{"id": "card_solve_get_close", "kind": "reference", "title": "Get close — a bounded estimate (the approximate flip)", "body": "One step from the anchor, with a proven error: estimate f0 + f1·(x−x0), bound the remainder by Taylor (sup|f''|·(x−x0)^2/2) or Lipschitz. Fairly close, with a proven bound, is often the answer. The door is src/concordance/verifiers/approximation.py; 0 false positives — a closeness claim the truth does not satisfy is refused.", "source": {"label": "Narrow Highway — a step of the solve path", "url": "", "authority_tier": "engine_derived", "ref": "stick_get_fairly_close_with_a_proven_bound"}, "shelf": "codex", "box": "solve_step", "bands": ["solve path", "method", "get_close"], "subject": "Get close — a bounded estimate (the approximate flip)", "connections": [{"to_card_id": "card_spine_solve_path", "relationship": "member_of", "evidence": "a step of the solve path"}, {"to_card_id": "card_instr_approximation", "relationship": "connects_at", "evidence": "Get close: uses card_instr_approximation"}, {"to_card_id": "card_solve_converge", "relationship": "builds_on", "evidence": "get_close follows converge on the solve path"}, {"to_card_id": "card_solve_refine", "relationship": "enables", "evidence": "refine follows get_close 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": ["get_close", "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_spine_solve_path", "title": "The solve path — a spine", "relationship": "on the shelf of", "why": "a step of the solve path", "href": "/card/card_spine_solve_path", "resolved": true}, {"id": "card_instr_approximation", "title": "Get close - a bounded estimate", "relationship": "connects at", "why": "Get close: uses card_instr_approximation", "href": "/card/card_instr_approximation", "resolved": true}, {"id": "card_solve_converge", "title": "Converge from inside — anchor on what you know exactly", "relationship": "builds on", "why": "get_close follows converge on the solve path", "href": "/card/card_solve_converge", "resolved": true}, {"id": "card_solve_refine", "title": "Refine — tighten the bound, each step sealed", "relationship": "enables", "why": "refine follows get_close on the solve path", "href": "/card/card_solve_refine", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_solve_get_close", "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_get_close"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}