"""Executable examples for Chapters 13-16.

Shows (a) what the engine records when Isabelle and SageMath are absent and
(b) the L0 declared-binding audit for three Lorentz claims.

Run from the repository root:

    PYTHONPATH=src uv run python content/examples/math/tool-chapters/ch13_16_probe_and_audit_demo.py

Illustrative teaching script, not an evidence-bundle producer.
"""

from pathlib import Path

from math_engine.adapters.external import ExternalProofAdapter, default_tool_specs
from math_engine.equivalence import audit_claim_bindings
from math_engine.experiments.lorentz import load_math01_claims
from math_engine.models import Claim

root = Path(__file__).resolve().parents[3]

print("== Chapters 13/14: probes for tools that may be absent")
claims = {c.claim_id: c for c in load_math01_claims(root)}
for spec in default_tool_specs():
    if spec.system not in ("isabelle", "sagemath"):
        continue
    adapter = ExternalProofAdapter(spec)
    cap = adapter.probe()
    print(spec.system, "available:", cap.available, "| reason:", cap.reason)
    if spec.claim_id:
        r = adapter.verify(claims[spec.claim_id], root)
        print("  ", r.result_id, "|", r.status.value, "|", r.execution_status.value)

print("== Chapter 15: L0 declared-binding audit")
for name in ("lorentz-algebraic", "gamma-relation-1.1.0", "lorentz-physical-1.1.0"):
    path = root / "experiments/relativity/special" / f"{name}.claim.json"
    claim = Claim.model_validate_json(path.read_text(encoding="utf-8"))
    print(claim.key)
    for f in audit_claim_bindings(claim):
        print("  ", f.left_binding, "<->", f.right_binding, f.conclusion,
              list(f.mismatches), len(f.unresolved_obligations))