{ "model": "Hchain", "lattice": "chain", "n_sites": 10, "boundary": "O", "params": { "N_up": 5, "N_dn": 5, "R": 3.2, "basis": "none" }, "instance_id": "Hchain/chain_10_O_R3.2_none", "rows": [ { "energy": -5.24997, "sigma": 0.0007, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "ph-AFQMC", "ansatz": null, "method_detail": "multi-determinant trial (spinon excitations on the UHF state, k = 1); extrapolated: 1/M → 0 (complete basis)", "method_as_published": "AFQMC [phaseless, multi-determinant trial (spinon excitations on the UHF state, k = 1); extrapolated: complete basis set]", "family": "AFQMC / GFMC", "bound_type": "extrapolated", "bound_type_reason": "extrapolated to the complete basis set or to zero truncation error; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52499(7) per atom", "note": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/AFQMC_CBS: -5.24997 0.000706798 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null }, "corrections": [ { "field": "method_detail", "from": "phaseless; extrapolated: complete basis set", "to": "phaseless, multi-determinant trial (spinon excitations on the UHF state, k = 1); extrapolated: complete basis set", "checked_on": "2026-10-24", "reported_as": "-0.52499(7) per atom", "location": "Table III (first block), R = 3.2 row, AFQMC column (journal p. 031059-20); method from Appendix A", "version_read": "PRX 7, 031059 (2017), journal text sources/1705.01608-PhysRevX.7.031059.txt (published 2017-09-28, corrected 2021-03-24); arXiv:1705.01608v2 (dated 2017-11-08), sources/1705.01608.txt; dataset github.com/simonsfoundation/hydrogen-benchmark-PRX commit b99a183 (data committed in d54c7fa, 2017-10-09, by the first author)", "conversion": "none (method string only)", "reason": "Appendix A (p. 031059-15): \"For the two largest bond lengths (R = 3.2 and 3.6), motivated by the analogy between the H chain and the Heisenberg model, we employ in this work a new form of trial wave function, a linear combination of spinon excitations on top of the UHF state [...] We use k = 1, 2 for R = 3.2, 3.6, respectively.\" Sec. IV B (p. 031059-8): \"In AFQMC, a multideterminant trial wave function is used in the dissociation region (last two points, R > 3) as discussed in Sec. A, which improves its accuracy by ~0.36 mEHa over that with the UHF trial wave function (shown as half filled red circles).\" The dataset's AFQMC_CBS value lies above the single-determinant (AFQMC-SD) cc-pV5Z value and below the multi-determinant (AFQMC-MD) one: CBS -5.24997 vs MD 5Z -5.2494, SD 5Z -5.2525; a basis-set limit cannot sit above its own 5Z value, so the CBS number is the extrapolation of the MD series.", "source_entry": "h-motta17-afqmc-c1#59 (qmbl-verify 2026-10-23/24, correction; skeptic upheld)" }, { "field": "energy", "from": -5.2499, "to": -5.24997, "checked_on": "2026-10-24", "reported_as": "-0.52499(7) per atom", "location": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275", "version_read": "PRX 7, 031059 (2017) journal text and arXiv:1705.01608v2 text (the cells agree); data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183 (sources/1705.01608-data-b99a183.tsv), file N_10_OBC/R_3.2/AFQMC_CBS", "conversion": "repository total -5.24997 / 10 = -0.524997 per atom; the printed -0.52499 is that value truncated to 5 decimals, not rounded; per atom -0.52499 -> -0.524997, stored as totals (x 10)", "reason": "Ruling 1 (2026-10-24): where the paper's table truncates and the authors' data repository prints more digits, the row stores the repository digits; the printed value stays as reported_as.", "source_entry": "ruling 1, 2026-10-24" } ] }, { "energy": -5.2512, "sigma": 0.0006, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "DMET", "ansatz": null, "method_detail": "fragment of 2 atoms; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "DMET [fragment of 2 atoms; extrapolated: complete basis set]", "family": "other", "bound_type": "extrapolated", "bound_type_reason": "extrapolated to the complete basis set or to zero truncation error; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52512(6) per atom", "note": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/DMET_2_CBS: -5.25123 0.000606248 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null }, "sampled": false, "corrections": [ { "field": "sampled", "to": false, "reported_as": "-0.52512(6) per atom", "location": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/DMET_2_CBS: -5.25123 0.000606248", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.24987, "sigma": 0.00007, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "LR-DMC", "ansatz": "AGP", "method_detail": "cc-pVTZ trial basis", "method_as_published": "LR-DMC [AGP trial state, cc-pVTZ trial basis]", "family": "DMC", "bound_type": "projected", "bound_type_reason": "AFQMC, fixed-node or lattice-regularised DMC, coupled cluster, MRCI+Q or an embedding method; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.524987(7) per atom", "note": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/LRDMC_AGP_basis-TZ: -5.24987250108512 6.840897035041683E-005 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "PRX 7, 031059 journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608 text (sources/1705.01608.txt), regex parse in node; dataset github.com/simonsfoundation/hydrogen-benchmark-PRX b99a183 raw file fetched from raw.githubusercontent.com and the committed TSV", "location": "Table III (first block, H10 CBS), row R = 3.2, column LR-DMC(AGP); journal txt line 1293, arXiv txt line 1275; dataset N_10_OBC/R_3.2/LRDMC_AGP_basis-TZ", "reported_as": "-0.524987(7) per atom (journal and arXiv identical); dataset \"-5.24987250108512 6.840897035041683E-005\" (total, second number its uncertainty)", "conversion": "-0.524987 x 10 = -5.24987 Ha total; sigma 7e-6 x 10 = 7e-5 Ha. Dataset -5.24987250108512/10 = -0.524987250 rounds to the printed value; dataset bar 6.841e-6/atom rounds to the printed bar.", "note": "Instance