# Эксперимент: Smith-normal-form Cayley positional encoding (#256)

{
  "worked": true,
  "confidence": 7,
  "verdict": "Built an exact small-graph MVP for metric-parallel edge classes, fundamental cycle-class lattices, SNF invariants, and path/edge consistency certification. On C5, C6, 3x3 torus, and Petersen graphs, all tested fundamental cycles and edge increments passed with zero failures; nontrivial torsion factors included 2 for C6, 3 for the torus, and four 2-factors for Petersen. This verifies the core quotient/path-consistency phenomenon and shows modest coordinate compression on C5 and Petersen, but no neural-network accuracy or speed win was tested.",
  "metrics": {
    "baseline": "Raw generator-class coordinate dimensions: C5 5, C6 3, Torus3 1, Petersen 5.",
    "idea": "Quotient coordinate dimensions: C5 4 (1.25x raw/quotient), C6 3 (1.0x), Torus3 1 (1.0x), Petersen 4 (1.25x); path_failures=0 and edge_failures=0 for every graph."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "README.md",
    "cayley_posenc.py"
  ],
  "limitations": "No graph-transformer training, task accuracy, extrapolation, runtime, memory, Laplacian/random-walk baseline, or large-graph scalability evaluation was performed. The exact checks use tiny synthetic graphs and validate the constructed fundamental-cycle certificate; they do not establish distance preservation for arbitrary approximate partitions."
}