Pipeline audit report

This report is produced by `tools/run_pipeline.py` and is intended to be read alongside the payload JSON files.

Summary

• Regime classification: A \(obstruction=FAIL\)
• Mixing time L0: 1
• PA bridge beta_min/beta_max: 2.0 / 7.0
• Doeblin beta_min/beta_max: 1.0 / 3.0
• eta_coord lower bound: 0.16666666666666666
• Birkhoff contraction upper bound tau: 0.5000000000000001
• Verification harness: PASS
• Return constant W_star: 6

Inputs

• graph: `base_graph.json`
• templates: `templates.json`
• nucleus: `nucleus.json`
• uword: `uword.json`
• g_min: `g_min.json`

Outputs

• pa: `pa.json`
• doeblin: `doeblin.json`
• scg_regime: `scg_regime.json`
• pr_return: `pr_return.json`
• pipeline_bundle: `pipeline_bundle.json`
• audit_report: `audit_report.md`
• contract_generated: `contract_generated.md`
• verification_json: `verification.json`
• verification_report: `verification_report.md`

Notes on algorithms

• Mixing time uses boolean adjacency powers up to Wielandt bound (or a user override) to find the first k with A^k strictly positive.
• PA bridge uses v = w_star^{k0} where k0 is the primitivity exponent of the support graph of P(w_star).
• Doeblin bounds are computed from the exact min/max entries of P(u_star), and the contraction bound uses the entry-ratio-only estimate.
• Return check uses avoidance-automaton cycle detection (KMP prefix automaton crossed with the subgraph), producing a bounded-gap constant when acyclic.