Sparse Ruler Rigidity Experiment Suite

This project runs simulated annealing experiments for Erdős Problem #170 (sparse rulers / restricted difference bases). It builds candidate mark sets A ⊆ {0..N}, tracks distance multiplicities W(d), and searches for complete rulers with near-optimal energy.

Quick start

python -m venv .venv
source .venv/bin/activate
pip install -e .

Run a single experiment

sparse-ruler run 29 9 --runs 50 --steps 200000 --processes 4 --out-dir outputs

Outputs:

• outputs/results_N29_m9.csv with one CSV row of metrics.
• outputs/solutions/solution_N29_m9_*.json with the best 5 solutions.

Run the default scan

Small scan (N=1..120 with m0, m0+1, m0+2):

sparse-ruler small-scan --runs 200 --steps 200000 --processes 8 --out-dir outputs

Large scan (N in {1000,2000,5000,10000,20000,50000}):

sparse-ruler large-scan --runs 200 --steps 200000 --processes 8 --out-dir outputs

Compute metrics for a specific ruler

sparse-ruler metrics 13 0,1,6,9,11,13

Modal execution

If you are running on Modal, the CLI works the same way. Mount the repo, then run:

python -m sparse_ruler.cli small-scan --runs 200 --steps 200000 --processes 8 --out-dir /mnt/outputs

Notes

• The code keeps W(d) updated incrementally when marks move.
• The annealer uses H = alpha*M + beta*E + gamma*peak with alpha=1_000_000, beta=1, gamma=1000.
• If C(m,2) < N, the run is declared impossible and a CSV row is still written.

Tests

pytest

Paper Automation (GitHub + Overleaf)

Generate the latest paper bundle locally:

cd /Users/hema/Desktop/erdos170
export PYTHONPATH=src
python3 scripts/generate_research_report_to_date.py
python3 scripts/build_paper_artifacts.py --repo-root .

This writes:

• paper/main.tex
• paper/generated/tables.tex
• paper/generated/status_snapshot.json
• copies of generated markdown/json reports into paper/generated/

CI workflow: .github/workflows/paper-automation.yml

• Auto-runs on main pushes, nightly, and manual dispatch.
• Rebuilds paper artifacts and uploads erdos170-paper-bundle artifact.
• Optional Overleaf sync if repository secrets are set:
  • OVERLEAF_GIT_URL (required for sync; use Overleaf project Git URL, no token in URL)
  • OVERLEAF_GIT_TOKEN (required for sync; generated in Overleaf account Git settings)
  • OVERLEAF_GIT_BRANCH (optional, default master)

Cycle-3 Tail-Focused Run

cd /Users/hema/Desktop/erdos170
source .venv/bin/activate
export PYTHONPATH=src
python3 scripts/run_e_hunt_breakthrough_cycle3.py \
  --config configs/e_hunt_breakthrough_cycle3_tailfocus.json

Outputs land under:

• results/e_hunt_breakthrough_cycle3_tailfocus/

SAT Feasibility Lane (N=500, m=39)

Build DIMACS + attempt direct solve (requires python-sat):

cd /Users/hema/Desktop/erdos170
source .venv/bin/activate
pip install "python-sat[pblib,aiger]"
export PYTHONPATH=src
python3 scripts/run_sat_sparse_ruler_feasibility.py \
  --N 500 --m 39 \
  --mode solve \
  --dimacs-out results/sat_feasibility/sparse_ruler_N500_m39.cnf \
  --json-out results/sat_feasibility/sparse_ruler_N500_m39_result.json

DIMACS-only mode (external solver):

python3 scripts/run_sat_sparse_ruler_feasibility.py \
  --N 500 --m 39 --mode dimacs