{
  "input": {
    "dimension": 1,
    "band": 1,
    "grid": 3,
    "power": 3,
    "coefficients": [
      {
        "frequency": [
          -1
        ],
        "real": "1",
        "imaginary": "0"
      },
      {
        "frequency": [
          1
        ],
        "real": "1",
        "imaginary": "0"
      }
    ]
  },
  "result": {
    "input_record_sha256": "f965cf0bb73017f0615984351890b221f5fc5eb9a130b1bd52a1eadb07be4025",
    "source_connection": {
      "family": "371",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "source_proof_verification": "not_run"
    },
    "formal_program_verification": "not_run",
    "arithmetic": "exact_complex_rational",
    "coefficient_convention": "physical Fourier coefficients; no weighted Sobolev coordinates",
    "limits": {
      "work_budget": 200000,
      "support_cap": 4000,
      "intermediate_rational_bits": 1024,
      "wall_time_deadline": "none"
    },
    "dimension": 1,
    "band": 1,
    "grid": 3,
    "power": 3,
    "dense_grid_complex128_storage_bytes": 48,
    "storage_interpretation": "Illustration for a fully materialized tensor grid; not a runtime or memory lower bound for sparse/structured implementations.",
    "sufficient_central_projection_grid": false,
    "sufficient_full_reconstruction_grid": false,
    "status": "complete",
    "work_units": 17,
    "exact_nonlinearity": [
      {
        "frequency": [
          -3
        ],
        "real": "1",
        "imaginary": "0"
      },
      {
        "frequency": [
          -1
        ],
        "real": "3",
        "imaginary": "0"
      },
      {
        "frequency": [
          1
        ],
        "real": "3",
        "imaginary": "0"
      },
      {
        "frequency": [
          3
        ],
        "real": "1",
        "imaginary": "0"
      }
    ],
    "circular_grid_coefficients": [
      {
        "frequency": [
          -1
        ],
        "real": "3",
        "imaginary": "0"
      },
      {
        "frequency": [
          0
        ],
        "real": "2",
        "imaginary": "0"
      },
      {
        "frequency": [
          1
        ],
        "real": "3",
        "imaginary": "0"
      }
    ],
    "exact_retained_projection": [
      {
        "frequency": [
          -1
        ],
        "real": "3",
        "imaginary": "0"
      },
      {
        "frequency": [
          1
        ],
        "real": "3",
        "imaginary": "0"
      }
    ],
    "circular_retained_projection": [
      {
        "frequency": [
          -1
        ],
        "real": "3",
        "imaginary": "0"
      },
      {
        "frequency": [
          0
        ],
        "real": "2",
        "imaginary": "0"
      },
      {
        "frequency": [
          1
        ],
        "real": "3",
        "imaginary": "0"
      }
    ],
    "circular_minus_exact_retained": [
      {
        "frequency": [
          0
        ],
        "real": "2",
        "imaginary": "0"
      }
    ],
    "central_projection_matches": false,
    "full_polynomial_recovered": false,
    "interpretation": "Exact finite sparse polynomial and circular-fold comparison. This neither proves the source blowup theorem nor certifies a floating FFT, time integrator or chosen blowup power."
  }
}