chain, open boundary (dataset folder N_10_OBC; Table III is the finite H10 molecule), basis-free (real-space fixed-node LR-DMC, RULES 13.1), neutral S_z = 0 by RULES 13.1 default (no other sector stated). bound_type projected per RULES 13.4 (lattice-regularised DMC); the paper presents the a -> 0 limit of the lattice regularisation (Appendix A 2 b), i.e. the fixed-node energy. Trial state AGP Slater determinant/AGP with Jastrow, determinant basis cc-pVTZ per the dataset file name (basis-TZ, README 'TZ : cc-pVTZ'). Not a record row; no other LR-DMC row or same-number row on this instance in passes/track3 (data/Hchain does not exist, track 3 held).", "secondary_of": null, "source_entry": "h-motta17-lr-dmc#25 (qmbl-verify 2026-10-23/24, verified)" } } }, { "energy": -5.24974, "sigma": 0.00009, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "LR-DMC", "ansatz": "LDA determinant", "method_detail": "cc-pVTZ trial basis", "method_as_published": "LR-DMC [LDA trial state, cc-pVTZ trial basis]", "family": "DMC", "bound_type": "projected", "bound_type_reason": "AFQMC, fixed-node or lattice-regularised DMC, coupled cluster, MRCI+Q or an embedding method; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.524974(9) per atom", "note": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/LRDMC_LDA_basis-TZ: -5.24973919682442 9.869193738861033E-005 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "PRX 7, 031059 journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608 text (sources/1705.01608.txt), regex parse in node; dataset github.com/simonsfoundation/hydrogen-benchmark-PRX b99a183 raw file fetched from raw.githubusercontent.com and the committed TSV", "location": "Table III (first block, H10 CBS), row R = 3.2, column LR-DMC(LDA); journal txt line 1293, arXiv txt line 1275; dataset N_10_OBC/R_3.2/LRDMC_LDA_basis-TZ", "reported_as": "-0.524974(9) per atom (journal and arXiv identical); dataset \"-5.24973919682442 9.869193738861033E-005\" (total, second number its uncertainty)", "conversion": "-0.524974 x 10 = -5.24974 Ha total; sigma 9e-6 x 10 = 9e-5 Ha. Dataset -5.24973919682442/10 = -0.524973920 rounds to the printed value; dataset bar 9.869e-6/atom does not round to the printed last digit (9), off by one in the last digit; stored follows the printed (journal) bar.", "note": "Instance chain, open boundary (dataset folder N_10_OBC; Table III is the finite H10 molecule), basis-free (real-space fixed-node LR-DMC, RULES 13.1), neutral S_z = 0 by RULES 13.1 default (no other sector stated). bound_type projected per RULES 13.4 (lattice-regularised DMC); the paper presents the a -> 0 limit of the lattice regularisation (Appendix A 2 b), i.e. the fixed-node energy. Trial state LDA Slater determinant/AGP with Jastrow, determinant basis cc-pVTZ per the dataset file name (basis-TZ, README 'TZ : cc-pVTZ'). Not a record row; no other LR-DMC row or same-number row on this instance in passes/track3 (data/Hchain does not exist, track 3 held).", "secondary_of": null, "source_entry": "h-motta17-lr-dmc#26 (qmbl-verify 2026-10-23/24, verified)" } } }, { "energy": -5.25, "sigma": 0.0005, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "MRCI-F12+Q", "ansatz": null, "method_detail": "(10,10) CASSCF reference, Davidson and F12 corrections; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "MRCI-F12+Q [(10,10) CASSCF reference, Davidson and F12 corrections; extrapolated: complete basis set]", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "extrapolated to the complete basis set or to zero truncation error; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52500(5) per atom", "note": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/MRCI+Q+F12_CBS: -5.250000 0.000458 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "PRX 7, 031059 (2017) journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2 text (sources/1705.01608.txt, v2 stamp read from the PDF with pypdf); data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183, files re-fetched from GitHub (sources/1705.01608-data-raw-misc-1.json in the run folder), identical to the committed TSV; pdftotext layout text as committed, cells compared by script (tsvcheck.mjs) and by eye", "location": "Table III (first block), column MRCI+Q+F12, row R = 3.2", "reported_as": "-0.52500(5) per atom (Hartree)", "conversion": "-0.52500 x 10 = -5.2500 Ha total; sigma 5e-05 x 10 = 0.0005 Ha", "note": "value, sigma (fit uncertainty of the CBS extrapolation, 'combined uncertainty estimated from the fitting procedures', Sec. IV C), N = 10, OBC, basis = none (CBS limit, RULES.md §13.1/§13.4) and bound_type extrapolated agree; journal and arXiv v2 cells identical; dataset N_10_OBC/R_3.2/MRCI+Q+F12_CBS = '-5.250000 0.000458' agrees within the table's last digit. Sec. IV C: 'The final CBS results are verified with a separate set of MRCI + Q calculations augmented by F12 explicit correlation ... extrapolated using the same procedure as above.'", "secondary_of": null, "source_entry": "h-motta17-misc-1#18 (qmbl-verify 2026-10-23/24, verified)" } }, "sampled": false, "corrections": [ { "field": "sampled", "to": false, "reported_as": "-0.52500(5) per atom", "location": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/MRCI+Q+F12_CBS: -5.250000 0.000458", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.24995, "sigma": 0.0006, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "MRCI+Q", "ansatz": null, "method_detail": "(10,10) CASSCF reference, Davidson correction; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "MRCI+Q [(10,10) CASSCF reference, Davidson correction; extrapolated: complete basis set]", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "extrapolated to the complete basis set or to zero truncation error; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52499(6) per atom", "note": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/MRCI+Q_CBS: -5.249950 0.000619 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "arXiv:1705.01608 (sources/1705.01608.txt, layout text) and journal PRX 7, 031059 (2017) (sources/1705.01608-PhysRevX.7.031059.txt); dataset github.com/simonsfoundation/hydrogen-benchmark-PRX commit b99a183 (sources/1705.01608-data-b99a183.tsv); compared by out/h-motta17-mrci-q/check2.mjs", "location": "Table III first block, R = 3.2 row, column MRCI+Q (arXiv line 1275, journal line 1293); dataset N_10_OBC/R_3.2/MRCI+Q_CBS", "reported_as": "-0.52499(6) (Hartree per atom; journal prints the same cell)", "conversion": "-0.52499 x 10 = -5.2499 Ha total; sigma 0.00006 x 10 = 0.0006; dataset -5.249950 0.000619 (total) agrees to the printed digits", "note": "CBS extrapolation of MRCI+Q (RHF exponential + correlation alpha + beta/x^3, Eqs. 4-6) from 4 cc-pVxZ points (x = 2..5; Table IV); reproduced from the dataset's MRCI+Q and RHF values to within the stated uncertainty (unweighted fit). N = 10, OBC, neutral S_z = 0, R in bohr, nuclear repulsion included; basis = none and bound_type extrapolated per RULES 13.4. sigma is the CBS fit uncertainty, not a statistical error.", "secondary_of": null, "source_entry": "h-motta17-mrci-q#50 (qmbl-verify 2026-10-23/24, verified)" } }, "sampled": false, "corrections": [ { "field": "energy", "from": -5.2499, "to": -5.24995, "checked_on": "2026-10-24", "reported_as": "-0.52499(6) per atom", "location": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275", "version_read": "PRX 7, 031059 (2017) journal text and arXiv:1705.01608v2 text (the cells agree); data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183 (sources/1705.01608-data-b99a183.tsv), file N_10_OBC/R_3.2/MRCI+Q_CBS", "conversion": "repository total -5.249950 / 10 = -0.5249950 per atom; the printed -0.52499 is that value truncated to 5 decimals, not rounded; per atom -0.52499 -> -0.524995, stored as totals (x 10)", "reason": "Ruling 1 (2026-10-24): where the paper's table truncates and the authors' data repository prints more digits, the row stores the repository digits; the printed value stays as reported_as.", "source_entry": "ruling 1, 2026-10-24" }, { "field": "sampled", "to": false, "reported_as": "-0.52499(6) per atom", "location": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/MRCI+Q_CBS: -5.249950 0.000619", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.23025, "sigma": 0.0009, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "PC-NEVPT2", "ansatz": null, "method_detail": "(10,10) CASSCF reference; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "PC-NEVPT2 [(10,10) CASSCF reference; extrapolated: complete basis set]", "family": "FCIQMC / CC", "bound_type": "approximate", "bound_type_reason": "finite-order perturbation theory, GW, or a perturbative correction to coupled cluster (track 3, 2026-10-21); error of unknown sign (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52302(9) per atom", "note": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/PC-NEVPT2_CBS: -5.23025 0.000913586 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "arXiv:1705.01608v2 (2017-11-06; project PDF re-extracted with pypdf layout mode, out/h-motta17-pc-nevpt2/arxiv_layout.txt, byte-identical to sources/1705.01608.txt) and journal PRX 7, 031059 (2017) (publisher PDF fetched 2026-10-24 into the shared cache, sources/1705.01608-PhysRevX.7.031059.pdf, pypdf layout mode, out/h-motta17-pc-nevpt2/journal_layout.txt); dataset github.com/simonsfoundation/hydrogen-benchmark-PRX commit b99a183, every NEVPT2 file fetched raw from GitHub (sources/1705.01608-data-raw-pc-nevpt2.json) and compared with the committed TSV by out/h-motta17-pc-nevpt2/check.mjs", "location": "Table III, first block, R = 3.2 row, column PC-NEVPT2 (arXiv layout line 1275, journal layout line 1199); dataset file N_10_OBC/R_3.2/PC-NEVPT2_CBS", "reported_as": "-0.52302(9) (Hartree per atom; journal prints -0.52302(9) identically, arXiv v2 the same)", "conversion": "-0.52302 x 10 = -5.2302 Ha total; dataset -5.23025 0.000913586 (total) = -0.523025 per atom, the table truncates it to 5 decimals (table - dataset/10 = 0.000005)", "note": "basis = none instance (CBS extrapolation, RULES 13.1); method_detail '; extrapolated: complete basis set' right and bound_type approximate right (RULES 13.4: an approximate method stays approximate under CBS extrapolation). Re-derived: RHF_CBS -4.8695081 + alpha from a least-squares fit of E_corr,x = alpha + beta/x^3 to the dataset's PC-NEVPT2 - RHF energies at x = 2, 3, 4 (paper Eqs. 4-6) gives -5.229989, 0.26 mHa total from the dataset CBS -5.23025, so the value is the PC-NEVPT2 extrapolation over cc-pVDZ/TZ/QZ. Printed error (9) vs dataset uncertainty 9.14e-5 per atom: 9.14 in the last digit. No duplicate on the instance.", "secondary_of": null, "source_entry": "h-motta17-pc-nevpt2#33 (qmbl-verify 2026-10-23/24, verified)" } }, "sampled": false, "corrections": [ { "field": "sigma", "from": null, "to": 0.0009, "checked_on": "2026-10-24", "reported_as": "-0.52302(9) per atom", "location": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275", "version_read": "PRX 7, 031059 (2017) journal text and arXiv:1705.01608v2 text (the cells agree); data repository b99a183 for comparison", "conversion": "printed (..) read per atom: 0.00009 Ha per atom; per atom null -> 0.00009, stored as totals (x 10)", "reason": "Ruling 2 (2026-10-24): the printed complete-basis fit uncertainty of an approximate CBS row is stored as sigma, as on the paper's extrapolated CBS rows; the journal print wins where print and repository disagree. The generator dropped it (scripts/track3/motta2017.mjs, fixed).", "source_entry": "h-motta17-pc-nevpt2#34 (qmbl-verify 2026-10-23/24, ambiguous); ruling 2, 2026-10-24" }, { "field": "energy", "from": -5.2302, "to": -5.23025, "checked_on": "2026-10-24", "reported_as": "-0.52302(9) per atom", "location": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275", "version_read": "PRX 7, 031059 (2017) journal text and arXiv:1705.01608v2 text (the cells