{
  "model": "HEG2D",
  "lattice": "triangular",
  "n_sites": 169,
  "boundary": "P",
  "params": {
    "N_up": 169,
    "N_dn": 0,
    "rs": 30,
    "twist": "Gamma"
  },
  "instance_id": "HEG2D/triangular_169_P_169_0_30",
  "rows": [
    {
      "energy": -5.3834612,
      "sigma": 0.0000338,
      "energy_variance": null,
      "dof": 169,
      "einf": null,
      "v_score": null,
      "method": "Slater-Jastrow-backflow",
      "method_detail": "",
      "method_as_published": "SJB-VMC (Slater-Jastrow-backflow)",
      "family": "backflow / Pfaffian",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Gaggioli, Azadi & Fu, Accurate Self-Attention Wavefunctions at Large Scale, arXiv:2607.08616",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2607.08616 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": "−0.0318548(2)",
        "note": "Table I (main text), N_e=169 rs=30, row SJB-VMC, column E; sources/2607.08616.txt line 70; printed in Ha per electron; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Ha per electron, triangular cell, Gamma point ('we did not apply twist averaging'). The paper's E minus its E_corr gives HF = -0.0273098 Ha per electron at N = 91, rs = 30, which QMBL's HF energy reproduces to all seven digits (Madelung term included).",
        "secondary_of": null
      }
    },
    {
      "energy": -5.3944293,
      "sigma": 0.0000169,
      "energy_variance": null,
      "dof": 169,
      "einf": null,
      "v_score": null,
      "method": "Fixed-node DMC",
      "method_detail": "trial state: Slater-Jastrow-backflow; extrapolated: Δτ → 0",
      "method_as_published": "SJB-DMC (fixed-node DMC on the SJB nodes)",
      "family": "DMC",
      "bound_type": "projected",
      "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)",
      "reference": "Gaggioli, Azadi & Fu, Accurate Self-Attention Wavefunctions at Large Scale, arXiv:2607.08616",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2607.08616 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": "−0.0319197(1)",
        "note": "Table I (main text), N_e=169 rs=30, row SJB-DMC, column E; sources/2607.08616.txt line 71; printed in Ha per electron; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Ha per electron, triangular cell, Gamma point ('we did not apply twist averaging'). The paper's E minus its E_corr gives HF = -0.0273098 Ha per electron at N = 91, rs = 30, which QMBL's HF energy reproduces to all seven digits (Madelung term included).",
        "secondary_of": null
      }
    },
    {
      "energy": -5.39461013,
      "sigma": 0.00000507,
      "energy_variance": null,
      "dof": 169,
      "einf": null,
      "v_score": null,
      "method": "Self-attention NQS",
      "method_detail": "spatially weighted particle attention",
      "method_as_published": "NN-VMC (self-attention wave function)",
      "family": "transformer / ViT",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Gaggioli, Azadi & Fu, Accurate Self-Attention Wavefunctions at Large Scale, arXiv:2607.08616",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2607.08616 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": "−0.03192077(3)",
        "note": "Table I (main text), N_e=169 rs=30, row NN-VMC, column E; sources/2607.08616.txt line 72; printed in Ha per electron; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Ha per electron, triangular cell, Gamma point ('we did not apply twist averaging'). The paper's E minus its E_corr gives HF = -0.0273098 Ha per electron at N = 91, rs = 30, which QMBL's HF energy reproduces to all seven digits (Madelung term included).",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/HEG2D/triangular_169_P_169_0_30/",
  "per_site_divisor": 169,
  "per_site_label": "E/N (Ha)",
  "record": {
    "energy": -5.39461013,
    "sigma": 0.00000507,
    "method": "Self-attention NQS",
    "method_detail": "spatially weighted particle attention",
    "reference": "Gaggioli, Azadi & Fu, Accurate Self-Attention Wavefunctions at Large Scale, arXiv:2607.08616",
    "bound_type": "variational",
    "energy_per_site": -0.03192077
  },
  "no_record_reason": null
}