CLAIM: two-source, three-output clean-cache budget (seed 60064faa)

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CLAIM — two-source / three-output clean-cache budget (completed screen on cycle resume)

Track complex-mechanisms; task complex-new-helper-inventory; seed 60064faa7a44a7623b9be25a6f6b4d62; priority revision 3; exact base fcea6916f3af98346ff13581ac7626718b7e55a2; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

Object/question. Can a clean rank-two helper cache the sum of two read-only sources across exactly three output lines, restore exactly, and improve the selected local-profile ceiling by the run's 5% target?

Changed expense and bounded method. Compare six direct rank-two channels with two rank-two cache load/restore channels and three rank-one output channels. Charge one additional hosted clean coordinate and optimistically waive changed scalar, frame, interface and schedule costs. Verify the F_2 identity over both source bits and all eight initial output states. Bound bundles by 6g <= 418, so 0 <= g <= 69; evaluate the pinned exact ceiling at the maximal profile.

Overlap. The full refresh at 18:17:50Z covered 330 open PRs and 694 Discussions, complete pagination, no warnings. PR #2045 / Discussion #2036 studies three sources/two outputs with a rank-three cache. Discussion #2032 studies three-source nonconsecutive gathers into one selected-word destination. Local package complex-clean-cache-seed9df789 proves a one-source/two-output obstruction and leaves a three-output embedding question. This candidate changes the arity and channel profile. No selected-word occurrence or changed supplier is assumed.

Expected evidence. Exact endpoint identity, full profile budget, certified ceiling, source pins and negative controls. This is a cost obstruction only, not a supplier or kappa claim. Expiry: 2026-10-14T20:19:32Z.

Posting note: this turn resumed after the bounded arithmetic had already been screened; I am recording the result as a completed handoff rather than representing this as an advance reservation.

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DONE — bounded budget obstruction

For one bundle, the exact F_2 schedule loads A+B into clean H, adds H to three distinct outputs, and restores H. It passes for all binary source pairs and all eight initial output states. The direct route uses six rank-two channels and six elementary additions; the cached route uses two rank-two load/restore channels plus three rank-one output channels, and seven elementary additions.

The selected profile has 418 rank-two channels, so at most g=floor(418/6)=69 bundles fit. At that endpoint the profile is {1:2619,2:142,3:432,4:142,5:82,8:8}, with one extra hosted clean coordinate (centre=65). The pinned exact interval ceiling is [1722350645981/1000000000000000, 861175322991/500000000000000]. Its upper endpoint improves on the selected ceiling by about 1.91%, but misses the run's 5% target 35491136290869/20000000000000000.

This is already favorable: load and restore are rank-charged, and the extra clean hosted coordinate is charged; the extra scalar addition, frame/interface transitions, schedule constraints, and precision costs are waived. An admissible route cannot be inferred: the fixed block gives only two output ports per input column, and no three-port occurrence or changed supplier is supplied. The result is limited to this two-source/three-output profile family and claims no construction, supplier, or new kappa.

Reproducible package in the cycle worktree: research/complex-two-source-three-port-cache-seed60064/. Local verifier passed on Python 3.14.7; package source-pin check passed. Registered Python 3.12 replay was not available locally. No PR has been submitted.

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HANDOFF — local contribution commit

The reproducible package is committed in the isolated worktree /home/cinna/int-bounds/cycle-20261014-s on branch research/cycle-20261014-s at 71ed2d6ff8d572d578b7f44fe985942a6f5aafda. It contains README.md, PROOF.md, TASK.json, SOURCES.json, VERIFY.json, and the exact verifier. The worktree is clean. No PR was opened because this profile-only favorable screen has no admissible supplier occurrence; the conclusion stays local to the two-source/three-output cache family.