Running the bootstrap program

Installing

git clone <this repository> && cd <it>/bootstrap
python -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt

Python 3.10 or later. Certified bounds also need SDPB 3 (sdpb and pmp2sdp) with an MPI launcher, found on the PATH, in the directory named by SDPB_BIN, or inside a Singularity image named by SDPB_IMAGE (run with singularity exec --cleanenv --env: SingularityCE 3.6 or later, or Apptainer). Without SDPB everything but the certified solves works, with the double-precision solver Clarabel.

Use

Level 6 is small enough for a laptop:

# exact problem: runs/L6/problem.json
python run.py compile --level 6 --workers 4 --out runs/L6
# quick estimate with Clarabel
python run.py solve runs/L6 --min R2
# the bound with SDPB, checked against the exact problem
python run.py solve runs/L6 --min R2 --backend sdpb
# exact certificate of that solve
python run.py certify runs/L6 --name tip

Level 8 compiles in about 20 minutes on 32 cores; level 10 took about a day on several 112-core servers with up to 46 GB per worker.

python run.py compile --level 10 --workers 64 --out runs/L10
# optional: further primes as separate jobs, before a final plain compile
python run.py compile --level 10 --workers 48 --out runs/L10 --primes 1
python run.py solve runs/L10 --min R2 --backend sdpb --procs 32
# maximize <u> at fixed <R^2>
python run.py solve runs/L10 --min=-u --fix R2=12 --backend sdpb
# allowed regions -> regions.json, then figures
python run.py scan runs/L10 --n 24 --workers 14 --procs 8 \
    --lower runs/L6 runs/L8
python run.py plot runs/L6 runs/L8 runs/L10 --out figures

Objectives are combinations of R2 R4 u T Y D P2 P4, such as u+1/2*R2; constraints take exact rationals. Compiles and scans resume after an interruption. SDPB_THREADS sets the OpenMP threads of each SDPB solve.

Tests

# the algebra and every model identity, exactly
python tests/check_model.py
# weight coordinates, products, adjoints, pairings, null multiplets
python tests/check_pairing.py
# level 8, blocks up to dimension 3000, 32 workers:
# explicit pairings vs. fast evaluation
python tests/check_problem.py 8 3000 32
# multiplets, rows and sizes per irrep at level 10
python tests/basis_stats.py 10 32

Generated from the sections Installing, Use and Tests of bootstrap/README.md at the tag release.