Scoped negative result: no further helper-donor kernels or exact read re-timings on the #1297/#1305/#1324 words (no new kappa)

[mdumitrean]

Summary

Scoped negative result, no new κ. Revision 2 (9e944899) adds a rigorous true-moment bound and narrows the optimality wording, in answer to the review continuation point; details are below. Revision 3 (c9da5f27) follows #1186's portable revision 3 (c37dfb07), so regenerate.py keeps working if #1186 merges as is; the evidence is unchanged.

The census runs on #1297's two local words. #1305, #1324 and #1319's T74 exact fill use the same Git blobs. #1305 and #1324 were later withdrawn by their author, because their idle overlays move axes across Z4 families. Kernels in richer families were later found on these words: #1625 (pivot 566) and #1672 (pivot 554). Both lie outside the two families searched here.

On those words, two kernel families give no further gain over all 306 helper pivots read before their first B write, where #1297 searched four:

• Conditional κ = 0.001676070884699375: exact helper-donor cold kernel for pivot 531 on the global mixed X54 fusions word #1274/Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels #1297's two-shock helper-donor kernels, with both restoration rules;
• exact re-timing of early reads.

Every neutral candidate is surrogate-optimal with a certificate, and none can lower the per-call moment at b by more than 1e-6 cost units (rigorous). #1305's idle overlay is the exact optimum of the donor-star class its own verifier admits; that is now a statement about a withdrawn class.

Package: research/frontier1305-kernel-census/. Claim and results: discussion #1314.

Starting point, validated locally (before the withdrawals)

• Conditional κ = 0.001677380107853623: idle rank-48 axis reassignments with simultaneous swaps toward rank 51 on #1305's four cold kernels #1324 @ 43c19465: a fresh checkout ran verify.py, including fresh native replays of both words and strict admission. Result: PASS_GLOBAL_MIXED_X54_IDLE_EXCHANGES_NATIVE_AND_STRICT_ADMISSION 0.001677380107853623 (156 s, no Boost).
• Conditional κ = 0.001677162029073474: four helper-donor cold kernels (pivots 531, 543, 555, 567) composed with multi-donor idle exchanges toward rank 51 #1305 @ a96a5d95: the same run gives ... 0.001677162029073474 (127 s).
• The Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186 kappa.kappa(H, 37) pricer reproduces both κ values, and Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels #1297's, exactly from their profiles.

Results (identical on both words)

Pricing uses #1186's harness, pinned at revision 3 (c37dfb07; its pricing code is revision 2's, 3855fd41):

• the auditor's static rules;
• an exact program-map screen;
• an unchanged derived compensation;
• recomputed cone caps, tail-mutable frames and cut equality;
• the surrogate optimum certified by integer duality;
• audit_local on every negative delta;
• a true-moment interval certificate for every priced candidate.

Family	Candidates	Neutral (Δ = 0)	Frame-infeasible	Inexact	Gains
#1297 relation rule, restore at end of early cleanup	61 (25 pivots)	32	8	21	0
Same relation, restore just before the pivot's first write (exact by construction)	292 (43 pivots)	52	240	0	0
Exact early-read re-timings within the target's suffix segment (152 pivots)	803	635	168	0	0

• True-moment bound (revision 2): this covers all 1,438 neutral candidates, both words:

  • the realized true delta is exactly 0, because the paid profile is unchanged;
  • no candidate can lower the per-call moment at b below the base word's frames by more than 1e-6 units, where one unit is 2^-40 of that moment. The exact rational bounds are about 1e-11 and are rounded up.

  Infeasible and inexact rows involve no cost. Every verdict, delta and profile equals revision 1's.

• Positive control: on Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels #1297's input word, the census reproduces its 5+5 hooks for pivots 555/567, including the committed donors 620/628. Each is priced at −11,707 surrogate units (H1 −3, H3 +1), the realized kernel worth 2.616e-7 κ. Its true value is −11,707.88 units, a certified gain, and audit_local passes all ten.

• Robustness: all base-word verdicts and profiles are identical at Conditional κ = 0.001677380107853623: idle rank-48 axis reassignments with simultaneous swaps toward rank 51 on #1305's four cold kernels #1324's endpoint weights.

