{"id": "card_joint_diophantine_rh", "kind": "note", "title": "The Riemann hypothesis is one Diophantine equation with no solutions", "body": "Davis, Matiyasevich and Robinson (1976): the Riemann hypothesis is equivalent to a specific polynomial Diophantine equation having no solutions in the integers. The hypothesis is a Pi-1 statement; its truth or failure is a fact about one computation that never halts, or does.", "source": {"label": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "url": "", "domain": "mathematics", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "joint", "bands": ["joint", "two trees", "millennium", "floor", "diophantine", "hilbert's tenth", "computability"], "subject": "The Riemann hypothesis is one Diophantine equation with no solutions", "connections": [{"to_card_id": "card_floor_millennium", "relationship": "part_of", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_question_riemann", "relationship": "connects_at", "evidence": "The Riemann hypothesis is one Diophantine equation with no solutions. davis matiyasevich robinson 1976. Cited, not sealed: no arithmetic to recompute"}, {"to_card_id": "card_question_p_vs_np", "relationship": "connects_at", "evidence": "The Riemann hypothesis is one Diophantine equation with no solutions. davis matiyasevich robinson 1976. Cited, not sealed: no arithmetic to recompute"}, {"to_card_id": "card_src_mill_davis_matiyasevich_robinson_1976", "relationship": "cites", "evidence": "the record the joint stands on"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.joint", "facets": {"subject": ["computability", "diophantine", "floor", "hilbert's tenth", "millennium", "two trees"]}, "presentation": {"glyph": "•", "kind_label": "joint", "by": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_millennium", "title": "The Millennium floor - seven open questions, and where they connect", "relationship": "part of", "why": "a joint that is proven or observed - a part of the floor", "href": "/card/card_floor_millennium", "resolved": true}, {"id": "card_question_riemann", "title": "The Riemann hypothesis", "relationship": "connects at", "why": "The Riemann hypothesis is one Diophantine equation with no solutions. davis matiyasevich robinson 1976. Cited, not sealed: no arithmetic to recompute", "href": "/card/card_question_riemann", "resolved": true}, {"id": "card_question_p_vs_np", "title": "P versus NP", "relationship": "connects at", "why": "The Riemann hypothesis is one Diophantine equation with no solutions. davis matiyasevich robinson 1976. Cited, not sealed: no arithmetic to recompute", "href": "/card/card_question_p_vs_np", "resolved": true}, {"id": "card_src_mill_davis_matiyasevich_robinson_1976", "title": "M. Davis 1976 — Hilbert's tenth problem: Diophantine equations: positive aspects of a negative solution", "relationship": "cites", "why": "the record the joint stands on", "href": "/card/card_src_mill_davis_matiyasevich_robinson_1976", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_joint_diophantine_rh", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_joint_diophantine_rh"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}