{
  "schema": "TENSOR.PUBLIC.EVIDENCE.v1",
  "product": "Tensor Spectral",
  "grade": "measured",
  "public_source": {
    "title": "Compact Exact Representation on the Integer Lattice: Characters, Divisors, and Cut-Cycle Coordinates for Grid and Mesh Problems",
    "doi": "10.5281/zenodo.23955545",
    "sections": [
      "8",
      "36-44"
    ],
    "note": "The mathematics is published there; the measurements below were taken on 4 November 2026 and are published in this receipt."
  },
  "case": "synthetic prestressed 3D payload-support truss lattice with a nonlinear center joint; all three displacement directions, consistent truss mass, geometric prestress stiffness; small-signal modes about the declared nonlinear equilibrium; two-node truss elements",
  "per_run_work": "mode counts below two frequency thresholds for three joint preload variants",
  "conditions": {
    "machine": "one desktop computer",
    "cores_per_solver": 1,
    "time": "cold wall time, median of three runs",
    "memory": "maximum observed whole-process peak resident memory, MB as Windows reports it (MiB)",
    "tensor_time_includes": [
      "model compilation",
      "output",
      "independent proof replay"
    ],
    "mumps": "MUMPS 5.8.2 given the whole matrix at every size, with no symmetry, reduction, or reused response supplied; ordering chosen per size by timed probes before the measured runs (METIS, AMF, AMD, QAMD through 10,125 degrees of freedom; METIS and AMF above); low-rank (BLR) compression measured at the two largest sizes and slower than full rank, so full rank was used",
    "date": "2026-11-04"
  },
  "rows": [
    {
      "dofs": 3,
      "mumps_ordering": "qamd",
      "tensor": {
        "seconds": 0.263,
        "memory_mib": 32.4
      },
      "mumps": {
        "seconds": 1.061,
        "memory_mib": 58.0
      },
      "faster": 4.0,
      "less_memory": 1.8
    },
    {
      "dofs": 81,
      "mumps_ordering": "amf",
      "tensor": {
        "seconds": 0.298,
        "memory_mib": 32.4
      },
      "mumps": {
        "seconds": 1.087,
        "memory_mib": 58.9
      },
      "faster": 3.7,
      "less_memory": 1.8
    },
    {
      "dofs": 1029,
      "mumps_ordering": "qamd",
      "tensor": {
        "seconds": 0.277,
        "memory_mib": 32.4
      },
      "mumps": {
        "seconds": 1.081,
        "memory_mib": 59.4
      },
      "faster": 3.9,
      "less_memory": 1.8
    },
    {
      "dofs": 10125,
      "mumps_ordering": "metis-user",
      "tensor": {
        "seconds": 0.271,
        "memory_mib": 32.4
      },
      "mumps": {
        "seconds": 1.335,
        "memory_mib": 65.2
      },
      "faster": 4.9,
      "less_memory": 2.0
    },
    {
      "dofs": 89373,
      "mumps_ordering": "metis-user",
      "tensor": {
        "seconds": 0.288,
        "memory_mib": 32.4
      },
      "mumps": {
        "seconds": 7.358,
        "memory_mib": 116.7
      },
      "faster": 25.6,
      "less_memory": 3.6
    },
    {
      "dofs": 750141,
      "mumps_ordering": "metis-user",
      "tensor": {
        "seconds": 0.327,
        "memory_mib": 32.4
      },
      "mumps": {
        "seconds": 178.021,
        "memory_mib": 729.2
      },
      "faster": 544.8,
      "less_memory": 22.5
    }
  ],
  "largest_size": {
    "dofs": 750141,
    "truss_elements": 762048,
    "faster": 544.8,
    "less_memory": 22.5
  },
  "accuracy": "every Tensor mode count independently certified for the declared discrete finite-element model; MUMPS agreed at every tested threshold and preload, at every size",
  "scope": "Mode counts for the declared discrete finite-element model of a structured synthetic lattice, compared with MUMPS 5.8.2 given the whole matrix, on one core each. The engine is the subject of U.S. Provisional Patent Application No. 64/190,840 and is not published."
}