{
  "schema": "bounded-canonical-fold-check/v1",
  "checks": [
    {
      "name": "full homogeneous relations in n=2,3,4",
      "passed": true,
      "bounded_evidence": "Both complete projection Jacobians, equal full canonical one-forms, ambient/restricted ranks, distinct kernel lines and nonzero marked radial independence; simple fold determinant factors retained."
    },
    {
      "name": "ordinary coefficients, full projections and signed one-form",
      "passed": true,
      "bounded_evidence": "n=1,2,3: both complete determinants and signed primitive v^3/12=2(x1-y1)^3/3, with exact factor two in the relation."
    },
    {
      "name": "actual homogeneous phase, critical equations and covector signs",
      "passed": true,
      "bounded_evidence": "Full conic phase in n+1 auxiliary variables: exact critical substitution, Euler degree-one identity, zero critical value, output/input covectors and independent marked critical gradients in n=2,3,4."
    },
    {
      "name": "full source charts for both converses and sheet exchanges",
      "passed": true,
      "bounded_evidence": "Exact half-degree normal, both full source Jacobians, invariant projection maps and squared input exchange; complete one-form cancellation and exact marked sheet coordinates."
    },
    {
      "name": "complete nonlinear canonical target changes",
      "passed": true,
      "bounded_evidence": "Nonlinear cotangent lifts on both targets preserve entire one-forms and both fold determinants; exact inverse changes recover the full relation, including mixed last-frequency terms."
    },
    {
      "name": "genuine excluded relation and missing-cubic-displacement defect",
      "passed": true,
      "bounded_evidence": "Two actual homogeneous cotangent projections fold with distinct kernels and product rank four, yet common pulled-back primitive is zero at the marked point. Omitting the cubic last position creates exact nonzero signed one-/two-form defects."
    }
  ],
  "passed": true,
  "lesson": "canonical-relations-with-two-folds.md",
  "lesson_sha256": "69518d9ee9afdcf7a965293c40bf3ae045ee2cc65eba1b7c1380e4b4afcd7e2b",
  "script_sha256": "7a8c3338ea00ba55ab3288c503e02f328fcff1e3d8f97f583562f9761fa9760f",
  "guard": "Bounded full relations/phases do not independently certify the arbitrary-relation reduction and full target extension proofs."
}