick Petalas. Coalesce owned register 770 with its existing source 791 in DreamingOfClouds' PR #6144 word. After the source's last frame-549 read, it performs the duplicate's continuation itself.

- local scalar units 189658; events 22818
+ local scalar units 189646; events 22815
- declared owned fields 29; owned lifetimes 31
+ declared owned fields 28; owned lifetimes 30

Peak live ownership remains 13. Public endpoints, all paid ranks and all productive ranks are retained. No new kappa, physical peak-space bound, supplier admission or complete multiplication theorem is claimed.

Package: research/owned770-descent-pruning/. PROOF.md gives the exact last-read substitution argument; construct.py deterministically emits the new word; RESULT.json is generated and bound to every package source. The unchanged predecessor word is retained in publication ancestry, with its original head, path, blob and SHA256 in PREDECESSOR.json.

The initial CLAIM targeted an interior descent-stage deletion, following JosieElliston's read-rerouting question in #6136. That paid-profile deletion was not obtained. The first smaller verified improvement was shipped instead. Frames 553 and 1047 remain in the coalesced trajectory. This changes owned lifetime identity, rather than replaying a predecessor census or repeating fixed-word scalar resynthesis.

Evidence

Before, INIT/COPY/SCALE created a second owned value while its source was left unread until CLEAR. After, the source is scaled in place and performs the same descent and reads. Removing one INIT, coefficient-one COPY and CLEAR saves exactly 2+8+2 = 12 scalar units.

Local CPython 3.12.15 on macOS 27.0.1 arm64 passes:

• Complete exact forward endpoint/ownership replay and a separate dense reverse replay on all 798 input columns and 636804 coefficients. All 770 arbitrary public inputs are retained; one initialized owned coordinate is deleted.
• Literal enumeration of all event prices and paid ranks; equal native frame-boundary multisets and public boundaries; nine rejected faults covering lifetime, scaling, read, descent and source-use conditions.
• Warning-strict normal and optimized direct checks, timed at 2.135 s and 1.896 s. Each registered check is below five minutes; both registered checks together pass in 4.139 s. These are timeout measurements, not a performance claim.
• PASS_REGISTERED_RESEARCH_PACKAGE; exact committed bytes and source-history preflight for all 11 files; official committed export integrity and all three declared inputs; normal and optimized Git-free export replay.

Exact reproduction from the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -I -B research/owned770-descent-pruning/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -I -O -B research/owned770-descent-pruning/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/owned770-descent-pruning
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/owned770-descent-pruning --check-source-history

A clean CPython 3.12 interpreter may replace the local path. Expected direct output is PASS_OWNED_LIFETIME_COALESCENCE columns=798 coefficients=636804 controls=9 scalar_saved=12.

Scientific base is canonical main 721c03822c421b7f7fcbb2598993b947c4d88419, priority revision 8, refreshed before publication. Consumed PR6144 word is exactly 4f3b67e7c37ae270da9584033132866d0cf63e42; its bytes are exported locally, so cold replay needs no unmerged Git object or network. The source checker is Ali Romman's unchanged main-branch PR5827 local.py. Source and mechanism credit remains with DreamingOfClouds, Ali Romman, Mason Hale, Pierre-Loic Doulcet, JosieElliston and the retained P104/native/controller/framework lineage. Last-read register coalescence is standard; the new result is this literal legal P104 substitution and its complete-word certificate.

Limitations and unrun obligations

No native operator replay, physical caller, compiler, outer ledger, rounded numerical analysis, selected cold replay, Lean or Docker run is included. No new frame pair is introduced, but actual physical placement is not re-certified. The existing caller reserve is not reduced. The five framework assumptions remain. Exact rational substitution does not establish an equal rounded error budget. Independent human and formal proof-kernel review are unclaimed.

Open next questions

• Can readers 169 and 206 be served by a different legal route that actually removes frame 553 or 1047? Preserve their other meetings and price the complete changed itinerary first.
• Can the actual caller exploit the 28-field declared inventory? Bind its aliases and lifetime schedule; unchanged peak occupancy alone does not establish a physical memory saving.
• Does a specified rounded COPY/SCALE implementation admit the substitution with no larger error budget? Bind its numerical and erasure semantics before reuse.

