Research: legal H6 compensation networks and cost screen (no new kappa)

[RossRichardson]

Current-main revision: integration with 67b122d33d6c599a49f65d50afa2f3fe8d790d02 preserves the original scientific pins and artifacts. The live selected record gained proof-supplement metadata, so the CI wrapper now reads only that historical price benchmark from its already pinned Git object and verifies its unchanged digest in the private export. All other 89 input pins remain strict against the checkout. The workflow separately verifies the live selected record, and six regression controls cover the boundary. The wrapper records both benchmark digests; it does not rewrite either input or reprice the result.

The H6 proposal gives a conditional helper budget but leaves compensation loading, frame chronology and dirty restoration open. This PR supplies a finite local word and its cost screen: complete compressed edge and address-bucket networks with legal [1,15,1] helper paths, arbitrary logical dirt restoration in both orientations, and an explicit 816-center K encoder. The bucket word uses 227,312,640 helpers, exceeding the largest allowance among tested L3/5/7 profiles (94,434 at L5). No new kappa or supplier admission is claimed.

This continues the H6 exchange in Discussion 1167 and DreamingOfClouds's pinned script publication. It includes the independent budget/Walsh audit and its construction successor. The finding and handoff are posted in the originating H6 thread. PR1698 independently overlaps the arithmetic; this adds exhaustive structural evidence, explicit legal words, exact frame recipes, coefficient streams and actual profile pricing. Research files stay in the three H6 directories, with one dedicated H6 CI workflow. Imported predecessors, PR606 inputs, upstream and the selected record are preserved.

Evidence and replay: readable summaries reference lossless compressed matrices, witnesses and fixtures by canonical decompressed JSON hashes, following CONTRIBUTING.md. All eight migrated payloads are unchanged from the originally submitted head. The package checks all 665,856 polynomial coefficients and 25,263,360 feature entries, finite all-column words, representative physical recipes, and exact rational invoices. Twelve optimized replay steps and the fresh-export mutation gate pass. The dedicated H6 workflow uses Python 3.12, pinned NumPy and full Git history, and runs the package in a disposable export to keep checked-out evidence unchanged. Its entry point passed locally in a real Linux container, and the dedicated hosted H6 job subsequently passed for synthetic merge f7babf9b0057f88271447b99bc05a5204ee0a1c9 of reviewed head a6578b3d into original base 0b1cccf8. The wider repository workflow has separate inherited failures and cancellations; no whole-repository CI pass or hosted pass on a later revision is claimed.

python3 -I -O -B research/h6-compensation-network/ci.py
python3 -I -B research/h6-compensation-network/test_ci.py
make selected-record-check

Revision ef03620dff68d5be924b338f40c5c310e9359557 passes the complete local H6 gate, six benchmark-boundary regressions and live selected-record integrity. Hosted CI on this revision remains separate. Use Python 3.12 with NumPy 2.3.5 and full Git history. Exact pins, receipts, credit and Open next questions are in the report and validation scope.

Open: the billion-event full word is not executed, and immutable bank/controller/pad/tape integration, approximate-child precision, all-size bit supply and analytic transfer remain unadmitted. The 60/27-bit grid bounds assume exact local children. Partial mask routes cannot compose with K for free; fixed-architecture exclusions do not lower-bound arbitrary mixed circuits.

Credit Dominik Scholz/PR606, DreamingOfClouds/H6/PR1590, Andrey Mas/PR1698 and the selected/pending lineage. Prepared for Ross Richardson with substantial OpenAI Codex assistance and ten specialist agents. Apache-2.0; no independent human or full-theorem verification claim.

[Mister-Meeseeks]

Scoped batch triage at a6578b3dfad3d0b3279b1b6db23940b0660f9e5f. This PR remains open.

The unified12-stage H6 successor replay passed in136.433s. Whole-head review remains open: audit the universal physical recipe and compositional factor/chronology proofs, successor export/mutation CI gate, and the additional inherited audit/pricing packages in the168-file change. The retained958521600-pair predecessor receipt is not a fresh reviewer replay; full tape/approximate-child admission is explicitly outside this package.

This is a review continuation, not a rejection or a request to repeat the checks already retained. Credit and source pins are preserved in the batch ledger. The selected bound is unchanged. Thank you for the contribution.

[RossRichardson]

Follow-up to the review continuation, with the mathematical review pinned to a6578b3dfad3d0b3279b1b6db23940b0660f9e5f. No concrete defect was found in the reviewed local phase/completion, factor, arbitrary-dirt composition, chronology or pricing arguments. The revision records the completed dedicated hosted job and makes its historical-benchmark export compatible with current main; the mathematical artifacts and inherited source pins are unchanged.

