Contents

Bootstrap program

Package, in pipeline order

bootstrap/bfss/kinematics.py
Exact algebra of positions, momenta and fermions.
bootstrap/bfss/model.py
Hamiltonian, Eq. (1), supercharges, Eq. (5), generators and observables.
bootstrap/bfss/basis.py
Operators up to a level as SU(2) × Spin(9) multiplets, keeping the combinations of finite norm.
bootstrap/bfss/pairing.py
Invariant pairing of multiplets.
bootstrap/bfss/moments.py
Positivity blocks and Ward identities at a level.
bootstrap/bfss/reduction.py
Exact reduction to a small semidefinite program.
bootstrap/bfss/problem.py
Problem file.
bootstrap/bfss/sdp.py
Solves it with SDPB, or unverified with Clarabel.
bootstrap/bfss/certify.py
Certifies a bound in exact arithmetic.
bootstrap/bfss/regions.py
Allowed regions of Fig. 4.
bootstrap/bfss/plots.py
Region figures, with the variational state’s moments.
bootstrap/bfss/__init__.py
Package marker.
bootstrap/run.py
Command line.

Records

bootstrap/results/L6/manifest.json, bootstrap/results/L8/manifest.json, bootstrap/results/L10/manifest.json
Problem structure.
bootstrap/results/L6/sectors.json, bootstrap/results/L8/sectors.json, bootstrap/results/L10/sectors.json
Multiplets per irrep.
bootstrap/results/L6/tip.json, bootstrap/results/L8/tip.json, bootstrap/results/L10/tip.json
Certified lower bound on ⟨R²⟩: 6.851, 7.498 and 7.798 at levels 6, 8 and 10.
bootstrap/results/L6/regions.json.gz, bootstrap/results/L8/regions.json.gz, bootstrap/results/L10/regions.json.gz
Allowed regions.
bootstrap/figures/regions_L6.png, bootstrap/figures/regions_L8.png, bootstrap/figures/regions_L10.png, bootstrap/figures/regions_L6_L8.png, bootstrap/figures/regions_L8_L10.png, bootstrap/figures/regions_L6_L8_L10.png
Regions of Fig. 4, per level and nested.
Allowed regions at levels 6, 8 and 10 in three planes of moments, nested, with the variational state as a point inside each
Fig. 4: allowed regions, with u the potential of Eq. (2). The black point is the variational state, Eq. (31); the insets zoom around it.

Tests

bootstrap/tests/check_model.py
Algebra and model identities, exactly.
bootstrap/tests/check_pairing.py
Fast pairings against the explicit algebra.
bootstrap/tests/check_problem.py
Compiled blocks against explicit polynomials.
bootstrap/tests/basis_stats.py
Multiplet counts against the characters.

Other files

bootstrap/README.md
Installation, use and tests.
bootstrap/RESULTS.md
Results per level.
bootstrap/requirements.txt
Dependencies.