{
  "model": "J1J2",
  "lattice": "honeycomb-7x7",
  "n_sites": 98,
  "boundary": "P",
  "params": {
    "J2": 0.2
  },
  "cluster": "7 x 7 rhombic two-site unit cells, periodic (arXiv:2110.06390 App. A.5.a Table I: b1 = 7 a1, b2 = 7 a2)",
  "instance_id": "J1J2/honeycomb-7x7_98_P_0.2",
  "rows": [
    {
      "energy": -177.4976,
      "sigma": 0.0784,
      "energy_variance": null,
      "dof": 98,
      "einf": 0,
      "v_score": null,
      "method": "VMC",
      "ansatz": "GNN",
      "method_detail": "",
      "method_as_published": "GNN (Table IV)",
      "family": "other NQS",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Kochkov, Pfaff, Sanchez-Gonzalez, Battaglia & Clark, Learning ground states of quantum Hamiltonians with graph networks, arXiv:2110.06390",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "source text of arXiv:2110.06390 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-20)",
        "reported_as": "-0.4528(2)",
        "note": "Table IV, Honeycomb, J2 = 0.2, N = 98, column GNN; version read: arXiv text; no journal version found (arXiv metadata) | Eq. (4) H = sum S_i.S_j + J2 sum S_i.S_j, spin-1/2, J1 = 1; Table IV '<E>/N', 'variational energies per spin'.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:2110.06390v1 PDF (pypdf layout mode) and the project's arXiv HTML (Table IV cells); only arXiv version, no journal (OpenAlex/Crossref 2026-10-24)",
          "location": "App. A.6.b Table IV, Honeycomb, J2 = 0.2, N = 98, column GNN",
          "reported_as": "-0.4528(2) (<E>/N, S.S units)",
          "conversion": "-0.4528 x 4 x 98 = -177.4976; sigma 2e-04 x 392 = 0.0784",
          "note": "Own computation (column order GNN 32/98, GNN-2 32/98, ResNet 32/98 confirmed in the HTML table); Eq. (4) S.S with J1 = 1, J2 = 0.2; 98-site cluster b1 = 7 a1, b2 = 7 a2, periodic (App. A.5.a Table I); Sz = 0; final MCMC estimate with 2x10^5 samples, variational, sampled; peer_reviewed false is right. No duplicate on the instance (the LCN paper's GNN/GNN-2 cells quote these and are not stored).",
          "source_entry": "famP6-shastrysutherland-j1j2-heisenberg#4 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -177.8112,
      "sigma": 0.196,
      "energy_variance": null,
      "dof": 98,
      "einf": 0,
      "v_score": null,
      "method": "VMC",
      "ansatz": "GNN",
      "method_detail": "GNN-2, separate amplitude and phase networks",
      "method_as_published": "GNN-2 (Table IV)",
      "family": "other NQS",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Kochkov, Pfaff, Sanchez-Gonzalez, Battaglia & Clark, Learning ground states of quantum Hamiltonians with graph networks, arXiv:2110.06390",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "source text of arXiv:2110.06390 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-20)",
        "reported_as": "-0.4536(5)",
        "note": "Table IV, Honeycomb, J2 = 0.2, N = 98, column GNN-2; version read: arXiv text; no journal version found (arXiv metadata) | Eq. (4) H = sum S_i.S_j + J2 sum S_i.S_j, spin-1/2, J1 = 1; Table IV '<E>/N', 'variational energies per spin'.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:2110.06390v1 PDF (pypdf layout mode) and the project's arXiv HTML (Table IV cells); only arXiv version, no journal (OpenAlex/Crossref 2026-10-24)",
          "location": "App. A.6.b Table IV, Honeycomb, J2 = 0.2, N = 98, column GNN-2",
          "reported_as": "-0.4536(5) (<E>/N, S.S units)",
          "conversion": "-0.4536 x 4 x 98 = -177.8112; sigma 5e-04 x 392 = 0.196",
          "note": "Own computation (column order GNN 32/98, GNN-2 32/98, ResNet 32/98 confirmed in the HTML table); Eq. (4) S.S with J1 = 1, J2 = 0.2; 98-site cluster b1 = 7 a1, b2 = 7 a2, periodic (App. A.5.a Table I); Sz = 0; final MCMC estimate with 2x10^5 samples, variational, sampled; peer_reviewed false is right. No duplicate on the instance (the LCN paper's GNN/GNN-2 cells quote these and are not stored).",
          "source_entry": "famP6-shastrysutherland-j1j2-heisenberg#5 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -176.2432,
      "sigma": 0.1568,
      "energy_variance": null,
      "dof": 98,
      "einf": 0,
      "v_score": null,
      "method": "VMC",
      "ansatz": "ResNet",
      "method_detail": "baseline of arXiv:2110.06390",
      "method_as_published": "ResNet (Table IV)",
      "family": "CNN / ResNet",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Kochkov, Pfaff, Sanchez-Gonzalez, Battaglia & Clark, Learning ground states of quantum Hamiltonians with graph networks, arXiv:2110.06390",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "source text of arXiv:2110.06390 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-20)",
