Code overview

Two Python programs accompany arXiv:2611.09837. They share no code; the bootstrap's figures take the variational state's moments as fixed numbers.

The variational program, variational/, builds a basis of trial wavefunctions, each a Gaussian profile times a polynomial singlet of the gauge group and Spin(9) (Sec. III B). It computes the overlaps between them and the matrix elements of H and H_aux rigorously, then finds the combination that minimizes ⟨H_aux⟩. That minimum bounds the state's overlap with the ground space from below (Eq. (21)). The program saves the state with its basis and measures its observables, and the scripts in variational/analysis/ compute from it the densities compared with the Coulomb-branch EFT (Sec. IV C).

The bootstrap program, bootstrap/, bounds the ground state's moments using only positivity, symmetry and supersymmetry (Sec. IV D). For all operators up to a given level, it imposes the Ward identities that follow from the ground state being annihilated by H, the supercharges and the symmetry generators, and reduces the resulting positivity problem exactly to a small semidefinite program. SDPB solves the program, and each bound is then certified in exact arithmetic. Minimizing ⟨R²⟩ gives its lower bound; minimizing combinations of two moments traces out the allowed regions of Fig. 4.

Paper to code

Sec. II and App. A: model and fermion conventions

variational/src/bfss/fock.py, variational/src/bfss/model.py; bootstrap/bfss/kinematics.py, bootstrap/bfss/model.py

Sec. III A and App. D: singlet space

variational/src/bfss/fiber.py

Sec. III B, Eqs. (17)–(19): variational ansatz

variational/src/bfss/covariants.py, variational/src/bfss/hilbert.py, variational/src/bfss/ansatz.py

Eqs. (20)–(22) and App. B: H_aux, fidelity bound and Rayleigh–Ritz method

variational/src/bfss/blocks.py, variational/src/bfss/variational.py

App. E: Wick contractions and angular integrals

variational/src/bfss/contract.py, variational/src/bfss/gaussian.py

Secs. IV A–C, Figs. 1–3: comparison with the Coulomb-branch EFT

variational/analysis/

Sec. IV D, Eq. (31): state and observables

variational/src/bfss/state.py

Reported results

• State: variational/results/seeded_state.json; observables, Eq. (31): variational/results/seeded_measurement.json.
• Figs. 1–3: variational/results/seeded_tail_fit.json and variational/results/seeded_eft_density.json.
• Rayleigh–Ritz convergence, Sec. IV D: variational/results/ansatz-search.md.
• Bound on ⟨R²⟩: bootstrap/results/L10/tip.json; regions of Fig. 4 and bound on ⟨R⁴⟩: bootstrap/results/L10/regions.json.gz, with levels 6 and 8 beside it.