agree); data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183 (sources/1705.01608-data-b99a183.tsv), file N_10_OBC/R_3.2/PC-NEVPT2_CBS", "conversion": "repository total -5.23025 / 10 = -0.523025 per atom; the printed -0.52302 is that value truncated to 5 decimals, not rounded; per atom -0.52302 -> -0.523025, stored as totals (x 10)", "reason": "Ruling 1 (2026-10-24): where the paper's table truncates and the authors' data repository prints more digits, the row stores the repository digits; the printed value stays as reported_as.", "source_entry": "ruling 1, 2026-10-24" }, { "field": "sampled", "to": false, "reported_as": "-0.52302(9) per atom", "location": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/PC-NEVPT2_CBS: -5.23025 0.000913586", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.2574, "sigma": 0.001, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "RCCSD(T)", "ansatz": null, "method_detail": "extrapolated: 1/M → 0 (complete basis)", "method_as_published": "RCCSD(T) [extrapolated: complete basis set]", "family": "FCIQMC / CC", "bound_type": "approximate", "bound_type_reason": "finite-order perturbation theory, GW, or a perturbative correction to coupled cluster (track 3, 2026-10-21); error of unknown sign (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52574(10) per atom", "note": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/RCCSD(T)_CBS: -5.25742 0.000972659 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null }, "sampled": false, "corrections": [ { "field": "sigma", "from": null, "to": 0.001, "checked_on": "2026-10-24", "reported_as": "-0.52574(10) per atom (Hartree)", "location": "Table III (CBS), column RCCSD(T), row R = 3.2; journal text and arXiv v2 text print the same cell '-0.52574(10)'; dataset file N_10_OBC/R_3.2/RCCSD(T)_CBS = '-5.25742 0.000972659'", "version_read": "journal Phys. Rev. X 7, 031059 (2017; published 2017-09-28, corrected 2021-03-24), publisher PDF text qmbl-wt-hydrogen/sources/1705.01608-PhysRevX.7.031059.txt; arXiv:1705.01608v2 (dated 2017-11-08, PDF stamp 'arXiv:1705.01608v2'), sources/1705.01608.txt; table cells parsed with python (out/h-motta17-rccsd-t--c1/compare.py)", "conversion": "printed (10) on the fifth decimal = 0.00010 Ha per atom; total sigma 0.0010 Ha. Dataset second number 0.000972659 (total) = 0.000097 per atom; per atom null -> 0.0001, stored as totals (x 10)", "reason": "The paper states the CBS value comes 'with a combined uncertainty estimated from the fitting procedures' (Sec. IV C, journal lines 477-479) and prints it in Table III. The generator keeps that uncertainty for every non-sampled CBS row whose bound_type is extrapolated (RCCSD, UCCSD, RHF, UHF CBS rows from the same table keep it) but drops it here only because §13.4 keeps CCSD(T) CBS approximate: line 125 tests bound_type, not CBS. The stated fit uncertainty belongs to the CBS extrapolation, not to the method class.", "source_entry": "h-motta17-rccsd-t--c1#41 (qmbl-verify 2026-10-23/24, correction; skeptic upheld)" }, { "field": "sampled", "to": false, "reported_as": "-0.52574(10) per atom", "location": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/RCCSD(T)_CBS: -5.25742 0.000972659", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.2419, "sigma": 0.0008, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "RCCSD", "ansatz": null, "method_detail": "extrapolated: 1/M → 0 (complete basis)", "method_as_published": "RCCSD [extrapolated: complete basis set]", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "extrapolated to the complete basis set or to zero truncation error; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52419(8) per atom", "note": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/RCCSD_CBS: -5.2419 0.000786923 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "journal PRX 7, 031059 (2017) publisher PDF, pypdf layout extraction (raw/journal-layout.txt), cross-read with the project text sources/1705.01608-PhysRevX.7.031059.txt; arXiv:1705.01608v2 PDF (dated November 8, 2017), pypdf layout (raw/arxiv-layout.txt) and sources/1705.01608.txt; data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183, files fetched raw from GitHub 2026-10-24 (raw/rccsd-files-b99a183.json) and compared with sources/1705.01608-data-b99a183.tsv by check.mjs", "location": "Table III (CBS), second block, column RCCSD, row R = 3.2; journal p. 031059-20 (my layout text line 1231; project journal text line 1305); arXiv v2 Table III (layout line 1309; sources/1705.01608.txt line 1288); dataset file N_10_OBC/R_3.2/RCCSD_CBS", "reported_as": "-0.52419(8) per atom (journal and arXiv v2 identical); dataset N_10_OBC/R_3.2/RCCSD_CBS: -5.2419 0.000786923", "conversion": "-0.52419 x 10 = -5.2419 Ha (total, nuclear repulsion included); sigma 0.000080 x 10 = 0.00080 Ha total; dataset -5.2419 0.000786923 -> -0.5241900 per atom, which the table rounds and truncates to print", "note": "Instance agrees: equally spaced H10 chain, open, R = 3.2 bohr, basis = none (CBS extrapolation of the cc-pVxZ sequence, Sec. IV C), N_up = N_dn = 5. bound_type extrapolated (RULES 13.4), sampled false, sigma 0.00008 per atom = the printed fit uncertainty agree. Same-instance values in the dataset: MRCI+Q -5.24995, AFQMC -5.24997; the row lies above the MRCI+Q, AFQMC and LR-DMC CBS values printed in Table III at this R. The cc-pVDZ input at R = 3.2 is itself below the DZ DMRG/MRCI+Q values (see the defect on chain_10_O_R3.2_ccpvdz); a refit of Eqs. (4)-(6) with DZ/TZ/QZ (cbs_refit.py) gives -5.24156, so the DZ point probably enters this extrapolation; the CBS value is not below the SBDMRG -0.52511(14) or MRCI+Q -0.52499(6) per atom, so no flag. Duplicate scan: no data/Hchain file exists (track 3 held); no row from another batch on this instance carries this number.", "secondary_of": null, "source_entry": "h-motta17-rccsd-c1#40 (qmbl-verify 2026-10-23/24, verified)" } }, "sampled": false, "corrections": [ { "field": "sampled", "to": false, "reported_as": "-0.52419(8) per