• Universal physical recipe. The weight-mod-four identity and completion induction supply the all-pair argument for the declared h17 norm-one lines and caps. The translation X_b fixes the exact phase, and the noncharacteristic endpoint condition keeps the remaining form nonalternating. The recipe and inverse implementation has the required adapter order. The package's 14,670 endpoint checks, 512 pair checks and 17 exact physical recipes are finite corroboration. Those finite checks corroborate the written proof; they do not replace it. This is not a formal-kernel proof or a claim about arbitrary gauge frames.
• Composition and chronology. The contract hypotheses and arbitrary-input derivation require the K word on arbitrary sources, targets and auxiliary dirt. They give y += x forward and x -= y in the same-order scalar inverse-transpose orientation, preserving the frame chronology. Logical restoration leaves each ordinary compensation helper's prescribed physical residual F. The private dual word is explicitly constructed, including its erasure; it is not inferred by transposing an erase operation.
• Factor and finite coverage. The polynomial identity is an exact all-pair factor argument on the specified sphere. The independent checker binds all 665,856 coefficients and 25,263,360 actual feature entries and replays the emitted 8/32-port fixtures. This is distinct from the historical 958,521,600-pair predecessor census, whose receipt remains pinned input evidence and was not freshly replayed.
• Source and export gate. The gate binds 90 inherited files to exact base blobs, executes the successor from a relocated export, rejects the semantic/coefficient/source mutations, and checks script/specification bindings and source preservation afterwards. Its explicit wrapper checks survive -O; the retained lowerer's legacy assertions do not. The CI wrapper additionally verifies that checked-out evidence is unchanged. The export still reads the original Git object database for provenance.

The dedicated H6 hosted job passed on 15 October 2026 with CPython 3.12.15 and NumPy 2.3.5. It tested synthetic merge f7babf9b0057f88271447b99bc05a5204ee0a1c9 of the reviewed head into original base 0b1cccf86e2f5132ed286a26ef0a681a495740ea, including the fresh-export gate, selected-record integrity and unchanged checkout. The separate repository workflow has five failures and 22 cancellations, so this is not a whole-repository CI pass or hosted evidence for a later revision.

The full billion-event physical program, integrated bank/controller/pad/tape realization, approximate-child error propagation, all-size supply and analytic transfer remain open. The reviewed construction remains a finite, explicitly priced but uncompetitive local result: 227,312,640 bucket helpers versus at most 94,434 in the tested comparison profiles. No new κ, selected-result change, supplier admission or whole-head maintainer approval is claimed. Credit and the existing scientific pins are preserved.

Current-main integration: the live certificates/selected-result.json gained only proof-supplement metadata relative to H6's original benchmark. The old wrapper would reject this legitimate update. The revised ci.py retrieves that one historical record from its already recorded Git commit, checks its original SHA-256 and writes its exact bytes only into the private export. All other 89 inputs still require exact working-tree pins. The inner gate still checks all 90 exported files against the original base; the workflow separately checks the current selected record. Current and historical digests are reported distinctly. Six tests cover live-record drift, ordinary-input corruption, wrong historical bytes/digest, missing Git history and a missing benchmark pin. No source manifest, scientific proof, matrix, invoice, predecessor package or retained receipt is changed.

Final revision ef03620dff68d5be924b338f40c5c310e9359557 integrates main 67b122d33d6c599a49f65d50afa2f3fe8d790d02. Its complete ci.py gate passes locally on CPython 3.12.14 / NumPy 2.3.5: all twelve stages, 90 inherited pins, 20 scripts, six specifications, 17 semantic controls plus K-coefficient and transitive-source mutations. All six new benchmark regressions and live selected-record integrity pass. Checked-out files remain unchanged, and the five revised files match their committed bytes. A final merge-tree check against refreshed main c7df0bb890cae0cc393cdd32dad19c3facc80992 is clean and all 90 runtime input bindings remain valid under the explicit historical-benchmark rule. Hosted CI for this revised head is separate and pending at publication.

python3 -I -O -B research/h6-compensation-network/ci.py
python3 -I -B research/h6-compensation-network/test_ci.py
make selected-record-check

Ross Richardson with substantial OpenAI Codex assistance. The source/export change received a separate machine-assisted review; no independent human or formal-kernel review is claimed.

[RossRichardson]

Fresh review of the existing revision ef03620dff68d5be924b338f40c5c310e9359557 found no further concrete defect requiring a code change.

The complete H6 CI entry point passes in 39.967 s on CPython 3.12.12 / pinned NumPy 2.3.5: twelve successor stages, all 90 inherited pins, 20 scripts, six specifications, 17 semantic controls, and the K-coefficient/transitive-source mutations. The checkout remains unchanged. All six benchmark-boundary regressions also pass. The current-main synthetic merge preserves every successor file and all 90 effective input bindings, including the explicit historical selected-record rule.

The written universal phase identity/completion induction, arbitrary-dirt compensation composition and explicit K/private-copy dual chronology were rechecked within their stated domain. The exact polynomial/all-feature evidence and pricing are consistent with that local scope. The full billion-event word and old 958,521,600-pair predecessor census were not freshly executed; the latter remains retained evidence. Independent explicit optimized guards are active; legacy assertions in the retained lowerer are not counted as active -O checks.

python3 -I -O -B research/h6-compensation-network/ci.py
python3 -I -B research/h6-compensation-network/test_ci.py

Full gate log SHA256: 46d52472997893aa12a6cade0fa74dde9a576446c18af446249a130c98500765. The 227,312,640-helper bucket network remains uncompetitive against at most 94,434 helpers in the tested profiles. Bank/controller/tape integration, approximate-child precision, all-size supply and analytic transfer remain open. No new kappa, supplier admission or whole-head maintainer approval follows.

All 62 hosted checks were queued at this exact head when checked; no hosted success is inferred. The earlier successful focused Linux receipt concerns its historical merge ref only. Existing scientific pins, receipts, notices and predecessor credit are preserved. Ross Richardson with substantial OpenAI Codex assistance; no independent human/formal-kernel review claimed.