Related open work

• Prove a receiver-only obstruction to a root-2 stage deletion (no κ) #6163 proves a receiver-only obstruction for the separate 772/497 root-2 stage-deletion attempt on PR6144; this coalesces the 791/770 owned lifetime and leaves that path unchanged. No conflicting shared quantity is reported.
• 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 is the exact input word and owned-relay descent predecessor; this adds only last-read lifetime coalescence.
• Conditional κ = 0.003127804 (+6.67e-7 over #6143): remove the 772/731 relay #6145 gives a separate 772/731 relay descent on the [Superseded by #6144] Conditional κ .003127137 (+1.333e-6 over #6030): owned registers 770 and 771 descend through the frames of helpers 705 and 706, which no longer relay them #6143 word; no combination or numerical comparison is claimed.
• PR6030's local P104 word has no chart-only headroom in five edit classes (no new κ) #6136 supplies the read-rerouting question and studies fixed-word chart edits; this changes owned lifetime identity.
• Reduce P104 chart-127 suffix by 119 events and 2,510 scalar units (no new κ) #6133 resynthesizes a later chart-127 block on PR6030; this starts from PR6144 and changes its owned copy, without composing the edits.
• Resynthesize P104 scalar prefix: 3,577 fewer events (No new κ) #6116 resynthesizes PR6030's first scalar prefix; this is a different owned-lifetime substitution.
• Audit #6030's deferred layer and current BIT stock #6115 studies deferred-layer and BIT-stock implications; this supplies no such admission.
• Bind the merged gate-table zero_state to the selected PR6030 primary replay: 2.4x normal, 1.5x -O, identical RESULT.json (no new κ) #6112 accelerates the PR6030 primary replay; the new verifier uses only the unchanged scalar and transpose checks.
• Bind PR6030's remaining 30 strict and 4 functional outer checks to written sources; stopped-recursion theorem's 1−c term has no row (no new κ) #6110 binds outer checks to sources; this does not evaluate or alter those checks.
• Bind PR6030 uniform compiler and nine outer rows to written theorems; j=47005 is first passing grid point (no new κ) #6109 binds compiler/outer conditions; this does not evaluate or alter that compiler.
• P104 leak corrections: third-engine check of #6067/#6069 on PR6030, and a scalar-level witness on PR5907 (no new κ) #6108 studies carrier/leak corrections; this neither injects new public inputs nor changes a productive boundary.
• P104: exclude two non-carrier ADDs across helper572’s chart seam (no new kappa) #6088 excludes a two-ADD helper572 seam; this uses an unrelated source-owned last-read interval.
• P104 cut enlargements (#6064) cannot fund separately paid coordinate delivery #6083 prices cut-coordinate delivery; this introduces no new coordinate delivery or productive credit.
• P104: certify fixed-word carrier and endpoint exclusions (no new κ) #6069 studies fixed-word carrier and endpoint exclusions; this changes a separate owned trajectory's identity.
• Exclude combination-carrier correction programs on the selected P104 word (no new κ) #6067 studies combination-carrier correction programs; this performs no helper overwrite or new correction program.
• No inserted carrier correction legalizes a PR5718-shape leak class on the PR6030 P104 word (no new κ) #6045 excludes specified leak corrections; its injection model is not used here.
• Corroborating audit of PR6030: fresh full dense replay, itinerary delta, invoice and crossing (no new κ) #6043 audits PR6030; this is a new finite edit of PR6144, without claiming to audit or admit either predecessor.
• Restore research CI navigation after the PR6030 selection #6050 repairs selected-result CI navigation; that shared documentation change is outside this isolated package.
• Conditional κ 0.00309871 from a prepared P104 split helper #5606 supplies an earlier prepared split-helper word; this changes no split or public helper count.
• Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553 studies successor handoffs on an earlier P104 word; this coalesces an owned copy on PR6144.
• Isolate explicit historical receipt adapters from P104 research #4103 concerns historical receipt adapters; this authenticates a direct exported word without such an adapter.
• Add P104 flag 0 coefficient transport audit #3915 studies flag-0 coefficient transport; this introduces no new transport or flag claim.
• Research P104 singular-mixing lifetime floor #3907 studies singular-mixing lifetime floors; this is an exact owned-copy substitution with unchanged public endpoints.
• research: price full P104 end-cut correction #3894 prices an earlier end-cut correction; this has no new end-cut correction.
• Non-dense fitting B: every E8 term with x·y ≠ 0 has rank ≥ 9; square root-code floors E8 ≥ 72, P112 ≥ 64, P104 ≥ 56, D4 ≥ 12 for any fitting B (no κ claim) #3045 concerns geometric fitting-rank floors including P104; this changes no decoder or geometric rank.
• Draft construction: P104 dirty-restored gather and low-rank channel with COPY56 (no new kappa) #1972 proposes a different P104 gather/channel construction; this uses the PR6144 word and no new channel.

CI notes

CI is uncertified. At head 8fbda6f437e5baaf0ded324ec25e6be7e6cb7cc0, run 40725600911 failed plan; replay (research/owned770-descent-pruning) was skipped. The package replay did not run in CI. The onboarding suite ran 678 tests with exactly two failures and 23 skips:

• test_research_current_status.CurrentStatusTests.test_current_section_matches_selected_record expects the exact **0.003125804** marker in docs/research/current-status.md. Its bold span instead includes the rational equality, so that exact marker is absent.
• test_research_current_status.CurrentCiNavigationTests.test_current_ci_section_matches_selected_record expects make frontier6030-verify in docs/ci.md, which still describes the Raise conditional kappa to 0.00310045 with independent helper splits #5599 replay and command.

Canonical main 721c03822c421b7f7fcbb2598993b947c4d88419, the PR6030 admission commit bearing [skip ci], changed the selected record without matching these documentation expectations. This package changes neither document nor either test. The failed-job logs for PR #6120 run 40691776027 show the same two assertions and the same failure/skip counts. Open #6050 targets that shared navigation repair. Both failed-job logs were read. A maintainer must re-run CI after main is fixed. Passing local checks are not hosted CI certification.

Merge danger

Door: two-way. Blast radius: package. All changes are isolated in the new research directory; no selected-frontier or shared-code change is requested.