[DreamingOfClouds]

Summary

Complete conditional kappa .0030814243 (+3.99e-5, +1.31% over #5551's .0030415312), tested at .0030814205, exact raw crossing in (.00308142433380, .00308142433381). Supporting word with free helper starts only: .0030768801 (+3.54e-5).

Package: research/p104-free-endpoint-retime/ (task card scalar-to-moment, recorded as scope_status: changed; the package retimes helper endpoint/stop frames of #5551's word rather than pursuing scalar A2 contractions).

What changed

A retime of helper endpoints and a collapse of 170 stops on #5551's pinned word. It is not an unchanged circuit: the scalar program (21,686 events, registers, coefficients, order) is identical, but 168 helper start spans and 23 helper final spans differ, 607 frame labels are relabelled, and 3,624 -> 3,454 MOVEs. All 208 main registers keep identical initial and final spans; productive fields (12,814) and rank-mass surplus (760) are unchanged; paid calls 69,912 -> 66,852.

The retime was found by an exact-lattice CP-SAT solve (multi-worker, not byte-reproducible), so the package ships both words plus retime.py, a stdlib checker proving each is a legal retime of #5551's pinned word. pricing*.py are #5551's pricing with literal-only changes (LITERAL-CHANGES.diff); the PR5545 local.py is used unmodified.

Conditional on

(a) the five framework assumptions retained by #5544/#5545/#5551; (b) the validity of #5551 (unreproduced at the time of writing); (c) free helper START frames and free helper FINAL frames. The verifier checks only nesting and rank = dimension gap for helpers; the canonical-start rule exists only in the #4610 verifier, and unmodified #5544 already has mid-frame helper starts and mixed finals. The supporting word needs only free starts. No independent human or proof-kernel acceptance is claimed. The selected record is not changed.

Verification

• python3 scripts/research_package.py --package research/p104-free-endpoint-retime --check-only
• verify.py --part headline and --part starts-only (each about 6 minutes): retime legality, unmodified Conditional κ = 0.00304117 (+6.0e-7 over #5544) #5545 replay/columns/native, physical caller, both moment engines, all 54 strict + 4 functional outer checks, exact crossing intervals.
• An internal AI audit (separate read-only Claude agent) reproduced an earlier Conditional κ = 0.00304117 (+6.0e-7 over #5544) #5545-based version of this retime and rated maintainer intent for free helper frames as unresolved.

Also cherry-picks the one-line wordram-ntt-kernel VERIFY.json input fix needed for onboarding tests on current main.

Credits

#5551 (thu-nmrc); #5544/#5545 (aliromman, P104 word line); #5472 (GamingPuzzled) for the free-start hand-off precedent. All predecessor credit retained.

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.

🤖 Generated with Claude Code

[DreamingOfClouds]

Clarification from an independent internal (AI) audit of this package, which re-ran verify.sh from scratch, reproduced both crossing intervals exactly, and confirmed the #5551 word and pricing hashes:

• The supporting starts-only figure should read .0030768800 (truncated). Its proved crossing is (.00307688008012, .00307688008013); ".0030768801" in the summary rounds above it. The headline claim .0030814243 (crossing (.00308142433380, .00308142433381)) is unaffected.
• Intermediate main-register frames are free under Improve complete conditional κ to 0.00304153 via coupled P104 contacts #5551's local.py/native() (only X-initial and Y-final are pinned). The paid-call drop 69,912 → 66,852 is exactly 18 calls × 170 deleted stops, and the rank-mass surplus stays 760.
• TASK.json describes the earlier audit loosely; the audit above is the one that covers this word.

[Matarener]

An independent audit of hypothesis (c), free helper start/final frames, against the #5550 P104 endpoint contract is in #5567: no new κ, CI green. The #5550 checker passes on both words of this PR.

---

Generated by Claude Code