• Idle: exact backtracking over every assignment in all 3,687 (replica, port) groups gives the optimum, and it equals 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 selection. No size-4 group admits a three-receiver donor in that class. Conditional κ = 0.001677380107853623: idle rank-48 axis reassignments with simultaneous swaps toward rank 51 on #1305's four cold kernels #1324's simultaneous swaps are the larger class that does reach (51,51,51,39).

• Deletion screen: prices the word with a pivot's early reads deleted and no compensation. The largest prices are pivots 439/444 (−67,944), 438/440 (−62,316) and ten pivots at −51,648 (≈ +1.16e-6 κ). This is reported as a screen, not a bound: on the control word the uncompensated deletion of 555/567 is frame-infeasible, while the kernels are feasible and gain.

Evidence and reproduction

• python3 -B research/frontier1305-kernel-census/verify.py: standard library, ~30 s. It checks the input pins, replays all five censuses exactly in rational arithmetic, binds every priced record to exactly one census match, and recounts all evidence against RESULT.json. It also checks every candidate's true-moment bound against RESULT.json and runs the positive control. It rejects five failure controls: a one-byte input change, a changed early-read coefficient, a forged negative price, a priced edit absent from the census, and a forged bound. It is a recount: it does not rerun the frame optimization or the interval certificates. Registered: PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=negative-result under Python 3.12.13. tests/test_research_*.py passes (20 tests, 1 skipped).
• regenerate.py --toolkit <PR #1186 at c37dfb07>/research/exact-frame-toolkit --out NEW reruns pricing, re-timing and deletion; with --idle-run it also reruns the idle check. It first checks the toolkit's pinned MANIFEST.json and every file that manifest lists. Two consecutive revision-2 runs reproduced all 15 toolkit-dependent evidence files byte for byte, in about 9 minutes each on 12 workers. Against revision 1's evidence, 8 files are byte-identical and the other 7 differ only by the added bound fields.
• Revision 3: regenerate.py now pins Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186 revision 3's MANIFEST.json. deletion.py used the harness's private SIGALRM handler, which revision 3 replaced with compat.deadline; it now uses the toolkit's compat.deadline and Timeout. verify.py and regenerate.py now refuse to run under -O; before, verify.py's guard was itself an assert, which -O strips, and regenerate.py had none. A fresh regeneration with revision 3, including the idle check, reproduced all 16 evidence files byte for byte (about 8 minutes on 12 workers). RESULT.json changes only in its toolkit pin.

Limitations

• These are finite searched families on two fixed words in Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186's frame model, at the stated b. The surrogate optimum is certified and true gains are bounded by 1e-6 units; exact true-moment optimality is not claimed.
• Not covered:
  • compensations with three or more shocks;
  • window donors on helper readers;
  • cleanup-side corrections;
  • other words, owner maps or hosting.
• Nothing is admitted, so no native or strict replay of candidates was needed or run.
• The idle statement holds only inside 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 verify_idle_overlay.py class.
• The pricing scripts need Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186's toolkit (open PR); verify.py does not.

Open next question

Do three-shock or window-donor relations exist for the high-screen pivots, 438/440 and the ten −51,648 pivots? #1625 and #1672 have since found kernels in such richer families, at pivots 566 and 554.

• First step: extend census.py's dictionary to windows x += c·q … x −= c·q on any register x, closing before the first write. Solve sparse dyadic combinations of at most three terms, then price with price.py.
• Blocker: about 2,500 distinct suffix vectors per pivot, so the search needs support-guided pruning.

Credit

• rohanarun: Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels #1297 words, relation rule and edit format (search_relations.py).
• Jeremy Kothe: Conditional κ = 0.001676070884699375: exact helper-donor cold kernel for pivot 531 on the global mixed X54 fusions word #1274 helper-donor mechanism; Conditional κ = 0.001677162029073474: four helper-donor cold kernels (pivots 531, 543, 555, 567) composed with multi-donor idle exchanges toward rank 51 #1305/Conditional κ = 0.001677380107853623: idle rank-48 axis reassignments with simultaneous swaps toward rank 51 on #1305's four cold kernels #1324 idle compositions and strict packages.
• Gonzalo-Mier: Idle pair exchanges improve the #1094 κ candidate #1252 idle exchanges and verifier.
• The Conditional kappa 0.001675809683500501: global mixed allocation with X54 and fusions #1218/Conditional κ = 0.001675809683500501: mixed T37 allocation with X54 and fusions #1193/Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148/Conditional κ = 0.001675658002271934: two source-holder fusions on #1148's joint-entrance k8 word #1195 lineage.
• Wronskode: Research: X54 mixed-T37 saturation — exhaustive local sweeps, exact Φ packing invariant and width/Φ prices (no new kappa) #1288 saturation sweeps on the Conditional kappa 0.001675809683500501: global mixed allocation with X54 and fusions #1218 words.
• PatatePatatePatate: Research: exact ceiling for #1094 idle rank-48 repartitions, #1252 recount and star-move lead (no new kappa) #1276 idle ceiling on Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges #1094.
• Pricing harness: Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186.

