{ "model": "Kitaev", "lattice": "honeycomb-6x6", "n_sites": 72, "boundary": "PO", "params": { "K": 1, "J": 0, "Gamma": 0 }, "cluster": "6 x 6 two-site unit cells on a cylinder, open along x and periodic along y (arXiv:2009.04129, Fig. 2(a))", "instance_id": "Kitaev/honeycomb-6x6_72_PO_K1", "rows": [ { "energy": -54.4698474903, "sigma": null, "energy_variance": null, "dof": 72, "einf": 0, "v_score": null, "method": "Exact solution", "ansatz": null, "method_detail": "free Majorana fermions, Wilson-loop sector Φy = +1", "method_as_published": "exact ground-state energy Eg(Φy = 1)", "family": "other", "bound_type": "exact", "bound_type_reason": "numerically exact reference as stated by the source (assigned during source reading)", "reference": "Jin, Tu & Zhou, Density matrix renormalization group boosted by Gutzwiller projected wave functions, Phys. Rev. B 104, L020409 (2021), doi:10.1103/PhysRevB.104.L020409, arXiv:2009.04129", "peer_reviewed": true, "source": "sweep-allresults-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:2009.04129 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": "-54.469847490329", "note": "Supplemental Material, numerical data for Fig. 3: Eg(Phi_y = 1) of the 6 x 6 cylinder; the Phi_y = -1 sector is higher (-54.385529432483, 'about 0.084' above, main text); version read: arXiv text (sources/2009.04129.txt); the journal version was not reached from this session, to be read on the verification pass (RULES.md 8) | Eq. (1) H3 = sum J_a sigma^a sigma^a + J3 sum sigma^x sigma^y sigma^z, Pauli matrices, J_a = 1, J3 = 0: K = +4 in the S = sigma/2 form, 4 times the instance's K = +1 (scale 4). Total energy of the 72-site cylinder (Supplemental Material, numerical data for Fig. 3); the boundary term of Eq. (S8) has deltaK -> 0+ and commutes with H3. QMBL's flux-free free-Majorana energy of the 6 x 6 cylinder gives -54.4698475.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "recomputed: free-Majorana solution, own code kitaev_majorana.py (numpy SVD per gauge class; torus: projection prod_j D_j = 1 via Pfaffian sign, checked against spin ED); checks/exact-recompute-2026-10-families/", "location": "recomputed (checks/exact-recompute-2026-10-families/)", "reported_as": "-54.469847490329", "conversion": "recomputed total (Pauli form, |K| = 1) -54.469847490329; stored -54.4698474903; difference -2.900e-11; printed-digit resolution of the stored total 5.0e-13", "note": "6 x 6 cylinder, flux-free; the two loop sectors give -54.469847490329 and -54.385529432483 (the source's Phi_y = -1 value, also reproduced); vortex configurations higher (gap 0.1166), so Eg(Phi_y = 1) is the global ground state; identical to all 12 printed decimals. Also read by famP7-kitaev-shastrysutherland#0 (arXiv:2009.04129v2 and v1 PDFs, pypdf layout mode (sources/2009.04129v{1,2}.famP7.txt); journal PRB 104, L020409 not reached (Cloudflare challenge page), arXiv v2 of 2021-05-04 read instead; Supplemental Material, 'Numerical data for Fig. 3 in the main text' (identical in v1 and v2); Eg(Φy = 1) =−54.469847490329): Eq. (1) Pauli form, Jx = Jy = Jz = 1, J3 = 0, sign + (K1 correct); 6 x 6 cylinder, Lx open, Ly periodic, N = 72; Phi_y = +1 sector, which the paper states is lower than Phi_y = -1 by about 0.084 (printed values differ by 0.0843181), so it is the cylinder ground state; boundary term deltaK -> 0+ commutes with H3; exact free-Majorana value, deterministic, no sigma; own computation (primary). No other row on the instance, no duplicate.", "source_entry": "famE-exact-recompute#4, famP7-kitaev-shastrysutherland#0 (qmbl-verify 2026-10-23)" } }, "normalised": { "factor": 4, "source_couplings": "H3 = +sum sigma^a sigma^a (Eq. 1, J_a = 1, J3 = 0, Pauli): K = +4 in the S = sigma/2 form", "note": "the source's Hamiltonian is 4 times the instance's; its printed energy (reported_as) is divided by 4" }, "corrections": [ { "field": "sampled", "to": false, "reported_as": "-54.469847490329", "location": "arXiv:2009.04129 Supplemental Material, numerical data for Fig. 3", "version_read": "arXiv text (sources/)", "conversion": "none", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate: the free-Majorana solution of the cylinder, printed to 12 decimals. The method string matches no deterministic marker, so the fallback in units.mjs read it as sampled (RULES.md 6).", "source_entry": "families pass 2026-10-20 (first reading and adversarial second reading)", "from": true } ], "sampled": false } ], "url": "https://qmbl.org/i/Kitaev/honeycomb-6x6_72_PO_K1/", "per_site_divisor": 288, "per_site_label": "E/N (S.S)", "best": { "exact": { "energy": -54.4698474903, "sigma": null, "method": "Exact solution", "ansatz": null, "method_detail": "free Majorana fermions, Wilson-loop sector Φy = +1", "reference": "Jin, Tu & Zhou, Density matrix renormalization group boosted by Gutzwiller projected wave functions, Phys. Rev. B 104, L020409 (2021), doi:10.1103/PhysRevB.104.L020409, arXiv:2009.04129", "bound_type": "exact", "energy_per_site": -0.189131414896875 }, "variational": null, "projected": null, "extrapolated": null, "approximate": null, "below_exact": [] }, "no_best_reason": null, "record": { "energy": -54.4698474903, "sigma": null, "method": "Exact solution", "ansatz": null, "method_detail": "free Majorana fermions, Wilson-loop sector Φy = +1", "reference": "Jin, Tu & Zhou, Density matrix renormalization group boosted by Gutzwiller projected wave functions, Phys. Rev. B 104, L020409 (2021), doi:10.1103/PhysRevB.104.L020409, arXiv:2009.04129", "bound_type": "exact", "energy_per_site": -0.189131414896875 }, "no_record_reason": null }