{
  "model": "TFIsing",
  "lattice": "square",
  "n_sites": 64,
  "boundary": "O",
  "params": {
    "h": 3
  },
  "instance_id": "TFIsing/square_64_O_3",
  "rows": [
    {
      "energy": -202.423,
      "sigma": 0.0096,
      "energy_variance": null,
      "dof": 64,
      "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": "−202.4230 (0.0099)",
        "note": "Table 2, row Euclidean 2DRNN , column Best, upper line (error in lower line); sources/2606.25600.txt line 471; 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, 0.0099 | 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": -202.4597,
      "sigma": 0.00768,
      "energy_variance": null,
      "dof": 64,
      "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": "−202.4597 (0.0074)",
        "note": "Table 2, row Lorentz 2DRNN Lmax=2.0, column Best, upper line (error in lower line); sources/2606.25600.txt line 474; 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, 0.0074 | 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": -202.5077,
      "sigma": null,
      "energy_variance": null,
      "dof": 64,
      "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": "-202.5077",
        "note": "Table 2, row DMRG (not exact); sources/2606.25600.txt line 477; 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
      }
    },
    {
      "energy": -201.4058,
      "sigma": 0.03136,
      "energy_variance": null,
      "dof": 64,
      "einf": 0,
      "v_score": null,
      "method": "RNN",
      "method_detail": "Euclidean cells, 1D on the unrolled lattice",
      "method_as_published": "Euclidean RNN (1D, unrolled 2D lattice)",
      "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": "-201.4058 (0.0314)",
        "note": "Table 8, row Euclidean RNN, column (N,N)=(8,8); error in the line below; sources/2606.25600.txt line 1037; 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, 0.0314 | 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": -201.7627,
      "sigma": 0.02688,
      "energy_variance": null,
      "dof": 64,
      "einf": 0,
      "v_score": null,
      "method": "RNN",
      "method_detail": "Poincaré (hyperbolic) cells, 1D on the unrolled lattice",
      "method_as_published": "Poincare RNN (1D, unrolled 2D lattice)",
      "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": "-201.7627 (0.0269)",
        "note": "Table 8, row Poincare RNN, column (N,N)=(8,8); error in the line below; sources/2606.25600.txt line 1039; 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, 0.0269 | 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": -201.5256,
      "sigma": 0.03136,
      "energy_variance": null,
      "dof": 64,
      "einf": 0,
      "v_score": null,
      "method": "RNN",
      "method_detail": "Lorentz (hyperbolic) cells, 1D on the unrolled lattice",
      "method_as_published": "Lorentz RNN (1D, unrolled 2D lattice)",
      "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": "-201.5256 (0.0315)",
        "note": "Table 8, row Lorentz RNN, column (N,N)=(8,8); error in the line below; sources/2606.25600.txt line 1041; 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, 0.0315 | 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": -200.9939,
      "sigma": 0.04416,
      "energy_variance": null,
      "dof": 64,
      "einf": 0,
      "v_score": null,
      "method": "RNN",
      "method_detail": "GRU, Euclidean cells, 1D on the unrolled lattice",
      "method_as_published": "Euclidean GRU (1D, unrolled 2D lattice)",
      "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": "-200.9939 (0.0441)",
        "note": "Table 8, row Euclidean GRU, column (N,N)=(8,8); error in the line below; sources/2606.25600.txt line 1043; 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, 0.0441 | 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": -201.7624,
      "sigma": 0.02944,
      "energy_variance": null,
      "dof": 64,
      "einf": 0,
      "v_score": null,
      "method": "RNN",
      "method_detail": "GRU, Poincaré (hyperbolic) cells, 1D on the unrolled lattice",
      "method_as_published": "Poincare GRU (1D, unrolled 2D lattice)",
      "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": "-201.7624 (0.0296)",
        "note": "Table 8, row Poincare GRU, column (N,N)=(8,8); error in the line below; sources/2606.25600.txt line 1045; 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, 0.0296 | 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": -200.8296,
      "sigma": 0.0448,
      "energy_variance": null,
      "dof": 64,
      "einf": 0,
      "v_score": null,
      "method": "RNN",
      "method_detail": "GRU, Lorentz (hyperbolic) cells, 1D on the unrolled lattice",
      "method_as_published": "Lorentz GRU (1D, unrolled 2D lattice)",
      "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": "-200.8296 (0.0445)",
        "note": "Table 8, row Lorentz GRU, column (N,N)=(8,8); error in the line below; sources/2606.25600.txt line 1047; 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, 0.0445 | 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_64_O_3/",
  "per_site_divisor": 64,
  "per_site_label": "E/N (Pauli)",
  "record": {
    "energy": -202.5077,
    "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": -3.1641828125
  },
  "no_record_reason": null
}