Research-Stack/shared-data/proof_traces/canary_induct_mul_zero.decomp.json
Brandon Schneider 153a8da5c5 feat(pist): Tier 2 trace canary — 24 multi-tactic Lean theorems
- 24/24 processed, 0 errors (12 verified, 12 failed)
- Average 2.0 steps per proof (max 5 steps)
- 11 tactic families detected
- Verified proofs: avg gap=2.50 vs Failed: avg gap=1.50
- proof_traces/*.trace.json + *.decomp.json stored per theorem
2026-05-26 02:37:22 -05:00

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JSON

{
"trace_summary": {
"theorem_name": "induct_mul_zero",
"status": "failed",
"n_steps": 1,
"n_unique_goal_states": 1,
"n_flexure_joints": 1
},
"spectral": {
"n_states": 1,
"eigenvalue_max": 1.0,
"spectral_gap": 1.0,
"laplacian_eigenvalue_max": 1.0,
"rank_estimate": 1,
"zero_rows": 0,
"frobenius_norm": 1.0,
"trace": 1,
"density": 1.0
},
"feature_vector": [
1,
1,
1.0,
1.0,
0,
1,
0.0,
0.0,
0.0,
-0.0,
0.0,
1076
],
"feature_names": [
"n_steps",
"n_unique_goal_states",
"transition_density",
"spectral_gap",
"laplacian_zero_count",
"rank_estimate",
"avg_delta_goal_count",
"avg_delta_hypothesis",
"avg_delta_symbol",
"tactic_family_entropy",
"verified_ratio",
"total_elapsed"
],
"tactic_family_distribution": {
"normalization": 1
},
"delta_stats": {
"avg_goal_delta": 0.0,
"avg_hypothesis_delta": 0.0,
"avg_symbol_delta": 0.0,
"max_delta_score": 0
},
"flexure_joints": [
{
"step": 0,
"tactic": "induction n with | zero => simp | succ k ih => simp [mul_add, add_comm, ih]",
"tactic_family": "normalization",
"delta_score": 0,
"delta": {
"symbol_delta": 0,
"hypothesis_delta": 0,
"goal_count_delta": 0
},
"result": "failure"
}
]
}