Conditional κ = 0.001730809033576552081734 (+1.458e-7 over #3945): three staged helper entries and an LP-exact T360 fill

[rohanarun]

Author-checked conditional candidate; not maintainer-reviewed. This stages three more helpers on #3945's staged544 words and builds a new literal T360 owner fill.

Result. The new complete moment root lies in [0.001730809033576552081734, 0.001730809033576552081735], so

κ = 0.001730809033576552081734 − 10⁻⁴⁶ − 10⁻⁷⁰

That is +1.458·10⁻⁷ over #3945 (+0.0084%). It inherits #3945's source, hosting, analytic and multiplication-model hypotheses.

	#3945	this PR
local profile per call	{1:2482, 2:712, 3:218, 4:109, 5:20, 8:8}	{1:2488, 2:714, 3:223, 4:102, 5:20, 8:8}
helper widths 5/6/7/8/9	28 / 18 / 53 / 96 / 213	28 / 18 / 56 / 93 / 213
owner idle	{3:23328, 5:4320, 48:137952}	{3:22842, 5:1890, 48:138438}
root lower bound	0.001730663236534549309146	0.001730809033576552081734

Construction.

• Words. Helpers 608, 609 and 600 each get one extra entrance dimension, lose four early ¼-weight reads, and gain two exact releases after a common cut. This follows Research: census of staged entries on PR3734's other helpers; none found that pays (no new κ) #3949's staged-entry construction, extended so releases can land in other helpers. Each of the three narrows from width 8 to width 7.
• Frames and cleanup. The exact frame optimum is written back into A/B/restore, and cleanup is re-derived literally. Source-guarded literal records under recipe/ replay without any solver.
• Owner fill. A new literal T360 owner fill moves 70,876 of Raise conditional staged544 κ by filling idle owner slots #3945's 1,321,920 roles (owner/MOVES.json.gz) and reaches the window-free pattern-LP optimum for the narrowed inventory.

Replay (Python 3.12, standard library only):

python3.12 -B scripts/research_package.py --package research/staged544-triple-entry-fill

That gives PASS_REGISTERED_RESEARCH_PACKAGE, with all registered commands passing:

• word reconstruction and arbitrary-dirty semantics;
• an independent GF(2) frame ledger, with 10 controls;
• the exact rational root, with 4 controls;
• a full owner audit of every role in both fills, with 7 controls;
• byte-equal fill regeneration;
• recipe controls in both normal and optimized Python.

Fresh five-stage native runs pass for both changed words. The root bracket was also re-checked with a second, independent rational engine.

Admission status (stated plainly). admission/full_replay.py rebuilds #3945's closure plus the six staged-entry files and runs the inherited admission engine end to end. Every stage through the outer ledger and the independent outer check passed. The final release stage is still pending. It was still running when this was submitted, and it needs at least 8 GB of RAM with --jobs 1. admission/authenticate.py is therefore not in VERIFY.json yet.

Credit.

• Staged-entry mechanism: Ross Richardson (Reduce helpers 644/660 from width 8 to 7; conditional κ > 0.00173 #3605) and dataisfire (Stage helper544 after a returning producer excursion; improve conditional kappa #3734).
• Census and assembler: ChaloupeMusic / Erwan Secousses (Research: census of staged entries on PR3734's other helpers; none found that pays (no new κ) #3949).
• T360 clock and fill: Research: certify the staged544 packing ceiling and reach it on PR3734's T360 clock (no new κ; same value as #3802) #3815, with Match the staged-width conditional κ frontier with a smaller T360 allocation #3638 lineage.
• Terminal-width-5 words, owner walk, frame walker, root enclosures, native runner and admission adaptation: Dugongue (Raise conditional staged544 κ by filling idle owner slots #3945).
• Exact frame solver: Marius-Paul Dumitrean.
• Audit core: Sagar Thakrar (Independent verification: PR3605's staged 644/660 words pass an exact audit against the PR3133 control (no κ claim) #3687) and roger-sato (Audit complete retimed and delayed supplier words #3693).
• Comparison claim: zxv (Consume retimed staged releases with smaller T360 stock #3682).
• Independent audits of Raise conditional staged544 κ by filling idle owner slots #3945 (Independently audit staged544 terminal-to-owner cost bridge #3969, Audit staged544 native phases and expose the binary-inverse lift defect #3987, Research: certify staged544 internal-error reserves and arbitrary-dirty restoration #3994) were read.

NOTICE.md has the full lineage.

Open next questions.

• A fourth 8→7 entry loses about 9.06·10⁻⁸. Could a staged entry that narrows a width-9 or width-7 helper pay instead?
• Are there more release triads like 608/609/610? Swapping 600 for a 608-type helper would give roughly +1.74·10⁻⁷.
• Is there a smaller move set or a clock change that admits a cheaper narrowing schedule?

Prepared by Rohan Arun with Anthropic Claude assistance.

🤖 Generated with Claude Code

https://claude.ai/code/session_01F5n4jqR72j3QDY71gGBVb1

[tekuuu]

CLAIM — adversarial audit, seed69; base bb4bccb. I am auditing the three delayed-entry rewrites at exact head9744f9df268590295a9872b1952c695a678192b9. Method: a new no-import exact free-operator implementation will isolate the pre-cleanup defect, check whether the three edits compose without cross terms, and verify projected dirty-helper cleanup. This differs from the existing binary-frame ledger and retained audit_core endpoint replay. Deliverable: sparse defect witnesses and a scoped composition argument, or an explicit counterexample; no owner, native-phase or kappa admission. Expected finish16:25UTC. Tekalign (tekuuu), with substantial OpenAI Codex assistance; predecessor credit retained.

DONE / RELEASED — PR4087, exact head a96431e. Both actual providers have the same rank-two register-coefficient defect before cleanup: delta417=(h608+h609)/2, delta565=h600/2, delta602=−h600, delta610=−h608−h609; every other row is zero. All8 algebraic subsets/provider compose without cross terms, realize y←y+x, and return all91 arbitrary dirty buffers. The physical D-dimensional defect rank is2D, not2; no physical sharing or kappa admission is inferred. A new no-import rational free-group implementation, six complete noncommuting matrix-oracle assignments,24 regenerated-cleanup semantic mutants,4 source mutants and6 algebra controls pass. Official16-file committed bytes/history and export/check pass; all3 commands pass normally/-O from a read-only Git-free export with17 files unchanged. Source/publication ancestry are distinguished explicitly. New4085 receiver sharing remains outside scope. Next useful task: validate an actual new coupled release with this boundary test before pricing frames/owners/numerical costs. All claims released. Hosted CI is separate from the completed local checks; exact status is on PR4087. Predecessor/AI credit retained in the package.