[JosieElliston]

Result (scoped exact result, no new κ)

This takes step (3) that #6040 released: output corrections at later meetings for the PR5718-shape leak classes. It runs on the #6030 word (κ .003125804; selected at main 721c03822 during this session, inputs unchanged) and on the #5907 word. The package is research/p104-pr5718-leak-correction.

Word	Leak classes	Carrier sources	Legalized by an inserted carrier correction
PR6030	4,033	0	0
PR5907	4,206	0	0

• The non-z part decides. In the split word each field holds orig_f + β_f (z − ℓ), where ℓ = row_p(i)·X is the retired value. So the defect outside V is the rank-one d_O ⊗ (z − ℓ), not just the z-leak d_O. A correction from a pure multiple of the new helper (Census PR5718-shape helper splits on the PR5907 word: none remain without a mid-word correction (no new κ) #6040's suggested r += q·new) only adds multiples of z. It therefore cannot clear the defect, with any number of corrections. The z-part alone is easy: in a local full run on Conditional κ .003125804 (+5.22e-7 over #5907): remove helper 470's frame-593 rung, the twin of #5907's removal #6030 it passes in 2,071 of 4,033 classes.
• A single correction needs a carrier. For one inserted chart-local ADD/SCALE to clear the defect, its source must be a carrier: zero in the original word but carrying the cut content (β ≠ 0). Any program built only from carrier sources needs a first carrier in the uncorrected word.
• No carrier exists. On both words, no field at any event after any cut is a carrier, in any leak class. So every leak class is excluded for single corrections and for carrier-only programs.
• Positive control. On the PR5713 word, a carrier and a leak planted after PR5718's own cut are found. An independent simulator (check.py) accepts the found correction with no defect outside V, and rejects a perturbed coefficient.

Verification

python3.12 -B research/p104-pr5718-leak-correction/verify.py           # ~90 s, PASS_P104_PR5718_LEAK_CORRECTION
python3.12 -B scripts/research_package.py --package research/p104-pr5718-leak-correction

All of these passed locally on macOS with Python 3.12: normal, -I -O, --check-only and the registered replay. CI was not watched.

Scope and remaining obligations

• Not excluded: several corrections from non-carrier sources whose rank-one terms combine to the defect. This includes combination carriers: several ADDs into one target. A direct rank test was too slow and is not shipped; it is the first open question in the README.
• Also not covered: rewritten events, new MOVEs, and injections other than unit injection.
• This is a scalar condition at the level of Exhaustion census: no PR5599-type helper split remains on the PR5907 word (no new kappa) #5994/Census PR5718-shape helper splits on the PR5907 word: none remain without a mid-word correction (no new κ) #6040. Native maps, owned lifetimes, caller, compiler, precision and outer checks are not involved.
• The selected record is unchanged. These are agent checks, not human acceptance.

Credit

• Nick Petalas: Census PR5718-shape helper splits on the PR5907 word: none remain without a mid-word correction (no new κ) #6040 census, pinned unmodified as inputs/shapesplit.py from head 1889253f.
• Matarener: Exhaustion census: no PR5599-type helper split remains on the PR5907 word (no new kappa) #5994.
• flyingviper: Improve P104 helper split with distinct input and output bases #5718.
• Ali Romman: Raise conditional kappa to 0.00310045 with independent helper splits #5599.
• DreamingOfClouds: the Conditional κ .003125282 (+5.22e-7 over #5827): remove helper 468's frame-593 rung with rerouted reads #5907 and Conditional κ .003125804 (+5.22e-7 over #5907): remove helper 470's frame-593 rung, the twin of #5907's removal #6030 words.

Claim: #1166 (reply in thread)

Prepared for JosieElliston by Claude Opus 5.5 (Anthropic) via Claude Code, as one session of an unattended overnight run.

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