{
  "schema": 1,
  "lean_version": "Lean (version 4.19.0, x86_64-unknown-linux-gnu, commit 6caaee842e94, Release)",
  "source": "proofs/AnatomicalArm.lean",
  "source_sha256": "843f04f8e8f5c81a902d6816f0136726d006be6574aff5245360b8c2006ef025",
  "claims_sha256": "a56d39ba3dfe805189ca13ef91f696b99b2762e7258e6b22246b81eba36baa83",
  "command": "lean -DwarningAsError=true proofs/AnatomicalArm.lean",
  "claims": [
    {
      "id": "upward-mass-event",
      "theorem": "Kenoma.Arm.upward_mass_event_work_numerator",
      "claim": "At unchanged pose and velocity, the point-mass inertia and upward-positive gravitational potential increments give the external mass-event energy numerator.",
      "implementation": "web/anatomical-arm.mjs: changeAnatomicalMass; +Z superior, V=+mgz.",
      "assumptions": "Exact integer quantities in compatible common scales; squared grip radius is fixed and inertia changes by deltaMass times that radius squared. Factors of two represent the kinetic denominator.",
      "limitations": "Does not establish browser state preservation, numerical equality, actual anatomical geometry or handling of a physical dumbbell.",
      "numerical_evidence": "Actual-arm mass-event/state tests and source-bound arm experiment receipts are required separately.",
      "status": "checked",
      "axioms": [
        "propext",
        "Quot.sound"
      ]
    },
    {
      "id": "shared-guide-balance",
      "theorem": "Kenoma.Arm.shared_guide_force_balance",
      "claim": "A supplied zero resultant at one shared biceps guide component makes the common distal force equal the negative sum of the two head, matrix and contact contributions.",
      "implementation": "web/anatomical-apparatus.mjs and web/anatomical-contact.mjs: both biceps heads, common distal branches, sheet matrix and contact act on the same nine free guide coordinates.",
      "assumptions": "Exact signed integer force-component numerators in a compatible scale; interpolated headA, headB, distal, matrix and contact contributions are supplied; their equilibrium is assumed.",
      "limitations": "Does not derive interpolation/geometry, verify the floating-point residual, prove Newton convergence or validate an anatomical aponeurosis.",
      "numerical_evidence": "tests/anatomical_apparatus.test.mjs checks shared coordinates, source faces, objective derivatives and actual attachment torque; equilibrium receipts are checked separately.",
      "status": "checked",
      "axioms": [
        "propext",
        "Quot.sound"
      ]
    },
    {
      "id": "contact-area-partition",
      "theorem": "Kenoma.Arm.contact_partition_area_numerator",
      "claim": "Reference-area child shares preserve the parent area numerator when their sum equals the parent scale.",
      "implementation": "web/anatomical-contact.mjs: rebuildSurfaceSamples; web/anatomical-contact-refinement.mjs: splitMaterialTriangle, rebuildBoneSamples.",
      "assumptions": "Exact integer compatible area/share scales; the geometric partition supplies a+b+c=scale. Positive child areas are checked numerically.",
      "limitations": "Does not prove the triangulation, positive floating-point weights, geometric clearance, continuous collision detection, Newton convergence or biological contact.",
      "numerical_evidence": "tests/anatomical_contact_refinement.test.mjs independently checks positive children, reference-area conservation, saved missed intersections and material-rule replay.",
      "status": "checked",
      "axioms": [
        "propext"
      ]
    },
    {
      "id": "conservative-contact-gap",
      "theorem": "Kenoma.Arm.conservative_contact_gap",
      "claim": "A supplied lower unsigned distance envelope gives a gap no greater than the exact outside distance or the negative inside distance.",
      "implementation": "web/anatomical-contact.mjs: regularizedSoft; outside gap=u, inside gap=u-2*d. Raw signed distance and full geometry remain the acceptance gates.",
      "assumptions": "Exact integer distance numerators in compatible SI scales; the bound u<=d is supplied.",
      "limitations": "Does not prove the numerical simplex solver, floating-point bounds, signed-distance queries, derivative correctness, Newton convergence or collision clearance.",
      "numerical_evidence": "tests/anatomical_contact_differential.test.mjs checks envelope bounds/weights and tests/anatomical_contact_refinement.test.mjs checks the preserved loaded closest-face corner and original collision gates.",
      "status": "checked",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ]
    }
  ]
}