{
  "schema": "AN04-real-principal-finite-check/v1",
  "passed": true,
  "checks": [
    {
      "name": "both fundamental signs and constant difference",
      "passed": true,
      "scope": "Exact decaying Gaussian input and both signed antiderivatives; reversed backward sign gives minus the input. Distributional and compact-support claims use the written transpose proof."
    },
    {
      "name": "entire kernel coordinate transpose and input twist",
      "passed": true,
      "scope": "Exact invertible four-variable Jacobian; includes tau=0 flow covectors and tau-nonzero diagonal covectors."
    },
    {
      "name": "both-frequency half-line asymptotic and nonvanishing",
      "passed": true,
      "trials": 18,
      "scope": "Exact transform of H(v)exp(-a*v), with positive a. This integrable exponential model tests the sign and second-order remainder; the compact smooth-cutoff proof is the two integrations in RP7a."
    },
    {
      "name": "time-translation commutator and failed absolute-time cutoff",
      "passed": true,
      "scope": "Exact sum of both time derivatives; spatial factors allowed. The general compact difference-cutoff construction and full symbol remainder are the written proof."
    },
    {
      "name": "positive degree reduction and radial characteristic",
      "passed": true,
      "scope": "Full Hamilton product rule for a nonconstant homogeneous degree-two symbol, degree-one reduction, and exact x*xi radial field. Flow invariance uses the earlier full uniqueness proof."
    },
    {
      "name": "smooth primitive sign and conormal order",
      "passed": true,
      "scope": "Exact mixed-variable primitive and eleven ambient/phase dimension balances, retaining the ambient dimension 2n."
    },
    {
      "name": "signed finite Volterra controls and exact interval factors",
      "passed": true,
      "models": [
        {
          "dimension": 8,
          "direction": 1,
          "norm": 0.6773719654662137,
          "bound": 1
        },
        {
          "dimension": 8,
          "direction": -1,
          "norm": 0.6773719654662135,
          "bound": 1
        },
        {
          "dimension": 17,
          "direction": 1,
          "norm": 0.6555639345139033,
          "bound": 1
        },
        {
          "dimension": 17,
          "direction": -1,
          "norm": 0.6555639345139032,
          "bound": 1
        },
        {
          "dimension": 32,
          "direction": 1,
          "norm": 0.6466298931440388,
          "bound": 1
        },
        {
          "dimension": 32,
          "direction": -1,
          "norm": 0.6466298931440385,
          "bound": 1
        }
      ],
      "scope": "Finite quadrature operators satisfy the interval-product bound; continuous constant-input examples attain its factors. General L2 continuity is proved by Cauchy-Schwarz and product integration."
    }
  ],
  "lesson_sha256": "8fad8186f56e9ef083eb00dde72755c6da8c69b30c771547802970145761889c",
  "script_sha256": "e24543d5f0630b218028fe58257d828dd86e32b82e47c954c82cd50bf99849b4",
  "exercise_solutions": 3,
  "generality_guard": "Finite and exact model checks support the written general distribution, wavefront, support and propagation proofs; they do not certify those theorems.",
  "full_course_complete": false,
  "public_release_authorized": false
}