Tooling: exact helper-donor cold-kernel search — rediscovers #1297's kernels, census on #1305/#1324 words (no new kappa)

[Wronskode]

Adds research/helper-donor-kernel-search/, the first published search tool for the helper-donor cold-kernel mechanism. That mechanism was introduced by #1274 (pivot 531) and extended by #1286/#1297; it is the largest local gain on the X54 line. No new κ.

How the search works

For every write p += k·Y that has earlier reads of p, the tool:

• deletes a subset of those early reads;
• cancels p through Y at a cut, with an early-cleanup tail restore;
• computes the exact program-map change D mod 2³¹−19;
• solves a single-donor relation q·v_hook = −D with dyadic q;
• prices each candidate exactly with Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186's frame solver.

Results

• Positive control. On Conditional kappa 0.001675809683500501: global mixed allocation with X54 and fusions #1218's word (no kernel yet), the tool rediscovers Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels #1297's pivot-555 kernel exactly: delete reads 466/502/734, donor 620 with coefficient 2 at hook 112, cost −11,676, profile H1 −3, H3 +1. It also finds the five equivalent donor hooks.
• Census. On Conditional κ = 0.001677162029073474: four helper-donor cold kernels (pivots 531, 543, 555, 567) composed with multi-donor idle exchanges toward rank 51 #1305's final words, which Conditional κ = 0.001677380107853623: idle rank-48 axis reassignments with simultaneous swaps toward rank 51 on #1305's four cold kernels #1324 (the current best claim) uses unchanged, I searched every register and write: 1,048 write instances per word, both words. No further single-donor kernel exists. Further local gains need two-donor relations or other cancel forms; see Open next questions.
• Negative control. The already-applied pivot 555 gives no gain.

Reproduce

python3 -B research/helper-donor-kernel-search/verify.py --toolkit <PR1186>/research/exact-frame-toolkit   # ~1 min

Output: PASS_HELPER_DONOR_KERNEL_SEARCH_CONTROLS. Inputs are vendored and pinned: #1305 a96a5d95 and #1218 0aa14797.

A candidate the tool finds is nomination data, not an admitted construction. All inherited conditions remain.

Credit: #1274 (Jeremy Kothe), #1286/#1297 (Rohan Arun), #1186 (Marius-Paul Dumitrean), #1305/#1324 (jeremykothe2). Prepared by Wronskode with substantial AI assistance (Claude Code). Apache-2.0.

🤖 Generated with Claude Code

[Mister-Meeseeks]

100-PR batch review at a668059ec7df16192e91e02b33616d64b52f6e72.

This remains open after scoped triage. Next review step: The submitted head a668059 omits evidence/SWEEP-K4-BASE.log required by verify.py. Supply the evidence files or make the declared replay regenerate and validate them; then review the inherited rounded-cost scope separately.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.