{
  "schema": "TENSOR.PUBLIC.EVIDENCE.v1",
  "product": "Tensor Mesh",
  "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": [
      "85"
    ]
  },
  "lattice_impact": {
    "machine": "one desktop computer; one run at a time",
    "dates": "2026-10-31 to 2026-11-03",
    "case": "slab of body-centred-cubic cells, 1,848 quadratic tetrahedra per cell, four layers, periodic at the sides, clamped at the base; E = 1, density 1, Poisson's ratio 0.35, alpha = beta = 0.002; striker of mass 3.4 at speed 1e-3; 512 implicit-midpoint steps of dt = 0.2",
    "width_12": {
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      "unknowns": 6438528,
      "tensor": {
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      "mumps_5_8_2_metis": {
        "seconds": 2872.1,
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      "pardiso_onemkl_2026_1_0": {
        "seconds": 2692.9,
        "memory_gib": 67.9
      },
      "comsol_documented_method_rebuilt": {
        "method": "generalized-alpha with Newton iterations on PARDISO, rebuilt on the same equations",
        "seconds": 6352.1,
        "memory_gib": 67.0
      },
      "versus_mumps": {
        "faster": 34,
        "less_memory": 31
      }
    },
    "agreement_widths_2_to_12": {
      "largest_difference": 4.1e-10,
      "total_contact_force": 8.8e-11,
      "same_contact_nodes_every_step": true
    },
    "width_120": {
      "elements": 106444800,
      "unknowns": 643852800,
      "tensor": {
        "seconds": 5081.3,
        "memory_gib": 1.8
      }
    },
    "width_384": {
      "elements": 1089994752,
      "unknowns": 6593052672,
      "tensor": {
        "seconds": 57012.3,
        "memory_gib": 1.8
      }
    },
    "memory_range_gib_widths_2_to_384": [
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    "nine_speed_design_study_width_12": {
      "tensor_seconds": 83.8,
      "pardiso_seconds": 17093.9,
      "faster": 204
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    "contact_force_stepping_error": {
      "implicit_midpoint_dt_0_2": "about 2.5%",
      "radau_iia_convolution_quadrature": "0.011%"
    }
  },
  "coupled_multiphysics": {
    "machine": "Google Cloud n2-standard-8, one processor per arm unless stated",
    "comparator": "a MOOSE application built for the same equations, framework commit 167ee97da2",
    "thermoelastic_cell_32_steps": [
      {
        "tetrahedra": 1840,
        "tensor": {
          "seconds": 4.46,
          "memory_mib": 308
        },
        "moose": {
          "seconds": 27.58,
          "memory_mib": 708
        },
        "faster": 6.2
      },
      {
        "tetrahedra": 2824,
        "tensor": {
          "seconds": 6.82,
          "memory_mib": 437
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        "moose": {
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          "memory_mib": 970
        },
        "faster": 6.4
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    ],
    "thermoelastic_agreement": 3.17e-13,
    "coupled_slab_growth": {
      "tetrahedra_range": [
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      "tensor_memory_gib": [
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        3.14
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      "moose_memory_gib_at_six_cells": 23.78,
      "moose_process_limit_gib": 26,
      "moose_reached_limit_at_cells": 9,
      "six_cells": {
        "tensor_seconds": 154.7,
        "moose_seconds": 1624.8
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    },
    "six_grid_nonlinear_two_impacts": {
      "date": "2026-11-02",
      "endpoints": 192,
      "grids": [
        {
          "grid": "1x1",
          "tetrahedra": 2824,
          "unknowns": 22285,
          "tensor": {
            "seconds": 147.94,
            "memory_mib": 480.27
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          "moose": {
            "seconds": 1150.35,
            "memory_mib": 476.25
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          "time_ratio": 7.78
        },
        {
          "grid": "2x1",
          "tetrahedra": 5648,
          "unknowns": 44569,
          "tensor": {
            "seconds": 293.11,
            "memory_mib": 486.14
          },
          "moose": {
            "seconds": 2319.0,
            "memory_mib": 694.5
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          "time_ratio": 7.91
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        {
          "grid": "2x2",
          "tetrahedra": 11296,
          "unknowns": 89137,
          "tensor": {
            "seconds": 557.95,
            "memory_mib": 513.25
          },
          "moose": {
            "seconds": 4659.13,
            "memory_mib": 1150.02
          },
          "time_ratio": 8.35
        },
        {
          "grid": "3x2",
          "tetrahedra": 16944,
          "unknowns": 133705,
          "tensor": {
            "seconds": 815.54,
            "memory_mib": 520.32
          },
          "moose": {
            "seconds": 6966.72,
            "memory_mib": 1599.82
          },
          "time_ratio": 8.54
        },
        {
          "grid": "3x3",
          "tetrahedra": 25416,
          "unknowns": 200557,
          "tensor": {
            "seconds": 1192.4,
            "memory_mib": 573.69
          },
          "moose": {
            "seconds": 10647.49,
            "memory_mib": 2301.43
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          "time_ratio": 8.93
        },
        {
          "grid": "4x3",
          "tetrahedra": 33888,
          "unknowns": 267409,
          "tensor": {
            "seconds": 1566.12,
            "memory_mib": 610.39
          },
          "moose": {
            "seconds": 14545.7,
            "memory_mib": 2998.34
          },
          "time_ratio": 9.29
        }
      ],
      "every_endpoint_passed": true
    },
    "million_element_nonlinear": {
      "dates": "2026-11-03 to 2026-11-04",
      "grid": "19x19",
      "tetrahedra": 1019464,
      "unknowns": 8044525,
      "tensor": {
        "seconds": 47005.04,
        "hours": 13.057,
        "memory_gib": 5.385
      },
      "machine": "Google Cloud n2-standard-8 (8 vCPUs, 32 GB), one solver processor",
      "every_endpoint_passed": true,
      "moose_projected": {
        "hours": [
          126.625,
          136.347
        ],
        "memory_gib": [
          34.598,
          56.797
        ],
        "grade": "projected from the six-grid records, frozen before the run"
      }
    }
  },
  "scope": "Measured records as published in section 85 of the cited preprint; the projected MOOSE values at a million elements are labelled as projections. The engine is the subject of U.S. Provisional Patent Application No. 64/190,840 and is not published."
}