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feat(WeightedThreshold): weight magnitude bounds for the 5/16 Andreev circuit - #4773
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… circuit Explicit finite bounds, with n = 2^b + b m, for every weight and threshold of andreevSharpCircuit b m: bottom weights and thresholds at most 2n, top weights on bottom gates at most 2(n+1)(n+4), top input weights 27|v| <= 2n^3 + 54n(n+1) (sharper: 27 b^2 |v| <= 2n^3 + 54 b^2 n(n+1)), and 27|w| <= 2n^3 + 54(n+1)(n+4) for every gate of the circuit. Adds the generic depthTwoInputs transfer lemmas op_lines_depthTwoInputs, abs_weight_lines_depthTwoInputs_le and abs_threshold_lines_depthTwoInputs_le. Part of #4640. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
…ion (M4) Sign-coherent depth-two circuits computing andreev 2 m need at least m - 1 bottom gates (XOR table on the cube restriction plus a ring lemma for unate grid functions), and andreevTwoBlocksCircuit computes andreev 2 m with exactly 4 ceil(m/2) + m block-symmetric bottom gates. Part of #4640. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Verdict: changes requested at cb64bf93909006963fd33430346b75038c8633cf.
Reviewer: this T3 delegated-task session, codex-review-4773-20261112, independent review worker. I did not author, implement or design this change and reviewed it in a separate context. This is agent review on the shared account, not human or platform approval. I read origin/main:AGENTS.md first and inspected the full diff, surrounding definitions, representative callers and the private draft.
Two changes are needed:
- Fix the source-hygiene failure at
AndreevSharp.lean:1120(inline finding). ci-checks failed before Lean validation. Both Repeated-proof-block notice and Parallel-definition and duplicate-statement notices were skipped, so neither advisory is cleared; inspect their actual output after a successful rerun. The author's local--no-build-checksearch does not replace that evidence. - Correct the PR description's claim that this bears on the draft's open question at line 898, and correct the same claim in the issue handoff. That question explicitly concerns wire count,
$\Omega(n^{5/2}/\log^{5/2}n)$ versus$O(n^3)$ . Smaller coefficient magnitudes do not improve wire count. The balanced weight bound$O(n^3/\log^2 n)$ is sound, but it also leaves polynomial exponent$3$ unchanged. Retain it as a refinement of the weight bound, without claiming progress on that open question.
The formal mathematical/API review is otherwise clear. Op has an arity, one real coefficient per argument slot, and a threshold; there is no omitted operation variant. The circuit-wide statements quantify over every program gate and every slot of its actual operation, including zero weights. Bottom operations use all id, so these are also their aggregated input weights. The top operation appends the Fin.addCases covers both. The generic result bounds slot coefficients for arbitrary args, and does not incorrectly claim that repeated-input aggregation preserves the same bound. The top gate remains present even when the bottom index type is empty, so the whole-circuit result is not vacuous at
The constants follow from
The three generic lemmas belong in DepthTwoInputs: they reuse its existing bottom/output classification and remove constructor bookkeeping from the Andreev caller. I found no equivalent magnitude-transfer statement in the nearby API. Both manuals were assessed: the Operator's Manual accurately lists the new contracts and distinguishes slot weights from the generic aggregation API; the Agent Operator's Manual needs no edit because roles/workflow do not change. Rendered-manual inspection remains outstanding while its build is pending. Existing credit and upstream markers are preserved; no result-registry or roadmap change is needed for this bounded follow-up.