Vendored inputs are unmodified Apache-2.0 copies; see NOTICE.md and inputs/PINS.json.

Prepared by Marius-Paul Dumitrean with substantial AI assistance (Anthropic Claude, via Claude Code). Apache-2.0.

Workflow note (optional feedback): this used the selected-packing card with the scope changed to local-word kernels on the highest open claim. The main friction was that the frontier moved during the session: #1324 landed with the same words, which was easy to check with blob ids. One suggestion: the overlap helper could list open PRs that share Git blobs with a package's inputs.

[mdumitrean]

Note: #1305 and #1324, cited in this PR as the frontier, were withdrawn by their author (invalid idle overlay). The census is unaffected, because the current top open claims #1319 and #1377 use the same #1297 words byte-identically. Correction and details: #1314 (reply in thread)

[Mister-Meeseeks]

100-PR batch review at abd7384d9a5e35048723512ae70d970909ffd522.

This remains open after scoped triage. Next review step: Finite census replay and controls pass, but the claim of exactly moment-optimal frames inherits PR1186 rounded integer costs. Supply a rigorous rounding/separation bound or narrow the optimality claim to that integer objective; the submitted verifier does not regenerate all priced optimization evidence.

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.

[mdumitrean]

Revision 2 is pushed (9e944899) for the continuation point above. It supplies the rigorous separation bound and narrows
the wording.

Bound. Every census and re-timing candidate is re-priced with #1186 revision 2's true-moment interval certificate
(3855fd41; see #1186 for the method).

• Lower end: a chain-dual (or exact-elimination) bound with outward-floored weights floor(2^224·(lo_r − λr)), computed
  in Python integers, plus λ·(rank mass).
• Upper end: the engines' upper bound of the base word's frames.

Results at b = 0.001679979627113687, both words:

Family (per word)	Neutral candidates	Realized true delta	Largest possible true gain
two-shock, restore in tail	32	exactly 0	≤ 1e-6 units
two-shock, restore before first write	52	exactly 0	≤ 1e-6 units
early-read re-timings	635	exactly 0	≤ 1e-6 units

One unit is 2^-40 of the per-call moment. The exact rational bounds are about 1e-11 and are stored rounded up to the 1e-6
grid, so the evidence does not depend on the platform. Infeasible and inexact rows involve no cost: there is no legal frame
assignment, or the map differs over Q. Every verdict, delta and profile is identical to revision 1. Positive control:
−11,707 surrogate units, −11,707.88 true units, a certified gain, and audit_local passes all ten hook words.

Wording. "Exactly optimal" now reads "surrogate-optimal (integer certificate) with true gains at b bounded by 1e-6
units". Exact true-moment optimality is listed as not established. The text also records the withdrawal of #1305/#1324 and
the later pivot-566/554 kernels (#1625, #1672) on these words, which lie outside the two searched families.

Coverage. verify.py's docstring and VERIFY.json now say it is a recount. It binds and recounts the stored evidence,
including every candidate's bound against RESULT.json, and adds a forged-bound control (5 controls rejected). It does not
rerun the optimization. regenerate.py reruns all prices and re-timings with the toolkit, after checking the toolkit's
pinned MANIFEST.json and every file it lists.

• Two consecutive runs reproduced all 15 toolkit-dependent evidence files byte for byte, in about 9 minutes each on 12
  workers.
• Against revision 1, 8 files are identical and 7 differ only by the added bound fields.

Registered check: PASS_REGISTERED_RESEARCH_PACKAGE research/frontier1305-kernel-census outcome=negative-result under
Python 3.12.13.

Prepared with substantial AI assistance (Claude Code).