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Formal Verification Status

hyperpolymath edited this page Jun 11, 2026 · 1 revision

Formal Verification Status

Honest cross-prover snapshot. The guiding rule for this repo (and the estate) is truth before vision: a green badge means a machine actually checked it.

Summary

Prover Artefacts Status (2026-06-11)
Lean 4 TropicalSessionTypes.lean, TropicalAdapterPath.lean Green. lake build clean under pinned 4.13.0; axiom-audited (propext / Quot.sound only; no sorry, no Classical.choice).
Isabelle/HOL Tropical*.thy, ROOT ⚠️ Version drift. Built green under Isabelle 2024; under 2025-1 there are proof-failure sites (version-drift, not sorry). See the in-repo build status.
Julia impl/ Reference checker — illustrative, not a verifier.

Lean 4 — what is proved

  • Soundness (soundness): static tropical grade = dynamic wall-clock cost, exactly.
  • QTT refinement (tropical_grade_le_sequentialTotal): tropical budget ≤ sequential billing (max ≤ sum).
  • Hub ceiling (hub_ceiling): the no-go corollary closing the universal-interop claim.
  • Duality (dualGrade_invol, dual_tcAdd_is_max, dual_tcMul_is_min): the min-max ⇄ max-plus De Morgan anti-isomorphism.

Full detail and the theorem/axiom table: Lean 4 Formalization.

Isabelle/HOL — drift note

The Isabelle development (5,600+ LOC of Isar, no sorry/oops in proof bodies) regressed under Isabelle 2025-1 due to version drift (e.g. a HOL.Permutations/HOL.Bij class-instance change and a hypothesis weakness in path_weight_cycle_excise). The body of work is intact; the failures are mechanical version reconciliation. Authoritative detail:

A note on a corrected claim

The Lean migration found and corrected a false theorem inherited from the source (dual_tcMul_bounded). This is recorded openly in the changelog, the source comments, and the Lean 4 Formalization page — consistent with the repo's documented preference for closing claims honestly rather than re-narrating them.

See also: Home · Lean 4 Formalization