{
  "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",
  "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",
    "tensor_time_includes": ["model compilation", "output", "independent proof replay"],
    "mumps": "MUMPS 5.8.2, given the same separation of the three displacement directions (it factored 250,047 of the 750,141 unknowns at the largest size) and reusing the joint's attachment response across preloads; AMF ordering for the five smaller sizes; METIS for the largest, the fastest of five orderings measured there (AMF, METIS, automatic, QAMD, AMD)",
    "date": "2026-11-04"
  },
  "rows": [
    {"dofs": 3, "tensor": {"seconds": 0.239, "memory_mib": 32.5}, "mumps": {"seconds": 0.954, "memory_mib": 58.0}},
    {"dofs": 81, "tensor": {"seconds": 0.241, "memory_mib": 32.4}, "mumps": {"seconds": 0.928, "memory_mib": 58.9}},
    {"dofs": 1029, "tensor": {"seconds": 0.247, "memory_mib": 32.3}, "mumps": {"seconds": 0.920, "memory_mib": 58.5}},
    {"dofs": 10125, "tensor": {"seconds": 0.255, "memory_mib": 32.3}, "mumps": {"seconds": 0.965, "memory_mib": 64.1}},
    {"dofs": 89373, "tensor": {"seconds": 0.262, "memory_mib": 32.3}, "mumps": {"seconds": 1.819, "memory_mib": 142.4}},
    {"dofs": 750141, "tensor": {"seconds": 0.321, "memory_mib": 32.3}, "mumps": {"seconds": 22.222, "memory_mib": 1306.7}}
  ],
  "largest_size": {"dofs": 750141, "faster": 69, "less_memory": 40},
  "accuracy": "every Tensor mode count independently certified for the declared discrete finite-element model; MUMPS agreed at every tested threshold and preload",
  "scope": "Mode counts for the declared discrete finite-element model of a structured synthetic lattice, compared with MUMPS 5.8.2 on one core each. The engine is the subject of U.S. Provisional Patent Application No. 64/190,840 and is not published."
}