{
  "model": "tJ",
  "lattice": "square",
  "n_sites": 64,
  "boundary": "P",
  "params": {
    "t": 1,
    "J": 0.2,
    "N_up": 25,
    "N_dn": 25,
    "nn_term": true
  },
  "cluster": "8 x 8 torus (arXiv:cond-mat/0104067 Table I and 'periodic boundary condition', line 577)",
  "instance_id": "tJ/square_64_P_h14_J0.2",
  "rows": [
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      "energy": -41.2352,
      "sigma": 0.0064,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL0 on the d-wave RVB state with antiferromagnetic correlation, power 0",
      "method_as_published": "PL0, power = 0",
      "family": "AFQMC / GFMC",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
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        "reported_as": "-0.6443(1)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL0, power 0 (line 410); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
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          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 0, column PL0 (shared layout line 410, page 8)",
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          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#0 (qmbl-verify 2026-10-23)"
        }
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      "energy": -42.9376,
      "sigma": 0.0064,
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      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
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      "method_detail": "PL1 on the d-wave RVB state with antiferromagnetic correlation, power 0",
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      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
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        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "-0.6709(1)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL1, power 0 (line 410); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
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          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 0, column PL1 (shared layout line 410, page 8)",
          "reported_as": "-0.6709(1) (per site, units of t)",
          "conversion": "-0.6709 per site x 64 sites = -42.9376 (stored -42.9376); sigma 0.0001 x 64 = 0.0064 (stored 0.0064); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#1 (qmbl-verify 2026-10-23)"
        }
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    },
    {
      "energy": -43.6416,
      "sigma": 0.0704,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
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      "method_detail": "PL2 on the d-wave RVB state with antiferromagnetic correlation, power 0",
      "method_as_published": "PL2, power = 0",
      "family": "AFQMC / GFMC",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
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        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "-0.6819(11)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL2, power 0 (line 410); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
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          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 0, column PL2 (shared layout line 410, page 8)",
          "reported_as": "-0.6819(11) (per site, units of t)",
          "conversion": "-0.6819 per site x 64 sites = -43.6416 (stored -43.6416); sigma 0.0011 x 64 = 0.0704 (stored 0.0704); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#2 (qmbl-verify 2026-10-23)"
        }
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    {
      "energy": -42.0672,
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      "method": "Power-Lanczos",
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      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
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        "reported_as": "-0.6573(4)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL0, power 2 (line 411); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
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          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 2, column PL0 (shared layout line 411, page 8)",
          "reported_as": "-0.6573(4) (per site, units of t)",
          "conversion": "-0.6573 per site x 64 sites = -42.0672 (stored -42.0672); sigma 0.0004 x 64 = 0.0256 (stored 0.0256); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#3 (qmbl-verify 2026-10-23)"
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      "method": "Power-Lanczos",
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      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
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        "reported_as": "-0.6768(2)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL1, power 2 (line 411); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
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          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 2, column PL1 (shared layout line 411, page 8)",
          "reported_as": "-0.6768(2) (per site, units of t)",
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          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#4 (qmbl-verify 2026-10-23)"
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      "method": "Power-Lanczos",
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        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "-0.6833(11)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL2, power 2 (line 411); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 2, column PL2 (shared layout line 411, page 8)",
          "reported_as": "-0.6833(11) (per site, units of t)",
          "conversion": "-0.6833 per site x 64 sites = -43.7312 (stored -43.7312); sigma 0.0011 x 64 = 0.0704 (stored 0.0704); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#5 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -42.6048,
      "sigma": 0.0384,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL0 on the d-wave RVB state with antiferromagnetic correlation, power 4",
      "method_as_published": "PL0, power = 4",
