{
  "model": "Hubbard",
  "lattice": "rectangular-4x12",
  "n_sites": 48,
  "boundary": "P",
  "params": {
    "Nf": 21,
    "U": 8
  },
  "instance_id": "Hubbard/rectangular-4x12_48_P_21_8",
  "rows": [
    {
      "energy": -36.77184,
      "sigma": 0.00048,
      "energy_variance": null,
      "dof": 42,
      "einf": 73.5,
      "v_score": null,
      "method": "HFPS",
      "method_detail": "GCNN",
      "method_as_published": "HFPS + GCNN (Table IV)",
      "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": "A. Chen, Z.-Q. Wan, A. Sengupta, A. Georges & C. Roth, Neural Network-Augmented Pfaffian Wave-functions for Scalable Simulations of Interacting Fermions, Proc. Natl. Acad. Sci. 123, e2535288123 (2026), arXiv:2507.10705, doi:10.1073/pnas.2535288123",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2507.10705 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": "-0.76608(1)",
        "note": "TABLE IV, 12x4 row; sources/2507.10705.txt line 970; version read: arXiv v1 (sources/2507.10705.txt); PNAS copy not reached (Cloudflare 403, 2026-10-16) | Eq. (15): H = -t sum_<ij> + U sum n_up n_dn, t = 1, t' = 0, periodic; all tables per site (E/Nsite).",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Hubbard/rectangular-4x12_48_P_21_8/",
  "per_site_divisor": 48,
  "per_site_label": "E/site",
  "record": {
    "energy": -36.77184,
    "sigma": 0.00048,
    "method": "HFPS",
    "method_detail": "GCNN",
    "reference": "A. Chen, Z.-Q. Wan, A. Sengupta, A. Georges & C. Roth, Neural Network-Augmented Pfaffian Wave-functions for Scalable Simulations of Interacting Fermions, Proc. Natl. Acad. Sci. 123, e2535288123 (2026), arXiv:2507.10705, doi:10.1073/pnas.2535288123",
    "bound_type": "variational",
    "energy_per_site": -0.76608
  },
  "no_record_reason": null
}