{
  "schema": "TENSOR.PUBLIC.EVIDENCE.v1",
  "product": "Tensor Grid",
  "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": [
      "27.2",
      "28.5",
      "28.6",
      "84"
    ]
  },
  "machine": "one desktop computer",
  "dates": "2026-10-07 to 2026-10-08",
  "public_cases": "PGLib-OPF v23.07",
  "dc_atlas_1000000_buses": {
    "family": "rectangular DC mesh family of section 27.2, 1,024 to 1,000,000 buses",
    "firm_mw": 115,
    "single_line_outages": 1998000,
    "certificate_bytes": [
      785,
      794
    ],
    "tensor": {
      "query_ms": 0.0202,
      "memory_mib": 25.27
    },
    "warm_highs": {
      "query_ms": 605.607,
      "memory_mib": 2818.25
    },
    "memory_reduction_percent": 99.1,
    "grade": "conditional DC headroom: static, each outage redispatched independently, no load shed, no project curtailed",
    "demand_box_mw": {
      "q_every_bus": [
        0,
        10
      ],
      "r_alternating_buses_and_project": [
        0,
        5
      ]
    },
    "query_speedup": 29925,
    "highs": "HiGHS 1.15.1, one solver thread, model and basis retained across queries",
    "startup_seconds": {
      "tensor_all_1998000_outages_proved": 16.502,
      "warm_highs_one_outage_prepared": 15.366
    },
    "conditional_120_mw": "safe throughout the demand box with the network intact; with either project-incident line out, safe exactly when q + r <= 10 MW and physically infeasible above that line",
    "queries_100000_seconds_by_size": {
      "1024": 2.601,
      "4096": 2.733,
      "16384": 2.866,
      "62500": 3.095,
      "250000": 3.266,
      "1000000": 2.575
    }
  },
  "ac_atlas_1000000_buses": {
    "family": "AC mesh family of section 28.6, 2% demand growth",
    "guaranteed_mw": 27.529101,
    "proved_upper_bound_mw": 28.0,
    "single_line_outages": 1998000,
    "certificate_bytes": 439,
    "tensor": {
      "query_microseconds": 6.52,
      "memory_mib": 25.98
    },
    "warm_newton_with_replay": {
      "query_seconds": 3.094,
      "memory_mib": 211.73
    },
    "query_speedup": 474474
  },
  "dc_opf_exact_certificates": {
    "public_cases_certified": 14,
    "public_cases_attempted": 14,
    "largest_buses": 78484,
    "largest_build_seconds": 108.0,
    "largest_verify_seconds": 68.7,
    "result": "certified optimal and independently verified"
  },
  "dc_opf_250000_bus_mesh": {
    "tensor": {
      "seconds": 3.15,
      "memory_gib": 0.6
    },
    "sparse_mehrotra_interior_point": {
      "seconds": 481.89,
      "memory_gib": 4.08
    },
    "faster": 153
  },
  "ac_opf_250000_bus_mesh": {
    "tensor": {
      "memory_gib": 10.29
    },
    "mips_python": {
      "memory_gib": 22.36
    },
    "memory_reduction_percent": 54.0
  },
  "ac_opf_qualification": {
    "jobs_accepted": 297,
    "jobs": 297,
    "public_cases": 66,
    "meshes": 6,
    "note": "MIPS failed on case8387_pegase"
  },
  "scope": "Measured records from sections 27.2, 28.5, 28.6, and 84 of the cited preprint and the same 7-8 October 2026 runs, on PGLib-OPF v23.07 public cases and synthetic meshed network families with declared generation at every bus. DC headroom is conditional DC headroom; AC headroom is static nonlinear feasibility. The engine is the subject of U.S. Provisional Patent Application No. 64/190,840 and is not published.",
  "pglib14_dc_guard": {
    "network": "PGLib-OPF case14 (IEEE 14-bus), conservative DC guard study",
    "new_load_bus_14_mw": 61.1,
    "background_demand_bus_3_mw": [
      0,
      10
    ],
    "network_states": [
      "intact",
      "line 4-9 out",
      "line 9-14 out"
    ],
    "limit": "with line 9-14 out the project sits behind the 76 MW line 13-14, with 14.9 MW of local demand",
    "new_generation_companion_study_mw": 90.9
  },
  "pglib14_ac_headroom": {
    "network": "PGLib-OPF case14 (IEEE 14-bus), full nonlinear AC with every original voltage, generator P/Q, Rate-A MVA, and angle limit",
    "new_load_bus_14_mw": 4,
    "background_growth_percent": [
      0,
      2
    ],
    "network_states": [
      "intact",
      "line 9-14 out",
      "line 13-14 out"
    ],
    "proof_cells": 18
  }
}