{
  "model": "ShastrySutherland",
  "lattice": "square-tilted",
  "n_sites": 32,
  "boundary": "P",
  "params": {
    "J": 0.6772,
    "Jd": 1
  },
  "cluster": "32-site square cluster tilted by 45 degrees (periodic vectors (4,4) and (4,-4)), periodic boundaries; drawn in arXiv:cond-mat/0605464 Fig. 6 (second N = 32 cluster), distinct from its 4 x 8 stripe",
  "instance_id": "ShastrySutherland/square-tilted_32_P_J0.6772_Jd1",
  "rows": [
    {
      "energy": -48,
      "sigma": null,
      "energy_variance": null,
      "dof": 32,
      "einf": 0,
      "v_score": null,
      "method": "ED",
      "ansatz": null,
      "method_detail": "Lanczos",
      "method_as_published": "exact diagonalisation (Lanczos)",
      "family": "other",
      "bound_type": "exact",
      "bound_type_reason": "numerically exact reference as stated by the source (assigned during source reading)",
      "reference": "Sindermann, Löw & Zittartz, Ground state properties of two spin models with exactly known ground states on the square lattice, Int. J. Mod. Phys. C 17, 1085 (2006), doi:10.1142/S0129183106009709, arXiv:cond-mat/0605464",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "source text of arXiv:cond-mat/0605464 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": "-0.374999999999945",
        "note": "Table I (square N = 32), x = 0.6772; version read: arXiv text (sources/cond-mat-0605464.txt); the journal version was not reached from this session, to be read on the verification pass (RULES.md 8) | Eq. (1) H = J2 sum S.S (square bonds) + J1 sum S.S (diagonal dimer bonds), x = J2/J1, E0/N per site in units of J1 (the Fig. 1 caption swaps the labels; the tables fix them: E0/N = -0.375, the dimer-product energy, for all x below xc, and x = 0.8 equals the 6 x 6 ED of arXiv:2311.16889).",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "recomputed: own Lanczos ed.c, Sz = 0 basis of the 32-site tilted cluster (601080390 states), dimer state deflated; checks/exact-recompute-2026-10-families/",
          "location": "recomputed (checks/exact-recompute-2026-10-families/)",
          "reported_as": "-0.374999999999945",
          "conversion": "recomputed -48.0000000000; stored -48; difference 0.00e+00",
          "note": "Lowest state orthogonal to the dimer-singlet product state: E1 = -47.9971979211 after 218 Lanczos steps (last 10 steps moved it by about 1e-10; Ritz values are upper bounds). The dimer state is an exact eigenstate at E = -48. Printed value x 128 = -47.99999999999. Cluster: tilted torus (4,4),(4,-4), orthogonal dimers. E1 lies 2.802e-03 above -48, so the ground state is the dimer state, E0 = -48 exactly (Pauli total; -0.375 per site in S units). The stored value is the exact -48. Also read by famP2-10-1142-s0129183106009709#4 (arXiv:cond-mat/0605464v1 PDF, pypdf layout mode (shared cache sources/cond-mat-0605464v1.layout.txt), checked against the plain extraction, the project's sources/cond-mat-0605464.txt and a 110 dpi render of page 11; Table I (square N = 32, left half), row J2/J1 = 0.6772; -0.374999999999945 (E0/N, per site, units of J1 = Jd, S.S form)): Value, x = J2/J1 = J/Jd, N, periodic boundaries, bound_type exact and method agree. Hamiltonian Eq. (1) in spin-1/2 S operators, J1 on the diagonal dimer bonds (E0/N = -0.375 = -3/8 J1 below xc fixes the dimer bond as the unit; the Fig. 1 caption swaps the labels). Cluster: the 32-site square cluster of Fig. 6 (second N = 32 row, diamond drawing); its Table III sector dimension 75,164,451 equals exactly the Burnside count for the (4,4),(4,-4) torus with the translations (2,2),(2,-2), Sz = 0 and spin inversion, so QMBL's tilted instance is consistent. Sector: the caption calls it 'the subspace containing the ground state' (Sz = 0, momentum, spin inversion). journal version (Int. J. Mod. Phys. C 17, 1085 (2006)) not reached: worldscientific.com /doi/pdf, /doi/epdf and /doi/abs all returned HTTP 403 with a Cloudflare JavaScript challenge on 2026-10-24; arXiv:cond-mat/0605464v1 (the only arXiv version, comment 'to appear in IJMPC 17') read alone. x is below this cluster's xc: the printed value is the Lanczos result 5.5e-14 per site above the dimer-product eigenvalue -0.375 (analytic total -48); the stored value reproduces the printed number, the 36-site rows above J = 0.5 keep the printed value (not recomputed; ruled 2026-10-24). Duplicate check (data/ShastrySutherland/square-tilted_32_P_J0.6772_Jd1.json, read-only): no other row on the instance carries this number.",
          "source_entry": "famE-exact-recompute#11, famP2-10-1142-s0129183106009709#4 (qmbl-verify 2026-10-23)"
        }
      },
      "corrections": [
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-0.374999999999945",
          "location": "arXiv:cond-mat/0605464 Table I (square N = 32), x = 0.6772",
          "version_read": "the row's published method string (arXiv text, sources/cond-mat-0605464.txt)",
          "conversion": "none",
          "checked_on": "2026-10-25",
          "reason": "Deterministic: an exact (Lanczos) diagonalization carries no statistical error, but the label \"exact diagonalisation (Lanczos)\" matches none of isSampled's deterministic markers, so the row read as a sampled energy without an error bar; set as on the t-J Lanczos rows (ruled 2026-10-25).",
          "source_entry": "ruling of 2026-10-25 on the families port: sampled false on the cond-mat/0605464 exact rows",
          "from": true
        }
      ],
      "sampled": false
    }
  ],
  "url": "https://qmbl.org/i/ShastrySutherland/square-tilted_32_P_J0.6772_Jd1/",
  "per_site_divisor": 128,
  "per_site_label": "E/N (S.S)",
  "best": {
    "exact": {
      "energy": -48,
      "sigma": null,
      "method": "ED",
      "ansatz": null,
      "method_detail": "Lanczos",
      "reference": "Sindermann, Löw & Zittartz, Ground state properties of two spin models with exactly known ground states on the square lattice, Int. J. Mod. Phys. C 17, 1085 (2006), doi:10.1142/S0129183106009709, arXiv:cond-mat/0605464",
      "bound_type": "exact",
      "energy_per_site": -0.375
    },
    "variational": null,
    "projected": null,
    "extrapolated": null,
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -48,
    "sigma": null,
    "method": "ED",
    "ansatz": null,
    "method_detail": "Lanczos",
    "reference": "Sindermann, Löw & Zittartz, Ground state properties of two spin models with exactly known ground states on the square lattice, Int. J. Mod. Phys. C 17, 1085 (2006), doi:10.1142/S0129183106009709, arXiv:cond-mat/0605464",
    "bound_type": "exact",
    "energy_per_site": -0.375
  },
  "no_record_reason": null
}