{"id": "card_floor_the_solve_path", "kind": "note", "title": "The solve path — two jaws that close on the answer", "body": "How the engine solves a hard problem when no rule finds the exact answer (the barriers). Two jaws: EXCLUDE from outside (the barriers, the moat — cut the dead branches) and CONVERGE from inside (anchor, then the two doors — GET CLOSE, the bounded estimate, and CHANGE OF DOMAIN, the eigenbasis flip — then REFINE). They meet at the ANSWER: a value with a proven bound, small enough to decide. The proposer stays free; the checks and the bounds carry the certainty. Found, never generated — the steps point at the doors (tools/seed_solve_path.py).", "source": {"label": "Narrow Highway — the solve path (operator seed)", "url": "", "ref": "project_the_solve_path_get_close_and_change_of_domain", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "floor", "bands": ["floor", "solve path", "method", "two trees", "approximation", "spectral", "one map"], "subject": "The solve path", "connections": [{"to_card_id": "card_solve_exclude", "relationship": "has_part", "evidence": "a jaw of the solve path (Exclude from outside)"}, {"to_card_id": "card_solve_converge", "relationship": "has_part", "evidence": "a jaw of the solve path (Converge from inside)"}, {"to_card_id": "card_capstone_narrow_way", "relationship": "connects_at", "evidence": "the method: two jaws converge on the one answer"}, {"to_card_id": "card_ham_eigenbasis", "relationship": "connects_at", "evidence": "the change-of-domain door IS diagonalizing H; eigenvectors = the stationary states"}, {"to_card_id": "card_lag_least_action", "relationship": "connects_at", "evidence": "a stationary point is an optimization: exclude the non-stationary, converge on delta S = 0"}, {"to_card_id": "card_game_nash", "relationship": "connects_at", "evidence": "the equilibrium is a fixed point - the solve path's converge step"}, {"to_card_id": "card_game_zero_sum", "relationship": "connects_at", "evidence": "the minimax value is an optimization - converge on the saddle point"}, {"to_card_id": "card_k_floor_of_discovery", "relationship": "part_of", "evidence": "the solve path on the one map"}, {"to_card_id": "card_floor_the_instruments", "relationship": "rests_on", "evidence": "the two doors are instruments: get close (approximation) and change of domain (spectral)"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.floor", "facets": {"subject": ["approximation", "method", "one map", "solve path", "spectral", "two trees"]}, "presentation": {"glyph": "•", "kind_label": "floor", "by": "Narrow Highway — the solve path (operator seed)", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_solve_exclude", "title": "Exclude from outside — the barriers and the moat", "relationship": "has part", "why": "a jaw of the solve path (Exclude from outside)", "href": "/card/card_solve_exclude", "resolved": true}, {"id": "card_solve_converge", "title": "Converge from inside — anchor on what you know exactly", "relationship": "has part", "why": "a jaw of the solve path (Converge from inside)", "href": "/card/card_solve_converge", "resolved": true}, {"id": "card_capstone_narrow_way", "title": "The narrow way — exclude, narrow, converge to one", "relationship": "connects at", "why": "the method: two jaws converge on the one answer", "href": "/card/card_capstone_narrow_way", "resolved": true}, {"id": "card_ham_eigenbasis", "title": "The energy eigenbasis — the stationary states", "relationship": "connects at", "why": "the change-of-domain door IS diagonalizing H; eigenvectors = the stationary states", "href": "/card/card_ham_eigenbasis", "resolved": true}, {"id": "card_lag_least_action", "title": "Least action — of all paths, the stationary one", "relationship": "connects at", "why": "a stationary point is an optimization: exclude the non-stationary, converge on delta S = 0", "href": "/card/card_lag_least_action", "resolved": true}, {"id": "card_game_nash", "title": "Nash equilibrium — a fixed point", "relationship": "connects at", "why": "the equilibrium is a fixed point - the solve path's converge step", "href": "/card/card_game_nash", "resolved": true}, {"id": "card_game_zero_sum", "title": "Zero-sum and minimax — the mixed value", "relationship": "connects at", "why": "the minimax value is an optimization - converge on the saddle point", "href": "/card/card_game_zero_sum", "resolved": true}, {"id": "card_k_floor_of_discovery", "title": "The Floor of Discovery — one floor, and by its design the fear of God", "relationship": "part of", "why": "the solve path on the one map", "href": "/card/card_k_floor_of_discovery", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_floor_the_solve_path", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_floor_the_solve_path"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}