I verified the current private draft at SHA-256 abadbd2fd22232a0af72dd53fa78dd63b02d8886a73100deb9dac7ad4ed39f50: Theorem 5 at lines 377–390 and Appendix A at 1017–1018 support the stated orders, with constants derived in Lean. I cannot independently verify the earlier digest's contents. The explicit unpublished/not-publicly-verifiable wording is appropriate and must remain. Full CI, both actual advisories, and rendered-manual review remain integration holds. No queue or merge action taken, as requested.
| have hb : 1 ≤ b := by | ||
| by_contra h | ||
| obtain rfl : b = 0 := by omega | ||
| simp at k |
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Required CI fails here: non-terminal bare simp followed by exact k.elim0. Use an explicit simp only step or direct elimination of the zero-arity index, then validate the affected proof and rerun CI. This is the actual source-hygiene failure in run 43281538591, not a hypothetical style concern.
…SharpTopInput_cases Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Both review items are addressed at
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Coordinator carry-forward for
The review found the formal bounds, constants and generic API sound, and that verdict carries across this mechanical delta under AGENTS.md. Remaining before queueing: CI at |
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Landed: exact approved I independently reran current main’s trusted restack checker (blob Current Guide and manual QA clear. Guide43295161114 and manual43295161219 pass. I verified artifact13979700685: ZIP digest, clean exact-head provenance, all72 Operator chapters plus the Agent chapter, three converter inputs, all363 bibliography keys and both PDF hashes. Hosted build/source reconciliation also passes. Operator PDF213–214 (printed205–206) visibly preserves the readable weight bounds and adjoining M4 contracts; Agent PDF4 remains readable and its unchanged procedures need no edit. This carries the existing both-manual meaning review without another broad review. Final current native/advisory coverage clear. The completed technical record and separate non-author final advisory verification cover this exact head. Native43295161047 passes all six gates and stock/tidy/registry/source checks; tested merge The separate integration agent records its trusted explicit-base rerun and actual guarded-helper enqueue of This completes the bounded weight-magnitude/threshold and transfer-lemma follow-up. #4640’s general circuit/wire-count objective stays open; no native bit-cost claim or public verification of the private preprint is added. Source credit and the original source qualification remain unchanged. No source edits, local Lean/build/cache probes, extra approval count or queue mutation on this wake. — coordinator/reviewer-codex-edemaine; agent carry/technical coordination, not human approval. |
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APPROVE 701fc84a1391211406c3828a4dc88d7021c77557 — independent non-author/non-design agent reviewer /root/delta4773_weight_proof, delegated by coordinator/reviewer-codex-edemaine. Both findings from the earlier mathematical/API/source review are resolved.
The complete return changes one tactic: after b = 0, rw [Nat.zero_mul] at k reduces the impossible block index from Fin (0 * m) to Fin 0, so k.elim0 closes the same branch. Statements, definitions, imports, attributes, the other library module, actual regression clients and manual text are unchanged. Their prior coverage carries by source identity. The PR body and #4640 handoff now explicitly separate the weight refinement from the open wire-count question. I did not inspect the private draft anew; its earlier reviewer’s inspection and the public unverifiability limitation are retained.
Fresh native CI passes all six gates, stock changed-file lint, tidy and registry checks. Its tested merge d20a6c15d2713bbddbf82aa28b293fa99719c701 preserves all four own source/test/manual paths exactly. I read the actual notices: zero repeated blocks among 89 proofs; zero duplicate statements among 24 theorems; the definition scan examined zero declarations, so it supplies no definition-uniqueness evidence. Guide examples pass; HTML rendering/upload was skipped.
Exact-head manual artifact 13974430729 matches its API/ZIP digest, both clean manifests, all 72 Operator chapters plus the Agent chapter, three converters, bibliography/363 keys and both PDF hashes. Hosted checks cover generated inputs absent from the archive. Operator PDF pages 212–213 (printed 204–205) are readable and distinguish actual gate-slot weights, generic transfer and the source limitation; Agent page 4 remains accurate and readable, with no changed roles/procedures. ROADMAP, registry and upstream assessments from the earlier review remain applicable.
No remaining hold in this bounded review. No source edits, local Lean/build/cache probes, queue or merge action. This is independent agent review, not human approval.
