{"anchors": [], "axis_coords": {"axis": "mathematics", "dimensions": ["reasoning"]}, "content_hash": "c91b041e82af9af480694ebb2b72f9ce50de2107b2087fa2eb53323070d7cb0b", "gate_results": [{"details": {"broken_at": null, "confirmed_steps": 2, "gap_at": null, "steps": 2, "verdict": "HOLDS"}, "gate": "RED", "reasons": ["derivation verdict: HOLDS"], "status": "PASS"}], "overall": "PASS", "schema_version": "2.0", "verifier_results": [{"data": {"claim": "sin²x + cos²x = 1", "domain": "mathematics", "link_ok": true, "uses": []}, "detail": "sin(x)**2+cos(x)**2 = 1; the two sides are equal -- each reduces to 1, so their difference simplifies to 0", "name": "t1", "status": "CONFIRMED"}, {"data": {"claim": "cos 2x = 1 − 2 sin²x", "domain": "mathematics", "link_ok": true, "uses": ["t1"]}, "detail": "cos(2*x) = 1-2*sin(x)**2; the two sides are equal -- each reduces to cos(2*x), so their difference simplifies to 0", "name": "t2", "status": "CONFIRMED"}]}