{
  "schema": 1,
  "lean_version": "Lean (version 4.19.0, x86_64-unknown-linux-gnu, commit 6caaee842e94, Release)",
  "mathlib": {
    "repository": "https://github.com/leanprover-community/mathlib4",
    "tag": "v4.19.0",
    "commit": "c44e0c8ee63ca166450922a373c7409c5d26b00b",
    "manifest_sha256": "5c6421b650bc87a2427a892a39e5522dc44543ca4ac1bd6e9f08d536c044a752",
    "toolchain": "leanprover/lean4:v4.19.0",
    "license": "Apache-2.0",
    "qualification": "Fresh compilation required; this lock alone is not proof evidence."
  },
  "source": "proofs/ContinuumProperties.lean",
  "source_sha256": "33945605131f1a0fc3568467cbc1026463867a8fa241fb25e2174c23a229f12e",
  "claims_sha256": "481b28474107cfcc8096b3364e140d842fc7751bacd45f19ffc4de35c033e4f3",
  "command": "lake env lean -DwarningAsError=true proofs/ContinuumProperties.lean (from pinned mathlib workspace)",
  "claims": [
    {
      "id": "volume-edge-translation",
      "theorem": "KenomaProperties.edge_translation_invariant",
      "claim": "Adding one real translation to all four vertices leaves the tetrahedral edge matrix unchanged.",
      "assumptions": "Four real three-dimensional vertex vectors; the same translation acts on each vertex. A meaningful physical deformation gradient additionally requires a nondegenerate reference tetrahedron.",
      "limitations": "No floating-point equivalence, boundary triangulation, inversion detection, equilibrium or biological claim is established.",
      "implementation": "web/continuum-properties.mjs: measureTetrahedron and boundaryMeasurements; numerical geometry and translation are checked separately.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    },
    {
      "id": "volume-det-compose",
      "theorem": "KenomaProperties.determinant_composition",
      "claim": "The determinant of a product of real 3 by 3 matrices is the product of their determinants.",
      "assumptions": "Real square matrices; this supports F=Ds*inverse(Dm) with separately assumed invertible reference geometry.",
      "limitations": "Does not certify JavaScript matrix multiplication/inversion, mesh orientation or boundary measurements.",
      "implementation": "web/continuum-properties.mjs: multiply3 and measured deformation gradient; separate nontrivial matrix and geometric tests.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    },
    {
      "id": "volume-diagonal",
      "theorem": "KenomaProperties.axial_determinant",
      "claim": "The real axial/lateral diagonal deformation diag(lambda,b,b) has determinant lambda \u00d7 b \u00d7 b.",
      "assumptions": "Real stretches; physical use additionally requires lambda>0 and b>0. Unit determinant follows whenever the stated product equals one.",
      "limitations": "A kinematic identity; no force equilibrium, finite-bulk incompressibility, material response or biological correctness follows.",
      "implementation": "web/continuum-properties.mjs: isochoricState; independent oriented boundary and area-times-length measurements.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    },
    {
      "id": "volume-isochoric-sqrt",
      "theorem": "KenomaProperties.isochoric_sqrt_construction",
      "claim": "For real lambda>0, b=1/sqrt(lambda) is positive and diag(lambda,b,b) has unit determinant.",
      "assumptions": "Positive real axial stretch and the exact real square-root construction.",
      "limitations": "Does not prove binary64 sqrt/division or measured browser volume is exact, and does not establish a passive or active equilibrium.",
      "implementation": "web/continuum-properties.mjs: the actual isochoric toggle; floating-point boundary-volume error is reported.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    }
  ]
}