      "family": "AFQMC / GFMC",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "-0.6657(6)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL0, power 4 (line 412); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 4, column PL0 (shared layout line 412, page 8)",
          "reported_as": "-0.6657(6) (per site, units of t)",
          "conversion": "-0.6657 per site x 64 sites = -42.6048 (stored -42.6048); sigma 0.0006 x 64 = 0.0384 (stored 0.0384); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#6 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -43.5392,
      "sigma": 0.0384,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL1 on the d-wave RVB state with antiferromagnetic correlation, power 4",
      "method_as_published": "PL1, power = 4",
      "family": "AFQMC / GFMC",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "-0.6803(6)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL1, power 4 (line 412); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 4, column PL1 (shared layout line 412, page 8)",
          "reported_as": "-0.6803(6) (per site, units of t)",
          "conversion": "-0.6803 per site x 64 sites = -43.5392 (stored -43.5392); sigma 0.0006 x 64 = 0.0384 (stored 0.0384); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#7 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -43.8464,
      "sigma": 0.1856,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL2 on the d-wave RVB state with antiferromagnetic correlation, power 4",
      "method_as_published": "PL2, power = 4",
      "family": "AFQMC / GFMC",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "-0.6851(29)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL2, power 4 (line 412); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 4, column PL2 (shared layout line 412, page 8)",
          "reported_as": "-0.6851(29) (per site, units of t)",
          "conversion": "-0.6851 per site x 64 sites = -43.8464 (stored -43.8464); sigma 0.0029 x 64 = 0.1856 (stored 0.1856); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#8 (qmbl-verify 2026-10-23)"
        }
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    {
      "energy": -43.104,
      "sigma": 0.0576,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL0 on the d-wave RVB state with antiferromagnetic correlation, power 6",
      "method_as_published": "PL0, power = 6",
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      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "-0.6735(9)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL0, power 6 (line 413); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
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          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 6, column PL0 (shared layout line 413, page 8)",
          "reported_as": "-0.6735(9) (per site, units of t)",
          "conversion": "-0.6735 per site x 64 sites = -43.104 (stored -43.104); sigma 0.0009 x 64 = 0.0576 (stored 0.0576); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#9 (qmbl-verify 2026-10-23)"
        }
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    },
    {
      "energy": -43.648,
      "sigma": 0.0512,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL1 on the d-wave RVB state with antiferromagnetic correlation, power 6",
      "method_as_published": "PL1, power = 6",
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      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "-0.6820(8)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL1, power 6 (line 413); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
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          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 6, column PL1 (shared layout line 413, page 8)",
          "reported_as": "-0.6820(8) (per site, units of t)",
          "conversion": "-0.682 per site x 64 sites = -43.648 (stored -43.648); sigma 0.0008 x 64 = 0.0512 (stored 0.0512); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#10 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -43.3216,
      "sigma": 0.0768,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL0 on the d-wave RVB state with antiferromagnetic correlation, power 8",
      "method_as_published": "PL0, power = 8",
      "family": "AFQMC / GFMC",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "-0.6769(12)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL0, power 8 (line 414); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 8, column PL0 (shared layout line 414, page 8)",
          "reported_as": "-0.6769(12) (per site, units of t)",
          "conversion": "-0.6769 per site x 64 sites = -43.3216 (stored -43.3216); sigma 0.0012 x 64 = 0.0768 (stored 0.0768); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#11 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -43.872,
      "sigma": 0.0832,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL1 on the d-wave RVB state with antiferromagnetic correlation, power 8",
      "method_as_published": "PL1, power = 8",
      "family": "AFQMC / GFMC",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "-0.6855(13)",
        "note": "Table I, 50 electrons on 8 x 8, J/t = 0.2, PL1, power 8 (line 414); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Table I ('Power-Lanczos energies of J/t = 0.2 for 50 electrons in a 8 x 8 lattice'), row power 8, column PL1 (shared layout line 414, page 8); the same number is Table II row 50/64, column E_PL (line 499), one row",
          "reported_as": "-0.6855(13) (per site, units of t)",
          "conversion": "-0.6855 per site x 64 sites = -43.872 (stored -43.872); sigma 0.0013 x 64 = 0.0832 (stored 0.0832); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type variational agrees: E(p) = <H^(2p+1)>/<H^(2p)> (page 4) is the energy of the state H^p|PL_n>, PL_n being n Lanczos steps on the d-wave RVB + AF trial state with C1 (C2) optimised variationally (Eqs. 31-35), pure estimator, no fixed node; the paper states 'the energy calculated from the power-Lanczos method is still a variational estimate and an upper bound of the ground state energy' (lines 391-393); the sign problem enlarges the error bar, it does not bias the estimator",
