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Prove Euclidean operator-norm rectangle bounds and the uniform discrepancy estimate, its division-free form and exact 2^n bit-cube specialization. Preserve the literal nonsymmetric eigenvalue statement as a source error. Checked clients show a nilpotent sign matrix with charpoly X^2 but a positive normalized rectangle sum, rectangular/empty cases and zero-bit discrepancy one. Extract the shared Cauchy-Schwarz and operator-norm estimates from Forster into the existing EuclideanOpNorm topic module; both Forster consumers migrate and old private copies disappear. Samuel Schlesinger source credit and public statements are preserved. New files credit Christian Reitwiessner. Validation: strict SpectralDiscrepancy, ForsterSignRank and result registry pass (13458 jobs); import aggregate, hygiene, source-only changed-file lints, encoding/projection ratchets and manual checker/72 controls pass. Local advisory reports examine 0 definitions, 8 statements and 22 proofs without candidates, omitting 4363 unbuilt modules from definitions/statements. Hosted full CI, complete actual advisory reports and rendered-manual provenance remain required. Independent source/API/manual review by /root/review_bpp_reconciliations is clear pending exact-commit return. Manual impact: Operator guidance covers L2 norm scope, finite/nonempty and column equality hypotheses, sign convention, source correction, raw empty cases and complete clients. Agent roles and procedures are unchanged. This is the bounded corrected endpoint #4955, not completion of #4711 or proof of the false box. Implementation and independent agent review used OpenAI Codex.
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Independent non-author reviewer The raw finite real rectangular-matrix estimate bounds absolute rectangle sums by the operator norm times square roots of the side cardinalities, including empty sides and empty index types. Uniform sign-matrix discrepancy is bounded by the norm divided by sqrt(|X||Y|) on finite nonempty input types with decidable column equality; the division-free form and equal-bit-cube denominator2^n are correct. The PMF normalization and overall sign reversal preserve the intended absolute quantities; no symmetry, spectral-radius interpretation or numerical norm-computation guarantee is introduced. Clients check the nilpotent sign-matrix obstruction (square zero, characteristic polynomialX^2, normalized rectangle sum1/4), a1×2 matrix, empty cases and discrepancy one for the zero-bit cube. The extracted bilinear Cauchy–Schwarz estimate derives the existing Mathlib inner-product inequality. Both the Forster operator-norm and Hadamard consumers reuse the shared matrix API, preserving their public statements and Samuel Schlesinger’s credit. Placement, scoped norm usage, imports and new-file credit are appropriate. The Operator’s Manual supplies the import/scope, hypotheses, normalization, empty-case distinction and complete-client command; Agent Manual roles/procedures/handoffs are unaffected and require no edit. Registry/source records accurately distinguish the corrected milestone from #4771’s source issue, #4764’s wider audit and #4711’s open book/theory/exercise objective. No remaining source finding. Final readiness remains held for complete hosted CI, all three complete actual advisory reports and fresh provenance/rendered review for both manuals. CI and manual generation are still running at this read; the local definition/statement comparison omitted4363 unbuilt modules and cannot clear that advisory hold. I made no edits, ran no builds, and took no queue/watch action. This is independent agent review, not human review. |
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Independent non-author Fresh artifact14011009271 has matching API/upload/download ZIP SHA256 Final readiness remains held: on the single status read, |
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Independent non-author coordinator Native CI43368220914 is now terminal SUCCESS. All six Lean gates, full changed-file lints, registry, tidy, hygiene and readability/projection checks pass; Guide43368220967 also passes. I inspected all three actual complete advisory reports: 0 changed definitions, 8 theorem statements and 22 proofs, with no candidates, omitted-module caveat or truncation. These heuristic reports supplement the retained semantic review. The tested merge Queue sequencing remains held. Current head and write authority are confirmed; the head merges cleanly with current main72a0132a. Actual merge-tree preflight against the current queue prefix finds a conflict with earlier queued #4764 in |
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The recorded lower-audit hold is cleared: #4764 actually landed as |
Proves the corrected operator-norm version of Arora–Barak draft Lemma12.13: absolute rectangle sums of finite real rectangular matrices are bounded by the Euclidean operator norm times the square roots of the side sizes. Uniform Boolean discrepancy is therefore at most the sign-matrix norm divided by sqrt(|X||Y|), with a division-free form and exact 2^n denominator on equal bit cubes. Finite/nonempty PMF domains and column decidable equality are explicit. The literal unrestricted eigenvalue claim remains a source issue under #4771.
Extracts the shared matrix estimates from Forster into the existing EuclideanOpNorm module and migrates both the operator-norm and Hadamard consumers, preserving source credit and public statements. Spectral dependencies stay in the new Discrepancy/Spectral module. Checked clients include a nilpotent sign matrix with characteristic polynomial X^2 but normalized rectangle sum1/4, a1×2 matrix, empty cases and zero-bit discrepancy one. No general spectral-radius bound or numerical norm-computation certificate is claimed. Closes #4955 after integration; #4711’s full book/theory objective stays open.
Validation: strict SpectralDiscrepancy, ForsterSignRank and registry build pass (13458 jobs), plus canonical imports, hygiene, source-only changed-file lints, encoding/projection ratchets and manual checks/72 controls. Local reports examine0 public definitions,8 statements and22 proofs without candidates, but definition/statement comparisons omit4363 unbuilt modules. Complete hosted CI/advisory reports and rendered-manual provenance remain required. Independent non-author source/API/manual review is clear; exact-head return requested.
Manual impact: Operator guidance gives the norm scope, imports, hypotheses, sign convention, source correction, boundary behavior and complete checked clients. Agent roles/procedures/handoffs do not change, so that manual needs no edit. The source audit retains the false-box classification and wider chapter-audit ownership.
Originated by Christian Reitwiessner. Implementation and independent agent review used OpenAI Codex.