DomTheDeveloper / DomTheDeveloper/crl

Independent review requested: Bernstein–Bézier coefficient-inner-cone grand theorem

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Since Jul 21, 2026.

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Description

We request independent review of the Bernstein–Bézier certified inner-cone theorem package in draft PR #133.

Current review branch: formal/bernstein-bezier-grand-canonical
Current repair head at issue creation: 735b96d0d5363c5135b2d536d763060f238e1c88

The broad Bernstein convex-hull property and general finite-element Mosco theory are acknowledged prior art. The candidate combined contribution is narrower:

  1. fixed-degree conforming simplicial Bernstein coefficient inner cones;
  2. constructive high-order recovery for that practical inner subset;
  3. globally assembled coefficient projection localized near an active interface;
  4. the defect-order/codimension/duality rate
    gamma = min(beta - 1 + kappa/q, (beta + kappa + sigma)/q);
  5. the balanced quadratic codimension-one 3/2 specialization;
  6. a Lean bridge from finite coefficient certificates through abstract Mosco, VI, and rate endgames.

Review panels:

  • A — numerical analysis / Mosco: convex-target density, positive Bernstein sampling, conformity, diagonal recovery, and prior-art boundary.
  • B — free boundary / contact: localization, patch scaling, multiplier pairing, exponent derivation, and restricted sharpness claim.
  • C — formal methods: theorem-to-Lean correspondence, explicit analytical hypotheses, full build, axiom transcript, and sorryAx audit.
  • D — novelty: search for a source containing the full coefficient-inner-cone recovery plus localized rate mechanism.
  • E — clean-room reproduction: independently reconstruct and run the numerical protocol.

Please report:

  • name and affiliation;
  • panel addressed;
  • exact commit reviewed;
  • verdict: PASS, PASS AFTER CORRECTION, or FAIL;
  • numbered findings with file/theorem references;
  • missing citations or collisions;
  • permission or refusal to publish the report.

Entry documents on PR #133:

  • math/bernstein_obstacle/EXTERNAL_REVIEW_REQUEST_2026-07-20.md
  • math/bernstein_obstacle/GRAND_THEOREM_FINAL_REVIEWED_2026-07-20.md
  • math/bernstein_obstacle/audit_packets/AI_RED_TEAM_PANEL_2026-07-20.md
  • math/bernstein_obstacle/audit_packets/EXTERNAL_REVIEW_STATUS.md
  • math/bernstein_obstacle/lean/GrandCanonicalAudit.lean
  • math/bernstein_obstacle/lean/BernsteinObstacle/ConvexConstraint.lean

The internal AI red-team report is disclosed but does not count as independent validation.

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