atom", "location": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/RCCSD_CBS: -5.2419 0.000786923", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -4.8695081, "sigma": 0.0000531, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "HF", "ansatz": null, "method_detail": "restricted; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "RHF [extrapolated: complete basis set]", "family": "mean field", "bound_type": "extrapolated", "bound_type_reason": "extrapolated to the complete basis set or to zero truncation error; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0; source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-4.8695081 0.0000531 (total for N = 10; second number the stated uncertainty)", "note": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_10_OBC/R_3.2/RHF_CBS in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX b99a183, raw file fetched from raw.githubusercontent.com (raw-rhf-b99a183.json) and compared with the committed TSV; Eq. (4) of the journal text refitted to the dataset's RHF cc-pVDZ..cc-pV5Z totals (cbs_fit.py, cbs_err.py)", "location": "dataset file N_10_OBC/R_3.2/RHF_CBS (number first printed in the dataset; the paper prints no RHF CBS table, journal Sec. IV C Eq. (4) defines it)", "reported_as": "-4.8695081 0.0000531 (total Hartree for N = 10; second number the fit uncertainty)", "conversion": "total -4.8695081 Ha; per atom -4.8695081/10 = -0.48695081 (stored eps identical); uncertainty 0.0000531 Ha total, 0.0000053100 per atom (stored sigma_per_site identical)", "note": "Reproduced: an unweighted least-squares fit of E_RHF,x = A + B exp(-xC) to the dataset's RHF cc-pVDZ, TZ, QZ, 5Z totals gives A = -4.8695081 and standard error of A (1 degree of freedom, s^2 = RSS) = 0.0000531, i.e. the dataset's two numbers to 1e-7. Fig. 11 caption: the Hartree-Fock energy \"is fitted to an exponential function of the index x = 2, 3, 4, 5 of the cc-pVxZ basis\". So the second number is the 1-sigma fit standard error of the total, not a statistical error bar. Instance chain N = 10, open (folder N_10_OBC), R = 3.2 bohr, basis = none (CBS row, RULES 13.1), N_up = N_dn = 5 (Sec. II 'We only consider spin-unpolarized systems, with N_up = N_dn = N/2'). bound_type extrapolated per RULES 13.4. No same-number row from another batch on this instance (the UHF CBS row, same paper, is a separate fit of the UHF energies).", "secondary_of": null, "source_entry": "h-motta17-rhf-c1#48 (qmbl-verify 2026-10-23/24, verified)" } }, "sampled": false, "corrections": [ { "field": "sampled", "to": false, "reported_as": "-4.8695081 0.0000531 (total for N = 10; second number the stated uncertainty)", "location": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_10_OBC/R_3.2/RHF_CBS in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.25114, "sigma": 0.0014, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "SBDMRG", "ansatz": null, "method_detail": "sliced basis, grid spacing 0.1; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "SBDMRG [sliced basis, grid spacing 0.1; extrapolated: complete basis set]", "family": "tensor network", "bound_type": "extrapolated", "bound_type_reason": "extrapolated to the complete basis set or to zero truncation error; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52511(14) per atom", "note": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/SBDMRG_CBS: -5.25114 0.00140136 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "PRX 7, 031059 (2017) journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2 text (sources/1705.01608.txt, v2 stamp read from the PDF with pypdf); data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183, files re-fetched from GitHub (sources/1705.01608-data-raw-misc-1.json in the run folder), identical to the committed TSV; pdftotext layout text as committed, cells compared by script (tsvcheck.mjs) and by eye", "location": "Table III (second block), column SBDMRG, row R = 3.2", "reported_as": "-0.52511(14) per atom (Hartree)", "conversion": "-0.52511 x 10 = -5.2511 Ha total; sigma 0.00014 x 10 = 0.0014 Ha", "note": "value, sigma (fit uncertainty of the CBS extrapolation, 'combined uncertainty estimated from the fitting procedures', Sec. IV C), N = 10, OBC, basis = none (CBS limit, RULES.md §13.1/§13.4) and bound_type extrapolated agree; journal and arXiv v2 cells identical; dataset N_10_OBC/R_3.2/SBDMRG_CBS = '-5.25114 0.00140136' agrees within the table's last digit. Method detail 'grid spacing 0.1' is from Appendix A 1 b ('For the data presented in Sec. V B, we use a grid spacing of a = 0.1, for which we estimate an error of about 0.1 mEHa per atom'), stated for the CBS data.", "secondary_of": null, "source_entry": "h-motta17-misc-1#53 (qmbl-verify 2026-10-23/24, verified)" } }, "sampled": false, "corrections": [ { "field": "energy", "from": -5.2511, "to": -5.25114, "checked_on": "2026-10-24", "reported_as": "-0.52511(14) per atom", "location": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288", "version_read": "PRX 7, 031059 (2017) journal text and arXiv:1705.01608v2 text (the cells agree); data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183 (sources/1705.01608-data-b99a183.tsv), file N_10_OBC/R_3.2/SBDMRG_CBS", "conversion": "repository total -5.25114 / 10 = -0.525114 per atom; the printed -0.52511 is that value truncated to 5 decimals (here equal to its rounding; the column truncates elsewhere and never rounds differently); per atom -0.52511 -> -0.5251140000000001, stored as totals (x 10)", "reason": "Ruling 1 (2026-10-24): where the paper's table truncates and the authors' data repository prints more digits, the row stores the repository digits; the printed value stays as reported_as.", "source_entry": "ruling 1, 2026-10-24" }, { "field": "sampled", "to": false, "reported_as": "-0.52511(14) per atom", "location": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/SBDMRG_CBS: -5.25114 0.00140136", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.2299, "sigma": 