{
  "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/NonuniformIsochoric.lean",
  "source_sha256": "99029516cf26fca5a82cbd2971c13f9d9d1e6a10face1d71704a6185b7a731ea",
  "claims_sha256": "b24637dae1f03d41ce99eff74fed32761bf702f1c0c7afd8e7954e05ac3fe53d",
  "command": "lake --no-cache env lean -DwarningAsError=true proofs/NonuniformIsochoric.lean (from pinned mathlib workspace)",
  "claims": [
    {
      "id": "nonuniform-gradient-determinant",
      "theorem": "KenomaNonuniform.gradient_determinant",
      "domain": "Real",
      "statement": "Off-axis shear leaves the determinant equal to lambda*b*b.",
      "statement_lean": "theorem gradient_determinant (lambda b shearY shearZ : \u211d) :\n    Matrix.det (gradientField lambda b shearY shearZ) = lambda * b * b",
      "assumptions": "Exactly the parameters and hypotheses in the full Lean statement.",
      "limitations": "Declared finite kinematics only; no formal derivative, integration, triangulation, floating-point or physical equilibrium refinement; no biological claim.",
      "claim": "Off-axis shear leaves the determinant equal to lambda*b*b.",
      "implementation": "contributions/nonuniform-isochoric-kinematics/model.mjs; prescribed map and measured boundary volumes, separately audited.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    },
    {
      "id": "nonuniform-positive-stretch",
      "theorem": "KenomaNonuniform.positive_stretch_on_interval",
      "domain": "Real",
      "statement": "Positive mean/length, -1<a<1 and 0<=S<=L imply positive local stretch.",
      "statement_lean": "theorem positive_stretch_on_interval (m a L S : \u211d)\n    (hm : 0 < m) (hL : 0 < L) (haLower : -1 < a) (haUpper : a < 1)\n    (hS : 0 \u2264 S) (hSL : S \u2264 L) : 0 < stretch m a L S",
      "assumptions": "Exactly the parameters and hypotheses in the full Lean statement.",
      "limitations": "Declared finite kinematics only; no formal derivative, integration, triangulation, floating-point or physical equilibrium refinement; no biological claim.",
      "claim": "Positive mean/length, -1<a<1 and 0<=S<=L imply positive local stretch.",
      "implementation": "contributions/nonuniform-isochoric-kinematics/model.mjs; prescribed map and measured boundary volumes, separately audited.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    },
    {
      "id": "nonuniform-pointwise-compensation",
      "theorem": "KenomaNonuniform.pointwise_isochoric_gradient",
      "domain": "Real",
      "statement": "Positive lambda and b=1/sqrt(lambda) give positive b and determinant one, for arbitrary shear entries.",
      "statement_lean": "theorem pointwise_isochoric_gradient (lambda shearY shearZ : \u211d)\n    (hlambda : 0 < lambda) :\n    0 < transverse lambda \u2227\n      Matrix.det (gradientField lambda (transverse lambda) shearY shearZ) = 1",
      "assumptions": "Exactly the parameters and hypotheses in the full Lean statement.",
      "limitations": "Declared finite kinematics only; no formal derivative, integration, triangulation, floating-point or physical equilibrium refinement; no biological claim.",
      "claim": "Positive lambda and b=1/sqrt(lambda) give positive b and determinant one, for arbitrary shear entries.",
      "implementation": "contributions/nonuniform-isochoric-kinematics/model.mjs; prescribed map and measured boundary volumes, separately audited.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    },
    {
      "id": "nonuniform-nonuniform-isochoric",
      "theorem": "KenomaNonuniform.nonuniform_isochoric_on_interval",
      "domain": "Real",
      "statement": "The declared nonuniform field has positive b and determinant one throughout the stated interval.",
      "statement_lean": "theorem nonuniform_isochoric_on_interval (m a L S shearY shearZ : \u211d)\n    (hm : 0 < m) (hL : 0 < L) (haLower : -1 < a) (haUpper : a < 1)\n    (hS : 0 \u2264 S) (hSL : S \u2264 L) :\n    0 < transverse (stretch m a L S) \u2227\n      Matrix.det (gradientField (stretch m a L S)\n        (transverse (stretch m a L S)) shearY shearZ) = 1",
      "assumptions": "Exactly the parameters and hypotheses in the full Lean statement.",
      "limitations": "Declared finite kinematics only; no formal derivative, integration, triangulation, floating-point or physical equilibrium refinement; no biological claim.",
      "claim": "The declared nonuniform field has positive b and determinant one throughout the stated interval.",
      "implementation": "contributions/nonuniform-isochoric-kinematics/model.mjs; prescribed map and measured boundary volumes, separately audited.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    },
    {
      "id": "nonuniform-straight-cell-error",
      "theorem": "KenomaNonuniform.straight_cell_error_factorization",
      "domain": "Real",
      "statement": "For positive endpoint square-root ratio r, the algebraic straight-cell volume error has the stated nonnegative factorization.",
      "statement_lean": "theorem straight_cell_error_factorization (r : \u211d) (hr : 0 < r) :\n    straightCellRatio r - 1 =\n      (r - 1) ^ 2 * (r ^ 2 + 3 * r + 1) / (6 * r ^ 2)",
      "assumptions": "Exactly the parameters and hypotheses in the full Lean statement.",
      "limitations": "Declared finite kinematics only; no formal derivative, integration, triangulation, floating-point or physical equilibrium refinement; no biological claim.",
      "claim": "For positive endpoint square-root ratio r, the algebraic straight-cell volume error has the stated nonnegative factorization.",
      "implementation": "contributions/nonuniform-isochoric-kinematics/model.mjs; prescribed map and measured boundary volumes, separately audited.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    },
    {
      "id": "nonuniform-straight-cell-volume-bound",
      "theorem": "KenomaNonuniform.straight_cell_ratio_ge_one",
      "domain": "Real",
      "statement": "For r>0 the algebraic straight-cell volume ratio is at least one; this does not certify a mesh implementation.",
      "statement_lean": "theorem straight_cell_ratio_ge_one (r : \u211d) (hr : 0 < r) :\n    1 \u2264 straightCellRatio r",
      "assumptions": "Exactly the parameters and hypotheses in the full Lean statement.",
      "limitations": "Declared finite kinematics only; no formal derivative, integration, triangulation, floating-point or physical equilibrium refinement; no biological claim.",
      "claim": "For r>0 the algebraic straight-cell volume ratio is at least one; this does not certify a mesh implementation.",
      "implementation": "contributions/nonuniform-isochoric-kinematics/model.mjs; prescribed map and measured boundary volumes, separately audited.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    }
  ]
}