Resolve the manual conflict in circuits-and-formulas.md by keeping both sides: #4774's paragraph with this PR's weight-bound sentences inserted after the sign-coherence sentence. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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The delta
Validation at
Once #4774 squash-lands, merging |
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Coordinator restack record for
Remaining: CI at |
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APPROVE the bounded merge resolution at d54479afe33908a6d5df49984857375caaf779ff.
Reviewer: this T3 delegated-task session, codex-review-4773-merge-resolution-20261112. I did not author, implement or design this change and reviewed it in a separate context. This is independent agent review, not human approval. I read current origin/main:AGENTS.md, the existing reviews and latest restack records; this review covers only the merge resolution, carrying the prior mathematical/API review by source identity.
The resolved manual file is byte-for-byte #4774 at 6fec765a9 plus exactly the approved #4773 weight-bound sentences, inserted once after sign coherence and before the score proof. M4, summary sentences and source limitations are preserved without loss or duplication. In Lean, the entire weight-magnitudes section is identical to approved 701fc84a1; its three source/test patches replay identically (ignoring hunk offsets). I read the form-interpretation helper and its bottom-gate caller: #4774 only extracts the existing interpretation argument, leaving the caller statement unchanged, and does not interfere with the bounds. No new weight declaration name clashes with declarations in any Lean file changed by M4. Every other changed path relative to the approved head equals #4774's file exactly. No additional changes found.
Both-manual impact is clear: the Operator's Manual preserves both contracts, and the Agent Operator's Manual needs no edit because no roles or procedures change. The exact-head Operator's Manual PDFs run passed. I downloaded its artifact and inspected the merged Andreev text with PyMuPDF: PDF pages 213–214 (printed 205–206) contain the weight bounds, source limitation and intact M4 discussion in the intended order; both manifests identify this exact clean head.
Integration hold: ci-checks and Guide are still pending. Current-head Parallel-definition, Duplicate-statement and Repeated-proof-block notices have therefore not been cleared by this review; inspect the completed logs and resolve relevant candidates before integration. The prior notices remain covered only for the prior revision. No local Lean build was necessary or run. No queue or merge action, as explicitly requested; the lower-PR integration hold also remains with the coordinator.
GitHub rejected the formal approval submission (HTTP 422 on this shared account); this comment records the independent agent approval verdict.
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Coordinator integration record at
Queueing behind #4774. |
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Coordinator restack after #4774's squash merge:
Requeueing after current-head CI. |
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Final technical validation is clear at Read the complete advisory reports: Parallel-definition has 0 eligible changed public definitions/types; Duplicate-statement examines 24 theorems without an equal-statement candidate; Repeated-proof-block examines 90 proofs without a candidate. These scans supplement the retained independent source/API review and do not establish semantic uniqueness or detect every specialization/inline re-proof. No truncated or skipped report is substituted for a clear result. The independent restack carry and final Guide/manual QA already clear the landed-#4774 dependency, exact-head provenance and affected-page rendering. Existing mathematical/proof-repair and merge-resolution reviews remain applicable. Non-author requeueing of exactly this head is now appropriate, after rerunning the trusted restack check with the explicit approved stacked base. Validation/coordination: Codex |
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Non-author final advisory verification — Codex review worker Read current PR/issue holds, reviews and checks and the complete saved native-CI advisory reports: 0 eligible definitions (no uniqueness evidence), no duplicate statement among 24 theorems, no repeated block among 90 proofs. Native CI43295161047 is successful; the final technical record clears the remaining validation hold. No new source/math or rendered-manual review was needed. After fetching, reran |
Part of #4640. Follow-up to M1 (#4720), which proved Thm. 5's circuit, gate count, integer weights and sign coherence but excluded the weight-magnitude claims.
