Variational program
The code calls the lower bound of Eq. (21) on the fidelity F_lb.
Package, in pipeline order
variational/src/bfss/algebra.py- Polynomials in the invariants and in symmetric 3×3 matrices.
variational/src/bfss/scalars.py- Exact rationals or rigorous ball arithmetic.
variational/src/bfss/fock.py- Exact operators on the fermion Fock space, App. A.
variational/src/bfss/model.py- Fermionic operators in the conventions of Sec. II and App. A.
variational/src/bfss/fiber.py- Invariant fermion space, Sec. III A and App. D.
variational/src/bfss/covariants.py- Seeds and polynomial singlets, Eq. (17).
variational/src/bfss/hilbert.py- Profiles, trial wavefunctions and bases, Eqs. (18) and (19).
variational/src/bfss/ansatz.py- Bases as data.
variational/src/bfss/reference.py- Imports the state of an earlier code addendum.
variational/src/bfss/contract.py- Exact fermionic contractions of polynomial singlets, App. E.
variational/src/bfss/gaussian.py- Gaussian and orientation integrals, Eqs. (E.9) and (E.15).
variational/src/bfss/blocks.py- Matrix elements of the norm, H, Haux and the moments, Eq. (22).
variational/src/bfss/variational.py- Gram–Schmidt, minimization of ⟨Haux⟩ and the fidelity bound, Eq. (21).
variational/src/bfss/state.py- State files, optimization and measurement, Eq. (31).
variational/src/bfss/cli.py,variational/src/bfss/__main__.py,variational/src/bfss/__init__.py- Command line and package entry.
Analysis scripts, Sec. IV C
variational/analysis/radial_tail.py- Radial density and its fit to Eq. (25), Fig. 1.
variational/analysis/curate_tail_fit.py- Condenses those fits into a tail record.
variational/analysis/eft_density.py- Joint and transverse densities, Eq. (26), Figs. 2 and 3.
variational/analysis/assemble_eft_density.py- Merges them into an EFT density record.
variational/analysis/slice_residual.py- Residual of Haux on the gauge slice, used to choose seeds.
variational/analysis/eft-density.md- How the tail and EFT density records were made.
Records
Reported state, in variational/results/:
variational/results/seeded_ansatz.json,variational/results/seeded_state.json,variational/results/seeded_measurement.json- Basis, state and observables, Eq. (31): ⟨Haux⟩ = 8.21165 × 10⁻⁷ and
F_lb= 0.9999978. variational/results/seeded_tail_fit.json- Radial density, Fig. 1.
variational/results/seeded_eft_density.json- Joint and transverse densities, Figs. 2 and 3.
variational/results/seed-search.md- Search that built the basis.
An intermediate, extended basis:
variational/results/extended_ansatz.json,variational/results/extended_state.json,variational/results/extended_measurement.json- Basis, state and observables: ⟨Haux⟩ = 2.7845 × 10⁻⁴ and
F_lb= 0.999265. variational/results/extended_tail_fit.json,variational/results/extended_eft_density.json,variational/results/extended_size.json- Densities and size moments.
variational/results/ansatz-search.md- Search that built it, with the convergence quoted in Sec. IV D.
Earlier code addendum, and benchmarks:
variational/results/ansatz.json,variational/results/optimized_state.json,variational/results/optimized_measurement.json- Basis, optimized state and observables: ⟨Haux⟩ = 3.4945 × 10⁻³ and
F_lb= 0.99078. variational/results/benchmarks.md- Performance comparisons.
Reference data, copied from that code addendum:
variational/tests/data/reference/README.md,variational/tests/data/reference/coefficients.json,variational/tests/data/reference/fermion-data.json,variational/tests/data/reference/moments.json- Origin and exact evaluation, state, fermion conventions and moments.
Tests
variational/tests/ checks the fermion algebra and supercharge identities (variational/tests/test_fermions.py), the contractions against brute force in the full Fock space and in the invariant fermion space (variational/tests/test_contractions.py, with variational/tests/fock_oracle.py), the seeds (variational/tests/test_covariants.py), the integrals and matrix elements against quadrature (variational/tests/test_gaussian.py, variational/tests/test_blocks.py, with variational/tests/quadrature.py), the Rayleigh–Ritz step (variational/tests/test_variational.py), state files (variational/tests/test_state.py), the earlier published state (variational/tests/test_reference.py), the records against their states and a measurement against its record (variational/tests/test_records.py) and the analysis scripts (variational/tests/test_radial_tail.py, variational/tests/test_slice_residual.py, variational/tests/test_eft_density.py). variational/tests/conftest.py holds shared fixtures.
Other files
variational/README.md- Installation, use, tests and results.
variational/docs/data-structures.md- Types and state files.
variational/pyproject.toml- Package definition.