0.0009, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "SC-NEVPT2", "ansatz": null, "method_detail": "(10,10) CASSCF reference; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "SC-NEVPT2 [(10,10) CASSCF reference; extrapolated: complete basis set]", "family": "FCIQMC / CC", "bound_type": "approximate", "bound_type_reason": "finite-order perturbation theory, GW, or a perturbative correction to coupled cluster (track 3, 2026-10-21); error of unknown sign (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52299(9) per atom", "note": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/SC-NEVPT2_CBS: -5.2299 0.000912688 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "PRX 7, 031059 journal PDF (sources/1705.01608-PhysRevX.7.031059.pdf), pypdf layout mode; arXiv text sources/1705.01608.txt line-for-line identical in this column; dataset raw file fetched at b99a183", "location": "Table III (first block), R = 3.2 row, column SC-NEVPT2 (journal page 20; extracted line: \"3.2 −0.52499ð7Þ −0.52512ð6Þ −0.524987ð7Þ −0.524974ð9Þ −0.52499ð6Þ −0.52500ð5Þ −0.52302ð9Þ −0.52299ð9Þ\")", "reported_as": "-0.52299(9) per atom", "conversion": "-0.52299 x 10 = -5.2299 (total, Hartree); dataset file N_10_OBC/R_3.2/SC-NEVPT2_CBS: \"-5.2299 0.000912688\" (total, then the fit uncertainty), per atom -0.5229900; table minus dataset 0", "note": "Table III value agrees with the authors' dataset within the table's truncation to five decimals (the table truncates: R = 2.0, 2.8, 3.6 dataset -0.560995, -0.535045, -0.514037 print as -0.56099, -0.53504, -0.51403); CBS extrapolation of a perturbative method on the basis = none instance stays approximate (RULES 13.4); N = 10 open chain, R in bohr, Hartree, nuclear repulsion included; method_detail correct. See the ambiguous entry on the dropped extrapolation uncertainty.", "secondary_of": null, "source_entry": "h-motta17-sc-nevpt2#33 (qmbl-verify 2026-10-23/24, verified)" } }, "sampled": false, "corrections": [ { "field": "sigma", "from": null, "to": 0.0009, "checked_on": "2026-10-24", "reported_as": "-0.52299(9) per atom", "location": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275", "version_read": "PRX 7, 031059 (2017) journal text and arXiv:1705.01608v2 text (the cells agree); data repository b99a183 for comparison", "conversion": "printed (..) read per atom: 0.00009 Ha per atom; per atom null -> 0.00009, stored as totals (x 10)", "reason": "Ruling 2 (2026-10-24): the printed complete-basis fit uncertainty of an approximate CBS row is stored as sigma, as on the paper's extrapolated CBS rows; the journal print wins where print and repository disagree. The generator dropped it (scripts/track3/motta2017.mjs, fixed).", "source_entry": "h-motta17-sc-nevpt2#34 (qmbl-verify 2026-10-23/24, ambiguous); ruling 2, 2026-10-24" }, { "field": "sampled", "to": false, "reported_as": "-0.52299(9) per atom", "location": "Table III (first block), R = 3.2 row; sources/1705.01608.txt line 1275; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/SC-NEVPT2_CBS: -5.2299 0.000912688", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.234, "sigma": 0.0008, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "UCCSD(T)", "ansatz": null, "method_detail": "extrapolated: 1/M → 0 (complete basis)", "method_as_published": "UCCSD(T) [extrapolated: complete basis set]", "family": "FCIQMC / CC", "bound_type": "approximate", "bound_type_reason": "finite-order perturbation theory, GW, or a perturbative correction to coupled cluster (track 3, 2026-10-21); error of unknown sign (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52340(8) per atom", "note": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/UCCSD(T)_CBS: -5.23399 0.000832091 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null }, "sampled": false, "corrections": [ { "field": "sigma", "from": null, "to": 0.0008, "checked_on": "2026-10-24", "reported_as": "-0.52340(8) per atom (Hartree)", "location": "Table III (CBS, second block), column UCCSD(T), row R = 3.2; journal text line 1305, arXiv v2 text line 1288, same cell '-0.52340(8)' in both; dataset file N_10_OBC/R_3.2/UCCSD(T)_CBS = '-5.23399 0.000832091'", "version_read": "journal Phys. Rev. X 7, 031059 (2017; published 2017-09-28, corrected 2021-03-24), publisher PDF text qmbl-wt-hydrogen/sources/1705.01608-PhysRevX.7.031059.txt; arXiv:1705.01608v2 (dated November 8, 2017), qmbl-wt-hydrogen/sources/1705.01608.txt; data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183a5a2dd2a471bbde3f3c4952cc3d2432ea (2017-10-09, repository HEAD on 2026-10-24, README: CC BY 4.0); all 90 UCCSD(T)_* files fetched raw from GitHub (sources/1705.01608-data-raw-uccsd-t.json, out/h-motta17-uccsd-t-/fetch_raw.mjs), byte-equal to the committed TSV qmbl-wt-hydrogen/sources/1705.01608-data-b99a183.tsv; comparison by out/h-motta17-uccsd-t-/check.py", "conversion": "printed (8) on the fifth decimal = 8e-05 Ha per atom; total sigma 0.0008 Ha. Dataset second number 0.000832091 (total) = 8.32e-05 per atom; per atom null -> 0.00008, stored as totals (x 10)", "reason": "Sec. IV C (journal lines 477-479): 'The CBS result is taken as alpha(N,R)+A(N,R), with a combined uncertainty estimated from the fitting procedures', printed in Table III. The generator keeps that uncertainty for non-sampled CBS rows whose bound_type is extrapolated (RCCSD, UCCSD, RHF, UHF CBS rows of the same table keep it) but drops it here because RULES 13.4 keeps CCSD(T) CBS approximate: line 125 tests bound_type, not CBS. Reproduced independently (cbs_refit.py, cbs_err.py): dataset UHF_CBS A plus the intercept alpha of a least-squares fit of E_UCCSD(T),x - E_UHF,x = alpha + beta/x^3 over x = 2,3,4 gives -5.233993 vs dataset -5.23399; the dataset uncertainty equals sqrt(sigma_A^2 + se(alpha)^2) = sqrt(6.17e-05^2 + 0.000829807^2) = 0.000832098.", "source_entry": "h-motta17-uccsd-t-#41 (qmbl-verify 2026-10-23/24, correction; skeptic upheld)" }, { "field": "sampled", "to": false, "reported_as": "-0.52340(8) per