        "reported_as": "-0.4496(4)",
        "note": "Table IV, Honeycomb, J2 = 0.2, N = 98, column ResNet; version read: arXiv text; no journal version found (arXiv metadata) | Eq. (4) H = sum S_i.S_j + J2 sum S_i.S_j, spin-1/2, J1 = 1; Table IV '<E>/N', 'variational energies per spin'.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:2110.06390v1 PDF (pypdf layout mode) and the project's arXiv HTML (Table IV cells); only arXiv version, no journal (OpenAlex/Crossref 2026-10-24)",
          "location": "App. A.6.b Table IV, Honeycomb, J2 = 0.2, N = 98, column ResNet",
          "reported_as": "-0.4496(4) (<E>/N, S.S units)",
          "conversion": "-0.4496 x 4 x 98 = -176.2432; sigma 4e-04 x 392 = 0.1568",
          "note": "Own computation (column order GNN 32/98, GNN-2 32/98, ResNet 32/98 confirmed in the HTML table); Eq. (4) S.S with J1 = 1, J2 = 0.2; 98-site cluster b1 = 7 a1, b2 = 7 a2, periodic (App. A.5.a Table I); Sz = 0; final MCMC estimate with 2x10^5 samples, variational, sampled; peer_reviewed false is right. No duplicate on the instance (the LCN paper's GNN/GNN-2 cells quote these and are not stored).",
          "source_entry": "famP6-shastrysutherland-j1j2-heisenberg#6 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -177.8896,
      "sigma": 0.1568,
      "energy_variance": null,
      "dof": 98,
      "einf": 0,
      "v_score": null,
      "method": "VMC",
      "ansatz": "LCN",
      "method_detail": "",
      "method_as_published": "LCN",
      "family": "CNN / ResNet",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Fu, Zhang, Zhang, Ling, Xu & Ji, Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems, Proc. 2024 SIAM Int. Conf. on Data Mining (SDM), pp. 490-498 (2024), arXiv:2206.07370",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "source text of arXiv:2206.07370 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-20)",
        "reported_as": "-0.4538(4)",
        "note": "Table 1, Honeycomb N = 98, J2 = 0.2, column LCN; version read: arXiv text (sources/2206.07370.txt); the journal version was not reached from this session, to be read on the verification pass (RULES.md 8) | Same Hamiltonian, lattices and references as arXiv:2110.06390 (Sec. 'Lattice': 'Following Kochkov et al. [27]'); Table 1 'energy per site'.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:2206.07370v1 (only arXiv version); SDM 2024 published text not reachable (epubs.siam.org HTTP 403)",
          "location": "Table 1 (p. 8), Honeycomb 98, J2 = 0.2, column 'LCN (ours)'",
          "reported_as": "-0.4538(4) (per site, S.S units)",
          "conversion": "-0.4538 x 392 = -177.8896; sigma 0.0004 x 392 = 0.1568",
          "note": "Value checked: Table 1 Honeycomb 98, J2 = 0.2, column 'LCN (ours)' prints -0.4538(4); -0.4538 x 392 = -177.8896 (stored -177.8896), sigma 0.0004 x 392 = 0.1568 (stored 0.1568); per site, S.S units (Reference column), Kochkov's periodic 98-site cluster, own computation, final 200,000-sample evaluation, variational. Published in refereed proceedings, Proc. 2024 SIAM SDM, pp. 490-498 (Crossref doi:10.1137/1.9781611978032.57); the SDM text itself was not read (epubs.siam.org 403).",
          "source_entry": "famP6-shastrysutherland-j1j2-heisenberg#9 (qmbl-verify 2026-10-23; skeptic upheld)"
        }
      }
    }
  ],
  "url": "https://qmbl.org/i/J1J2/honeycomb-7x7_98_P_0.2/",
  "per_site_divisor": 392,
  "per_site_label": "E/N (S.S)",
  "best": {
    "exact": null,
    "variational": {
      "energy": -177.8896,
      "sigma": 0.1568,
      "method": "VMC",
      "ansatz": "LCN",
      "method_detail": "",
      "reference": "Fu, Zhang, Zhang, Ling, Xu & Ji, Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems, Proc. 2024 SIAM Int. Conf. on Data Mining (SDM), pp. 490-498 (2024), arXiv:2206.07370",
      "bound_type": "variational",
      "energy_per_site": -0.4538
    },
    "projected": null,
    "extrapolated": null,
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -177.8896,
    "sigma": 0.1568,
    "method": "VMC",
    "ansatz": "LCN",
    "method_detail": "",
    "reference": "Fu, Zhang, Zhang, Ling, Xu & Ji, Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems, Proc. 2024 SIAM Int. Conf. on Data Mining (SDM), pp. 490-498 (2024), arXiv:2206.07370",
    "bound_type": "variational",
    "energy_per_site": -0.4538
  },
  "no_record_reason": null
}