Verification code for A sharp four-dimensional flow characterization of planarity

Description

This dataset contains the standalone verification code and deterministic run report accompanying Runda Li’s manuscript, A sharp four-dimensional flow characterization of planarity. The Python program enumerates binary flows on K4 in dimension three and K3,3 in dimensions three and four. It checks conservation and compatibility by exact binary Gaussian elimination, tests 4,716 boundary-selection cases, and verifies an explicit Petersen-graph obstruction. The JSON report records graph edge orders, cycle bases, rank distributions, witnesses, and the source-code SHA-256 digest. A README gives usage instructions. All computations use exact binary arithmetic and the Python standard library. These are finite cross-checks; the general mathematical results are established by the analytic proofs in the manuscript. They are not formal proof-assistant verification. The code was developed with generative-AI assistance through Codex. No personal, participant, or empirical research data are included.

Steps to reproduce

Use Python 3.10 or later. Place verify_small_graph_flows.py, README.md, and small_graph_flow_verification_receipt.json in one directory. Run: python verify_small_graph_flows.py --output replay.json --quiet. Compare replay.json byte-for-byte with small_graph_flow_verification_receipt.json. The report contains no timestamp or elapsed time. The reference report was generated with Python 3.13.5. No third-party Python packages are required. The code checks all 512 coordinate flows for K4 in dimension three, 4096 for K3,3 in dimension three, and 65536 for K3,3 in dimension four. The corresponding nowhere-zero counts are 210, 1092, and 35700; incompatible counts are 0, 0, and 20160.

Institutions

• Duke University

  North Carolina, Durham

Categories

Licence