atom", "location": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/UCCSD(T)_CBS: -5.23399 0.000832091", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.2303, "sigma": 0.0008, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "UCCSD", "ansatz": null, "method_detail": "extrapolated: 1/M → 0 (complete basis)", "method_as_published": "UCCSD [extrapolated: complete basis set]", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "extrapolated to the complete basis set or to zero truncation error; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.52303(8) per atom", "note": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/UCCSD_CBS: -5.23034 0.000798288 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "journal PDF PRX 7, 031059 (2017) (sources/1705.01608-PhysRevX.7.031059.pdf) and arXiv:1705.01608v2 PDF (dated November 8, 2017), both extracted with pypdf layout mode (out/h-motta17-uccsd-c1/raw/*-layout.txt); data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183, every UCCSD_* file fetched raw from GitHub on 2026-10-24 (raw/uccsd-files-b99a183.json), byte-equal to the committed TSV", "location": "Table III (second block, CBS), column UCCSD, row R = 3.2; journal and arXiv v2 print the same cell; dataset file N_10_OBC/R_3.2/UCCSD_CBS", "reported_as": "-0.52303(8) per atom (Hartree); dataset '-5.23034 0.000798288' (total)", "conversion": "-0.52303 x 10 = -5.2303; dataset -5.23034 differs by 4.0e-5 Ha total, inside one unit of the printed last digit x N", "note": "bound_type extrapolated on the basis = none instance (RULES 13.4); sigma 0.00008 per atom is the printed CBS fit uncertainty ('a combined uncertainty estimated from the fitting procedures', Sec. IV C), not a statistical error; dataset gives 0.000798288 total = 0.0000798 per atom; UCCSD - RCCSD = 11.60 mHa total (broken-symmetry UHF reference); N_up = N_dn = N/2, OBC, R in bohr, total with nuclear repulsion, bound_type and peer_reviewed agree; no data/Hchain file exists (track 3 held); no row from another batch on this instance carries this number", "secondary_of": null, "source_entry": "h-motta17-uccsd-c1#41 (qmbl-verify 2026-10-23/24, verified)" } }, "sampled": false, "corrections": [ { "field": "sampled", "to": false, "reported_as": "-0.52303(8) per atom", "location": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/UCCSD_CBS: -5.23034 0.000798288", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.096702, "sigma": 0.00006, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "HF", "ansatz": null, "method_detail": "unrestricted; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "UHF [extrapolated: complete basis set]", "family": "mean field", "bound_type": "extrapolated", "bound_type_reason": "extrapolated to the complete basis set or to zero truncation error; not a bound (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-5.096702(6) (printed as the H10 total, in a column of per-atom values)", "note": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/UHF_CBS: -5.0967023 0.0000617 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null }, "sampled": false, "corrections": [ { "field": "sigma", "from": 0.000006, "to": 0.00006, "checked_on": "2026-10-24", "reported_as": "-5.096702(6) (Table III second block, UHF column, R = 3.2; value printed as the H10 total)", "location": "Table III (second block), R = 3.2 row, UHF column: journal txt line 1305, arXiv v2 txt line 1288; dataset file N_10_OBC/R_3.2/UHF_CBS = '-5.0967023 0.0000617'", "version_read": "PRX 7, 031059 (2017) journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2 (sources/1705.01608.txt, PDF of 2017-11-07); both print the same cell. Dataset github.com/simonsfoundation/hydrogen-benchmark-PRX b99a183, raw file fetched from GitHub (raw-uhf-b99a183.json), equal to the committed TSV.", "conversion": "The parenthesis is a per-atom uncertainty: (6) on 6 decimals = 0.000006 Ha per atom; total = 0.000006 x 10 = 0.00006 Ha. Dataset second number 0.0000617 Ha is the total (standard error of A in Eq. (4), reproduced exactly by an unweighted 4-point DZ..5Z fit: A = -5.0967023, se 0.0000617); 0.0000617/10 = 0.00000617 per atom, ratio printed/(dataset/10) = 0.972. Stored sigma_per_site 6e-7 = paren / 10, i.e. total 0.000006 = 0.0972 x the dataset total.; per atom 6e-7 -> 0.000006, stored as totals (x 10)", "reason": "Every other column of Table III prints a per-atom value with a per-atom (..) that equals the dataset _CBS error / 10 to rounding (R = 2.0: AFQMC (6) vs 0.00059032/10, UCCSD(T) (1) vs 0.000135332/10; R = 3.2: RCCSD (8) vs 0.000786923/10, SBDMRG (14) vs 0.00140136/10). The UHF column prints the total but keeps the per-atom (..): its (..) tracks UHF_CBS error / 10 at all ten R (ratio 0.89-1.48). The generator divided the paren by N a second time, so the stored error bar is 10x too small. Proposed: the printed paren read per atom (alternative: the dataset value 0.00000617 per atom, total 0.0000617). It is a fit uncertainty of an extrapolated row, not a sampling error.", "source_entry": "h-motta17-uhf-c1#53 (qmbl-verify 2026-10-23/24, correction; skeptic upheld)" }, { "field": "sampled", "to": false, "reported_as": "-5.096702(6) (printed as the H10 total, in a column of per-atom values)", "location": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/UHF_CBS: -5.0967023 0.0000617", "checked_on": "2026-10-20", "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).", "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json" } ] }, { "energy": -5.24373, "sigma": 0.00004, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "VMC", "ansatz": "JAGP", "method_detail": "cc-pVTZ trial basis", "method_as_published": "VMC [AGP determinant with Jastrow factor, cc-pVTZ trial basis]", "family": "classic VMC", "bound_type": "variational", "bound_type_reason": "the energy of a stated wave function (Hartree-Fock, DMRG at a stated bond dimension, MRCI, VMC, a neural-network state); an upper bound in