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Numerical validation record

The computational package was validated in Linux/WSL on 2026-09-15. The Fortran tests used Intel mpiifx 2025.2.1 and MKL. Python ED used QuSpin 1.0.1, NumPy 2.4.4, SciPy 1.17.1, and Numba 0.65.1. Figure checks used NumPy 2.3.4 and Matplotlib 3.10.7.

  • All 35 imported Fortran model/propagation/measurement sources match their source-repository snapshots byte for byte. The shared numerical interfaces are the new portable code described in src/common/README.md.
  • Matrix reconstruction, Hermitian eigensystems, inversion, and the random sequence passed independent invariant checks. The modular random recurrence also matched 150000 transitions of the historical integer-wrap convention.
  • The number-conserving live regression completed its analytic free case and four interacting 100000-bin cases. Its Python, parameter-routing, and ED memory checks passed.
  • Paired live checks covered finite Delta and Delta=0. Independent small ED formulations agreed on 25 observables and energy derivatives.
  • Small complete DQMC -> ED -> analysis runs passed for both solvers. Production orchestration checks cover per-case copying, hashes, continuation, and restarting an interrupted chain from its original input.
  • A full paper-size paired ED calculation (7297 basis states at Delta=0.2) reproduced the archived four reference values within 5.3e-18 absolute.
  • All 22 archived cases were reblocked from their original 100000-sample measurement sequences before retaining the compact processed tables. The stored means and standard errors agree with that independent reconstruction. The compact package also passed without any raw archives present.
  • Both regenerated figure PDFs, rasterized to 1800 pixels wide with the same renderer, matched the manuscript figures pixel for pixel. PDF byte identity is not required because metadata can differ.

These checks cover the solvers, reference calculations, stored data, and production orchestration. The full 22-point campaign is the default reproduction command; its time and memory budget is based on the stage measurements in RESOURCES.md.

GNU Fortran/BLAS build settings and a GitHub Actions workflow are supplied. That compiler was not installed on the validation workstation, so local runtime results above refer to the Intel/MKL build. CI exercises the GNU setup when run.

Main-text and Supplemental Material mapping

The reproduction interface was checked against the benchmark layout on 2026-09-15. The default production comprises the eight-point U scan and seven-point Delta scan in the main text, plus the seven-point U1 scan in the SM.

  • All 13 reproduction tests passed, including real eight-bin BAFQMC/ED runs, continuation and interrupted-chain recovery, and selecting a single case for fresh reference calculation. Changing the selected cases is detected when resuming a campaign.
  • Scope selection preserves the original inputs, case ordering, and seeds. The 88 stored observable rows retain every original numeric value; added columns identify the current manuscript figures and notation.
  • The regenerated benchmark_combined.pdf and benchmark_attractive.pdf match the current manuscript figures pixel for pixel when rasterized to 1800 pixels wide. Individual main-text rows retain labels a–d and e–h.
  • A 172-state paired ED calculation at Delta=+0.2 and -0.2 gave identical density, physical energy, structure factors, pairing energy, and free energy. The anomalous pair_equal amplitude reversed sign, confirming the documented phase conversion between the solver and manuscript conventions.