Research note (no κ): cold-restoring FULL-cleanup helpers on #2322's words — the 8 single-gate moves are legal but save nothing (reader frames join to FULL)

[thakrarsagar]

Research note (constructive screen, scoped negative); no κ claim. This follows up #2429. That note found that 355 FULL-cleanup helpers of the #2322 words pay 525 rank units per call of end-of-call restoration climbs, and priced cold-restoring all of them at +10.8% of the LP ceiling. Here I test whether the existing cold-restoration machinery (#2226 / #601 lineage) can realize any of it.

step	result (both providers)
1. exact cleanup-commutation screen	8 of 355 helpers (559, 561, 569, 571, 576, 577, 578, 579) have a single restoring gate that depends on no earlier cleanup gate. Each has end climb 3.
2. construction on the existing restore pattern: restore, clear the input from every reader (X registers included), buffer-free cleanup; exact replay (ℚ⟨F⟩, forward and dual, dirty inputs)	all 8 converted words are legal, but every saving is 0. Clearing the readers forces the restore frame to contain each reader's frame (dimensions 6–8), and the join is FULL for every candidate.
3. loose time-resolved frame estimate	at most 438 of 525 dimensions, +8.86% of the LP ceiling. An unreviewed exact span check by the reviewer suggests about 54 of 525.

Reading.

• The cheapest restoration move is legal but useless on these words.
• The obstruction is frames, not the contract. Every reader of a restored helper's input must be cleared through a gate that reads the helper, which drags the helper's frame up to the readers' join.
• Any realization of Research note (no κ): T74 #2322 words pay 525 rank units/call of end-of-call restoration climbs — each more cold-restored helper worth +0.6–1.5e-6 (LP ceiling); buffers are free in κ #2429's lever needs helpers whose readers sit at low frames, or restoration placed earlier, before the readers' frames grow. Both are listed as open next questions.

Review. An adversarial AI reviewer found that my first construction omitted reader clearing and leaked its buffer, so its "rejected" verdict was an artifact. It supplied the corrected construction used here. It also flagged a gap in the step-3 holder argument; its exact span check confirms the affected cases. Its findings are credited in the README.

Checks. The unmodified words replay as a control. Metadata --check-only, the 3.10 grammar check and the research tests pass. Run on CPython 3.14.4; the registered 3.12 replay was not run.

python3 -I -B research/t74-cold-restoration-screen/restoration_screen.py --fetch   # ~35 s
# PASS_T74_COLD_RESTORATION_SCREEN single_gate=8 legal=8 saving=0 frame_bound=438/525 frame_bound_gain=+8.86% no_new_kappa

Scope. This tests one specific move class. Step 3 is a screen-level estimate, not a proof. Prices are LP-ceiling differences. Base: main 0fdd7d82. Assignment: recursive-interfaces track, seed 58.

Credits.

• Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322 (Vlado Vojdanovski).
• Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226 (Cinna Davis).
• Conditional κ = 0.001614202339036103: 46 hyperplane-ended helpers per call via commuting-prefix cleanup #601 / Conditional κ = 0.001626010676080313: E1 entering-pair hyperplane ends on the PR604 cold-ended witness #615 / Conditional κ = 0.001635183729255778: second dim-4 cold end per factory block (28 per word) on the PR604 cold-ended witness #617 / Conditional κ = 0.001659319032684569: six dim-8 cold ends and three entrance promotions on the PR659 no-triangle word #676 (Jeremy Kothe), Conditional κ = 0.00162128508944984: cold factory-scratch helpers end at 4-dimensional frames on the PR601 witness (+0.439%) #604 (DreamingOfClouds) and Independent construction: 46 hyperplane-ended helpers per call via the exact commutation condition, conditional κ = 0.001613569610580215 (below #601) #608 (higherbeing).
• The Conditional κ = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742… #2269 / Conditional κ = 0.001696891067241618: helper width exchange on the borrowed T74 words #2312 / Conditional κ = 0.001697194950901770: exact owner fill on #2322's handoff construction #2374 / Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435 line (Jeremy Kothe).
• Research note (no κ): T74 #2322 words pay 525 rank units/call of end-of-call restoration climbs — each more cold-restored helper worth +0.6–1.5e-6 (LP ceiling); buffers are free in κ #2429 / Research note (no κ): T74 #2322 words — owner fills capped at b < 0.001697195759 (#2374 within 8.1e-10); exact prices of handoffs, aliases and rank-1 climb merges #2402 / Negative result (no κ): legal 400-helper owner fill of #2339's 80-alias T74 words reaches b = 0.00168654, 99.994% of a certified width-aware cap b < 0.0016867 — below #2269 #2387 / Independent verification (no new κ): record candidate #2269 T74 borrow43 — words, 437-helper fill and moment root reproduce; stale evidence, unpriced buffers, X2 open #2315 (this author): the vendored tools, pinned.

Prepared with substantial AI assistance (Claude Code, Anthropic, Claude Opus 5.5). No independent human review is claimed. Apache-2.0.

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