the instance's basis (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.524373(4) per atom", "note": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/VMC_AGP_basis-TZ: -5.24372765577335 3.384158361392282E-005 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "PRX 7, 031059 journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2 PDF (dated November 8, 2017; own pypdf layout extraction, out/h-motta17-vmc/arxiv_layout.txt); dataset file fetched fresh from raw.githubusercontent.com at b99a183 and at master (identical to the committed TSV)", "location": "Table III (second block, H10 'extrapolated to the CBS limit' table), row R = 3.2, column VMC(AGP); journal text line 1305, arXiv layout line 1309; dataset N_10_OBC/R_3.2/VMC_AGP_basis-TZ", "reported_as": "−0.524373(4) (per atom, Hartree); journal and arXiv v2 identical", "conversion": "-0.524373 x 10 = -5.243730 Ha total; sigma 4e-6 x 10 = 4e-5 Ha. Dataset -5.24372765577335 3.384158361392282E-005 (total) -> -0.524372766 per atom, rounds to the printed value; dataset sigma/10 = 3.384e-6", "note": "chain of N = 10 atoms, open (finite molecule), R = 3.2 bohr, N_up = N_dn = 5 (paper Sec. II: \"We only consider spin-unpolarized systems, with N_up = N_dn = N/2\"), continuum all-electron Hamiltonian Eq. (1) with nuclear repulsion -> basis = none (RULES 13.1); bound_type variational (RULES 13.4); peer_reviewed (PRX 7, 031059). Stored eps and sigma_per_site equal the printed cell. VMC lies 0.614 mHa/atom above the same paper's LR-DMC(AGP) on this instance and 0.617 mHa/atom above MRCI+Q (CBS) (variational ordering holds).", "secondary_of": null, "source_entry": "h-motta17-vmc#25 (qmbl-verify 2026-10-23/24, verified)" } } }, { "energy": -5.23557, "sigma": 0.00005, "energy_variance": null, "dof": 10, "einf": null, "v_score": null, "method": "VMC", "ansatz": "SJ", "method_detail": "LDA determinant, cc-pVTZ trial basis", "method_as_published": "VMC [LDA determinant with Jastrow factor, cc-pVTZ trial basis]", "family": "classic VMC", "bound_type": "variational", "bound_type_reason": "the energy of a stated wave function (Hartree-Fock, DMRG at a stated bond dimension, MRCI, VMC, a neural-network state); an upper bound in the instance's basis (RULES.md 13.4; assigned during source reading)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "peer_reviewed": true, "source": "track3-2026-10-20", "provenance": "primary", "verified": { "checked_on": "2026-10-20", "method": "source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading", "reported_as": "-0.523557(5) per atom", "note": "Table III (second block), R = 3.2 row; sources/1705.01608.txt line 1288; version read: journal PDF (PRX 7, 031059, APS, sources/1705.01608-PhysRevX.7.031059.txt) and arXiv text; the table values agree digit for digit. Dataset file N_10_OBC/R_3.2/VMC_LDA_basis-TZ: -5.23556666449395 4.717928839959921E-005 | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.", "secondary_of": null, "second_read": { "checked_on": "2026-10-24", "scope": "value", "method": "PRX 7, 031059 journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2 PDF (dated November 8, 2017; own pypdf layout extraction, out/h-motta17-vmc/arxiv_layout.txt); dataset file fetched fresh from raw.githubusercontent.com at b99a183 and at master (identical to the committed TSV)", "location": "Table III (second block, H10 'extrapolated to the CBS limit' table), row R = 3.2, column VMC(LDA); journal text line 1305, arXiv layout line 1309; dataset N_10_OBC/R_3.2/VMC_LDA_basis-TZ", "reported_as": "−0.523557(5) (per atom, Hartree); journal and arXiv v2 identical", "conversion": "-0.523557 x 10 = -5.235570 Ha total; sigma 5e-6 x 10 = 5e-5 Ha. Dataset -5.23556666449395 4.717928839959921E-005 (total) -> -0.523556666 per atom, rounds to the printed value; dataset sigma/10 = 4.718e-6", "note": "chain of N = 10 atoms, open (finite molecule), R = 3.2 bohr, N_up = N_dn = 5 (paper Sec. II: \"We only consider spin-unpolarized systems, with N_up = N_dn = N/2\"), continuum all-electron Hamiltonian Eq. (1) with nuclear repulsion -> basis = none (RULES 13.1); bound_type variational (RULES 13.4); peer_reviewed (PRX 7, 031059). Stored eps and sigma_per_site equal the printed cell. VMC lies 1.417 mHa/atom above the same paper's LR-DMC(LDA) on this instance and 1.433 mHa/atom above MRCI+Q (CBS) (variational ordering holds).", "secondary_of": null, "source_entry": "h-motta17-vmc#26 (qmbl-verify 2026-10-23/24, verified)" } } } ], "url": "https://qmbl.org/i/Hchain/chain_10_O_R3.2_none/", "per_site_divisor": 10, "per_site_label": "E/N (Ha)", "best": { "exact": null, "variational": { "energy": -5.24373, "sigma": 0.00004, "method": "VMC", "ansatz": "JAGP", "method_detail": "cc-pVTZ trial basis", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "bound_type": "variational", "energy_per_site": -0.524373 }, "projected": { "energy": -5.24987, "sigma": 0.00007, "method": "LR-DMC", "ansatz": "AGP", "method_detail": "cc-pVTZ trial basis", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "bound_type": "projected", "energy_per_site": -0.524987 }, "extrapolated": { "energy": -5.2512, "sigma": 0.0006, "method": "DMET", "ansatz": null, "method_detail": "fragment of 2 atoms; extrapolated: 1/M → 0 (complete basis)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "bound_type": "extrapolated", "energy_per_site": -0.52512 }, "approximate": { "energy": -5.2574, "sigma": 0.001, "method": "RCCSD(T)", "ansatz": null, "method_detail": "extrapolated: 1/M → 0 (complete basis)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "bound_type": "approximate", "energy_per_site": -0.52574 }, "below_exact": [] }, "no_best_reason": null, "record": { "energy": -5.2512, "sigma": 0.0006, "method": "DMET", "ansatz": null, "method_detail": "fragment of 2 atoms; extrapolated: 1/M → 0 (complete basis)", "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059", "bound_type": "extrapolated", "energy_per_site": -0.52512 }, "no_record_reason": null }