How these numbers were read
Where each number below was read, and how it was checked.
-3.16977 — DMRG
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -316.9770
Table 3, row DMRG (not exact); sources/2606.25600.txt line 494; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); the paper's own DMRG, labelled 'DMRG (not exact)'; no bond dimension, code or reference given | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-3.16935(8) — 2D RNN (Lorentz (hyperbolic) cells, L_max = 2.0)
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. −316.9353 (0.0077)
Table 3, row Lorentz 2DRNN Lmax=2.0, column Best, upper line (error in lower line); sources/2606.25600.txt line 491; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0077 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-3.16899(9) — 2D RNN (Euclidean cells)
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. −316.8991 (0.0089)
Table 3, row Euclidean 2DRNN , column Best, upper line (error in lower line); sources/2606.25600.txt line 488; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0089 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-3.1535(4) — RNN (GRU, Poincaré (hyperbolic) cells, 1D on the unrolled...
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -315.3490 (0.0449)
Table 8, row Poincare GRU, column (N,N)=(10,10); error in the line below; sources/2606.25600.txt line 1045; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0449 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-3.1516(4) — RNN (Lorentz (hyperbolic) cells, 1D on the unrolled lattice)
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -315.1620 (0.0412)
Table 8, row Lorentz RNN, column (N,N)=(10,10); error in the line below; sources/2606.25600.txt line 1041; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0412 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-3.1486(5) — RNN (Poincaré (hyperbolic) cells, 1D on the unrolled...
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -314.8574 (0.0517)
Table 8, row Poincare RNN, column (N,N)=(10,10); error in the line below; sources/2606.25600.txt line 1039; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0517 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-3.1470(5) — RNN (GRU, Lorentz (hyperbolic) cells, 1D on the unrolled...
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -314.6966 (0.0537)
Table 8, row Lorentz GRU, column (N,N)=(10,10); error in the line below; sources/2606.25600.txt line 1047; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0537 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-3.1412(6) — RNN (GRU, Euclidean cells, 1D on the unrolled lattice)
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -314.1182 (0.0611)
Table 8, row Euclidean GRU, column (N,N)=(10,10); error in the line below; sources/2606.25600.txt line 1043; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0611 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-3.0913(8) — RNN (Euclidean cells, 1D on the unrolled lattice)
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -309.1322 (0.0780)
Table 8, row Euclidean RNN, column (N,N)=(10,10); error in the line below; sources/2606.25600.txt line 1037; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0780 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.