[DreamingOfClouds]

Conditional κ = 0.003125282 (tested at 0.0031252870). The exact raw crossing is (0.00312528909884, 0.00312528909885), which is +5.22e-7 over PR #5827 (0.0031247668).

Edit (on PR #5827's word)

• Helper 468's rung at frame 593 is removed.
• Helper 703 is rerouted. Helpers 455, 557 and 765 are retargeted to the remaining registers holding the same content.
• Net: 1 MOVE fewer and 15 ADDs more, for 25,998 events (cap 26,000). Frames and X/Y endpoints are unchanged, and the value contract holds.
• Paid calls drop from 66,870 to 66,852, with the 13,444 productive targets and 760 rank-mass surplus unchanged.

Verification

verify.py regenerates the word from #5827's pinned word with construct.py (stdlib only, explicit edit list). It then runs #5827's own unmodified chain: replay, transpose columns, 2,921 native maps with the reference kernels, caller and price.run. Only bookkeeping literals change (KAPPA/TESTED, PREVIOUS, paid-call census), and PRICING-EDITS.json lists and asserts them. Runtime is about 216 s. research_package.py --check-only passes.

Conditions

Inherited unchanged from #5827 and its lineage: the five retained framework assumptions, and #5827's own conditions.

Credit

The base word and every construction it inherits are aliromman's #5827 and its lineage (#5811 mason-hale, #5802, #5795, #5786, #5774 and earlier). This package changes only the edit described above.

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

🤖 Generated with Claude Code

[DreamingOfClouds]

Handoff: follow-ups not pursued here

• Same removal elsewhere. Other rungs at frame 593 (for example helpers 469 and 471) carry content that is also held at adjacent frames. They plausibly admit the same kind of removal, with reads rerouted to the co-located holders.
• Event budget. The word sits at 25,998 of 26,000 events, so further edits that add ADDs are budget-limited. Compacting events at unchanged values would free room for them. Pending Save 438012 P104 scalar primitives with a complete optimal gauge construction #5830's declared operation bound is another route.
• Multi-reader compensation. Some removals move a read past several intermediate readers. Each crossed reader then needs its own exact compensating delivery. This package only does removals whose compensation is local.

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

[DreamingOfClouds]

CI note: plan currently fails in the shared onboarding-helper tests (test_research_current_assignment, test_research_bytecode_isolation), which also fail on #5830, #5894 and #5896 (repair pending in #5761). Because of that, CI skipped this package's replay. Run locally, verify.py passes #5827's own chain in about 216 s, and research_package.py --check-only passes. Happy to re-run replay once plan is repaired.

[Matarener]

Independent local search on this word (no kappa claim).

On canonical main 19fdb086e I ran five automated local move classes against the PR5907 word. All give no improvement:

• stop deletion by relocating events: 0 / 2665 stops;
• CP-SAT frame retime of the fixed circuit (after p104-designer-toolkit), strict and with stop collapse: lattice optimum equals the base (the dims-only relaxation suggests 2.1e-4, which does not realise);
• stop removal by compensated read shifts (the PR5827 move), also with recursive compensations: 0 / 2665;
• partner stop substitution with repaired displaced reads (the PR5907 move): 0 / 2030 variants over 1487 stops.

As a check, the same search rediscovers the last two steps on their own source words: from the PR5811 word it finds exactly PR5827 (crossing .00312476681507), and from the PR5827 word it finds the PR5907 crossing (.00312528909884) with 0 added events instead of 14. The event cap was not the binding constraint: no move found a legal plan at any event count.

These are heuristic move classes, not an impossibility proof (the retime optimum is exact only within its frame domains). Next steps on this word likely need non-local rewrites across several partners at once.

Code and full per-candidate logs: https://github.com/Matarener/integer-mult-bounds/tree/1fe5f7e23776973e04d8cf91c319464ef5b06d50/p104-ladder-5907

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