{"id": "card_solve_exclude", "kind": "reference", "title": "Exclude from outside — the barriers and the moat", "body": "The first jaw. Cut every branch proven dead: the three barriers of P vs NP (relativization, natural proofs, algebrization) say where a proof cannot come from, and the moat (0 false positives) rejects every candidate a verifier breaks. Narrows the space from the outside, monotonically — once out, out.", "source": {"label": "Narrow Highway — a step of the solve path", "url": "", "authority_tier": "engine_derived", "ref": "docs/MILLENNIUM_PREPAREDNESS.md"}, "shelf": "codex", "box": "solve_step", "bands": ["solve path", "method", "exclude"], "subject": "Exclude from outside — the barriers and the moat", "connections": [{"to_card_id": "card_floor_the_solve_path", "relationship": "part_of", "evidence": "a jaw of the solve path (Exclude from outside)"}, {"to_card_id": "card_floor_p_vs_np", "relationship": "connects_at", "evidence": "Exclude from outside: uses card_floor_p_vs_np"}, {"to_card_id": "card_solve_answer", "relationship": "enables", "evidence": "answer follows exclude on the solve path"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.solve.step", "facets": {"subject": ["exclude", "method", "solve path"]}, "presentation": {"glyph": "•", "kind_label": "solve step", "by": "Narrow Highway — a step of the solve path", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_the_solve_path", "title": "The solve path — two jaws that close on the answer", "relationship": "part of", "why": "a jaw of the solve path (Exclude from outside)", "href": "/card/card_floor_the_solve_path", "resolved": true}, {"id": "card_floor_p_vs_np", "title": "The P versus NP chain - from the machine and the circuit to the three barriers", "relationship": "connects at", "why": "Exclude from outside: uses card_floor_p_vs_np", "href": "/card/card_floor_p_vs_np", "resolved": true}, {"id": "card_solve_answer", "title": "The answer — the surviving window closes", "relationship": "enables", "why": "answer follows exclude on the solve path", "href": "/card/card_solve_answer", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_solve_exclude", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_solve_exclude"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}