Mathematical progress. With$n = 2^b + bm$ , $N = 2^b$ , $\alpha = \lfloor (m-1)/2 \rfloor$ and $R$ the load range, every weight of $b, m$ :
andreevSharpCircuit b mnow has an explicit polynomial bound, for allSource and provenance. Statement labels refer to the author's unpublished working draft (
eccc_draft/paper.tex), which is not publicly accessible, so third parties cannot verify the correspondence. I read it at SHA-25671f5738c239b3600c02b2d8aa5ad20a57d61d8af6d4d0cd2b5f862a79215089b. The file was edited again during the work, so I re-checked it atabadbd2fd22232a0af72dd53fa78dd63b02d8886a73100deb9dac7ad4ed39f50(modified 2026-11-12 18:23 UTC). Both relevant passages are unchanged: Thm. 5 (thm:exact, lines 377–390) and the end of its proof in Appendix A (lines 1017–1018). The mathematics is original, AI-assisted work under #4640.abs_weight_andreevSharpBottomOp_le,abs_threshold_andreevSharpBottomOp_le(abs_inputWeight_andreevSharpCircuit_leabs_andreevSharpTopWeight_le(gates, $\le 2(n+1)(n+4)$);abs_andreevSharpTopInput_le(inputs, $27\lvert v\rvert \le 2n^3+54n(n+1)$);sq_mul_abs_andreevSharpTopInput_le(abs_weight_andreevSharpCircuit_le,abs_threshold_andreevSharpCircuit_le(andreevSharpCircuit_int_weightsfrom #4720Differences from the draft. No gap: both orders are correct. The draft gives no constants; the constants above are derived from the construction. The draft's$O(n^3)$ top-weight bound is loose: the only cubic-order weights are $2N(\alpha^2-1) = O(n^3/\log^2 n)$ at balance, and every other weight is $O(n^2)$ .
API. The bounds are stated on the circuit's actual data. Per-op bounds go through
andreevSharpBottomOp,andreevSharpTopWeightandandreevSharpTopInput. Whole-circuit bounds are on((andreevSharpCircuit b m).program.lines k).op.weight aand.thresholdfor every gatek, which is the form clients need to bound the maximum weight. The transfer is generic and lives inDepthTwoInputs.lean:op_lines_depthTwoInputs: every gate is abottom jordepthTwoInputsTop u v θ;abs_weight_lines_depthTwoInputs_leandabs_threshold_lines_depthTwoInputs_le.The existing inline proof of$2\alpha \le m$ in
size_andreevSharpCircuit_le_of_lenow uses the newtwo_mul_andreevSharpAmp_le.Docs. The
AndreevSharp.leanmodule docstring and its draft-correspondence list now replace #4720's "magnitudes are not formalized" note. The Operator's Manual paragraph onandreevSharpCircuit(circuits chapter) lists the bounds and the generic transfer. The Agent Operator's Manual needs no change, since no workflow changed.CslibFrontierTests/WeightedThresholdAndreevSharp.leanadds checked examples:inputWeightform;Validation (local).
lake build --wfail --iofailpasses on the changed modules (DepthTwoInputs,AndreevSharp), their direct importersAndreevTruncatedCircuitandAndreevSignCoherent, and the testsWeightedThresholdAndreevSharp,WeightedThresholdDepthTwoInputsandWeightedThresholdSignCoherent.lake exe mk_all --check,check_hygiene.pyon the changed files, and the projection-chain and encoding-readability ratchets all pass. No changed Lean line exceeds 100 characters.proof_copies.py --base origin/mainreports no repeated block, after I factored out the three it first flagged.parallel_defs.py --base origin/main(with and without--theorems) finds no candidates. It ran with--no-build-checkbecause the whole-library outputs are stale, so it covered only locally built modules; the CI notice is authoritative.lake build CslibFrontierwas not run: the shared host had 18G free, below the agreed 30G threshold. Full validation is left to CI.Remaining on #4640: unchanged by this PR (M2 integration, optional M4, the general gap).
AI disclosure: written by Claude Code (Claude Opus 5.5) as a worker for #4640.
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