{
  "model": "TFIsing",
  "lattice": "square",
  "n_sites": 144,
  "boundary": "O",
  "params": {
    "h": 2
  },
  "instance_id": "TFIsing/square_144_O_2",
  "rows": [
    {
      "energy": -346.850000001,
      "sigma": 0.00864,
      "energy_variance": null,
      "dof": 144,
      "einf": 0,
      "v_score": null,
      "method": "2D RNN",
      "method_detail": "Euclidean cells",
      "method_as_published": "Euclidean 2DRNN",
      "family": "RNN",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "H. L. Dao, Two-dimensional Hyperbolic RNN Neural Quantum State, arXiv:2606.25600 (v1, 2026-06-24; v2, 2026-10-10)",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "−346.8500 (0.0087)",
        "note": "Table 5, row Euclidean 2DRNN , column Best, upper line (error in lower line); sources/2606.25600.txt line 779; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0087 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.",
        "secondary_of": null
      }
    },
    {
      "energy": -346.343300001,
      "sigma": 0.01872,
      "energy_variance": null,
      "dof": 144,
      "einf": 0,
      "v_score": null,
      "method": "2D RNN",
      "method_detail": "Lorentz (hyperbolic) cells, L_max = 2.0",
      "method_as_published": "Lorentz 2DRNN (L_max = 2.0)",
      "family": "RNN",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "H. L. Dao, Two-dimensional Hyperbolic RNN Neural Quantum State, arXiv:2606.25600 (v1, 2026-06-24; v2, 2026-10-10)",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "−346.3433 (0.0183)",
        "note": "Table 5, row Lorentz 2DRNN Lmax=2.0, column Best, upper line (error in lower line); sources/2606.25600.txt line 782; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0183 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.",
        "secondary_of": null
      }
    },
    {
      "energy": -346.4035,
      "sigma": 0.01728,
      "energy_variance": null,
      "dof": 144,
      "einf": 0,
      "v_score": null,
      "method": "2D RNN",
      "method_detail": "Lorentz (hyperbolic) cells, L_max = 6.0",
      "method_as_published": "Lorentz 2DRNN (L_max = 6.0)",
      "family": "RNN",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "H. L. Dao, Two-dimensional Hyperbolic RNN Neural Quantum State, arXiv:2606.25600 (v1, 2026-06-24; v2, 2026-10-10)",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "−346.4035 (0.0172)",
        "note": "Table 5, row Lorentz 2DRNN Lmax=6.0, column Best, upper line (error in lower line); sources/2606.25600.txt line 785; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0172 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.",
        "secondary_of": null
      }
    },
    {
      "energy": -346.9828,
      "sigma": null,
      "energy_variance": null,
      "dof": 144,
      "einf": 0,
      "v_score": null,
      "method": "DMRG",
      "method_detail": "",
      "method_as_published": "DMRG (not exact)",
      "family": "tensor network",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "H. L. Dao, Two-dimensional Hyperbolic RNN Neural Quantum State, arXiv:2606.25600 (v1, 2026-06-24; v2, 2026-10-10)",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-346.9828",
        "note": "Table 5, row DMRG (not exact); sources/2606.25600.txt line 788; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); the paper's own DMRG, labelled 'DMRG (not exact)'; no bond dimension, code or reference given | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/TFIsing/square_144_O_2/",
  "per_site_divisor": 144,
  "per_site_label": "E/N (Pauli)",
  "record": {
    "energy": -346.9828,
    "sigma": null,
    "method": "DMRG",
    "method_detail": "",
    "reference": "H. L. Dao, Two-dimensional Hyperbolic RNN Neural Quantum State, arXiv:2606.25600 (v1, 2026-06-24; v2, 2026-10-10)",
    "bound_type": "variational",
    "energy_per_site": -2.4096027777777778
  },
  "no_record_reason": null
}