          "source_entry": "tjP3-10-1016-s0022-3697-01#12 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -44.0384,
      "sigma": 0.224,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL0 on the d-wave RVB state, exponential fit of the energies to infinite power",
      "method_as_published": "PL0, power → ∞ (exponential fit)",
      "family": "AFQMC / GFMC",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "−0.6881(35)",
        "note": "text below Fig. 6: E0 of the fit of the PL0 energies to infinite power, 50 electrons on 8 x 8, J/t = 0.2 (line 458); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Sec. II end, text after Eq. (36) 'E = E0 + ae^{-bp}', shared layout lines 458-459 (Fig. 6 shows the fit curves)",
          "reported_as": "E0 = −0.6881(35), a = 0.0438(33), and a = 0.174(26) (per site, units of t)",
          "conversion": "-0.6881 per site x 64 sites = -44.0384 (stored -44.0384); sigma 0.0035 x 64 = 0.224 (stored 0.224); t = 1 in the source, factor 1",
          "note": "Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type extrapolated agrees (fit of E(p) to p -> infinity, Eq. 36; no state reached it); an unweighted least-squares fit of E0 + a exp(-b p) to the five Table I PL0 points (p = 0..8) gives E0 = -0.6881, a = 0.0438, b = 0.175, the printed values; the third parameter printed as 'a = 0.174(26)' is b (a typo in the paper); an error-weighted fit gives E0 = -0.6883",
          "source_entry": "tjP3-10-1016-s0022-3697-01#13 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -44.1856,
      "sigma": 0.3072,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL1 on the d-wave RVB state, exponential fit of the energies to infinite power",
      "method_as_published": "PL1, power → ∞ (exponential fit)",
      "family": "AFQMC / GFMC",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0104067 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 (2026-10-22)",
        "reported_as": "−0.6904(48)",
        "note": "text below Fig. 6: E0 of the fit of the PL1 energies to infinite power, 50 electrons on 8 x 8, J/t = 0.2 (line 459); version read: arXiv text (sources/cond-mat-0104067.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum (c~+c~ + h.c.) + J sum (S_i.S_j - n_i n_j / 4); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0104067v1 (the only arXiv version), PDF in the shared cache sources/cond-mat-0104067v1.pdf (md5 135746f0..., identical to the project's sources/cond-mat-0104067.pdf), re-extracted independently on 2026-10-24 with pypdf layout mode (identical to sources/cond-mat-0104067v1.layout.txt, whose line numbers are cited). Journal version J. Phys. Chem. Solids 62(9-10), 1797-1811 (2001) not reached: doi.org resolves to ScienceDirect, whose article and /pdfft pages return 403 on 2026-10-24; arXiv version alone",
          "location": "Sec. II end, text after Eq. (36), shared layout lines 459-460 (Fig. 6 shows the fit curves)",
          "reported_as": "E0 = −0.6904(48), a = 0.0193(46), and b = 0.158(70) for PL1 energies (per site, units of t)",
          "conversion": "-0.6904 per site x 64 sites = -44.1856 (stored -44.1856); sigma 0.0048 x 64 = 0.3072 (stored 0.3072); t = 1 in the source, factor 1",
          "note": "RECORD ROW of tJ/square_64_P_h14_J0.2 (lowest unflagged; an extrapolation, 1 sigma below the lowest variational row PL1 power 8 at -43.872). Eq. (1) H = -t sum (c~+ c~ + h.c.) + J sum (S_i.S_j - 1/4 n_i n_j), each nearest-neighbour pair once, is the instance Hamiltonian (nn_term true, no shift; the paper's e_H = -1.169J per site in Sec. IV = -0.669 - 0.5 confirms the -n n/4 term); t = 1, J/t = 0.2; 50 electrons with Ne/2 up and Ne/2 down (Eq. 9) = N_up = N_dn = 25 (closed shell on the 8 x 8 torus: 1+4+4+4+8+4 = 25 k-points); 8 x 8 lattice (Table I caption), 'uniform trial wave functions and periodic boundary conditions' (line 577) and 'the same lattices and boundary conditions as those used by HM' (page 2), boundary P; energy per site in units of t (Table I unlabelled; per site from Eq. 37 'E x Ns' and Table II's comparison with Hellberg-Manousakis' per-site -0.6825(23); per site and not per electron, since 50/90 at -0.9184 per site is only consistent with a per-site kinetic energy); own computation; the only other rows on data/tJ/square_64_P_h14_J0.2.json are this group's 15, no duplicate; bound_type extrapolated agrees (fit of E(p) to p -> infinity, Eq. 36; no state reached it); an unweighted least-squares fit of E0 + a exp(-b p) to the five Table I PL1 points (p = 0..8) gives E0 = -0.6904, a = 0.0193, b = 0.159, the printed values; an error-weighted fit (1/sigma^2 from Table I) gives E0 = -0.6865, a = 0.0156, b = 0.236, 0.8 printed sigma above; the printed (48) is the fit-parameter error of a 3-parameter fit to 5 points",
          "source_entry": "tjP3-10-1016-s0022-3697-01#14 (qmbl-verify 2026-10-23)"
        }
      }
    }
  ],
  "url": "https://qmbl.org/i/tJ/square_64_P_h14_J0.2/",
  "per_site_divisor": 64,
  "per_site_label": "E/site",
  "best": {
    "exact": null,
    "variational": {
      "energy": -43.872,
      "sigma": 0.0832,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL1 on the d-wave RVB state with antiferromagnetic correlation, power 8",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "bound_type": "variational",
      "energy_per_site": -0.6855
    },
    "projected": null,
    "extrapolated": {
      "energy": -44.1856,
      "sigma": 0.3072,
      "method": "Power-Lanczos",
      "ansatz": null,
      "method_detail": "PL1 on the d-wave RVB state, exponential fit of the energies to infinite power",
      "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
      "bound_type": "extrapolated",
      "energy_per_site": -0.6904
    },
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -44.1856,
    "sigma": 0.3072,
    "method": "Power-Lanczos",
    "ansatz": null,
    "method_detail": "PL1 on the d-wave RVB state, exponential fit of the energies to infinite power",
    "reference": "Shih, Chen & Lee, Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Solids 62, 1797 (2001), doi:10.1016/S0022-3697(01)00112-3, arXiv:cond-mat/0104067",
    "bound_type": "extrapolated",
    "energy_per_site": -0.6904
  },
  "no_record_reason": null
}