{"id": "card_floor_millennium", "kind": "note", "title": "The Millennium floor - seven open questions, and where they connect", "body": "The seven Millennium Prize Problems on the one map of reality. The FLOOR is what is proven or observed: the joints where two of the questions meet at one established thing - the GUE statistics shared by zeta zeros and the lattice Dirac operator, the one L-function machinery, the Weil conjectures (the Riemann hypothesis over finite fields, a theorem by Deligne 1974 - the Riemann hypothesis itself stays open), the Tate conjecture that is Hodge's arithmetic twin and BSD over function fields, Bochner's vanishing under positive Ricci curvature, the renormalization group, the NP-hard sign problem, Manin's algorithm under finite Sha, the Diophantine form of RH, Arnold's geodesic flow. The questions are the OPEN ENDS hanging off that floor; one of them, Poincare, is closed (Perelman 2002-2003). Nothing is unified here: each joint is a join mathematics already made, found and cited, sealed where it is arithmetic. Riemann and Navier-Stokes share no joint - recorded as a miss. Historically the joints are where the proofs came from: Perelman imported a PDE into topology; Wiles' modularity gave BSD its L-function. A chain begins from a floor; the connections are where two chains become one.", "source": {"label": "Narrow Highway - the Millennium floor (operator seed)", "url": "https://www.claymath.org/millennium-problems/", "ref": "docs/MILLENNIUM_PREPAREDNESS.md", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "floor", "bands": ["floor", "millennium", "chain", "two trees", "mathematics", "physics", "computation"], "connections": [{"to_card_id": "card_k_floor_of_discovery", "relationship": "part_of", "evidence": "the Millennium floor rests on the one Floor of Discovery"}, {"to_card_id": "card_question_riemann", "relationship": "has_open_end", "evidence": "an open question hanging off the floor of what is proven"}, {"to_card_id": "card_question_bsd", "relationship": "has_open_end", "evidence": "an open question hanging off the floor of what is proven"}, {"to_card_id": "card_question_navier_stokes", "relationship": "has_open_end", "evidence": "an open question hanging off the floor of what is proven"}, {"to_card_id": "card_question_yang_mills", "relationship": "has_open_end", "evidence": "an open question hanging off the floor of what is proven"}, {"to_card_id": "card_question_p_vs_np", "relationship": "has_open_end", "evidence": "an open question hanging off the floor of what is proven"}, {"to_card_id": "card_question_hodge", "relationship": "has_open_end", "evidence": "an open question hanging off the floor of what is proven"}, {"to_card_id": "card_question_poincare", "relationship": "has_open_end", "evidence": "an open question hanging off the floor of what is proven"}, {"to_card_id": "card_joint_gue_statistics", "relationship": "has_part", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_joint_l_functions", "relationship": "has_part", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_joint_weil_conjectures", "relationship": "has_part", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_joint_tate_conjecture", "relationship": "has_part", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_joint_bochner_vanishing", "relationship": "has_part", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_joint_renormalization_group", "relationship": "has_part", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_joint_sign_problem", "relationship": "has_part", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_joint_manin_algorithm", "relationship": "has_part", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_joint_diophantine_rh", "relationship": "has_part", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_joint_arnold_geodesics", "relationship": "has_part", "evidence": "a joint that is proven or observed - a part of the floor"}], "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": ["chain", "computation", "mathematics", "millennium", "physics", "two trees"]}, "presentation": {"glyph": "•", "kind_label": "floor", "by": "Narrow Highway - the Millennium floor (operator seed)", "authority": "engine_derived", "posted": "", "standing": "", "link": {"url": "https://www.claymath.org/millennium-problems/", "host": "claymath.org", "provider": "", "titled": "The Millennium floor - seven open questions, and where they connect", "waybill_line": "", "reach": "", "embed": ""}}, "neighbors": [{"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 Millennium floor rests on the one Floor of Discovery", "href": "/card/card_k_floor_of_discovery", "resolved": true}, {"id": "card_question_riemann", "title": "The Riemann hypothesis", "relationship": "has open end", "why": "an open question hanging off the floor of what is proven", "href": "/card/card_question_riemann", "resolved": true}, {"id": "card_question_bsd", "title": "The Birch and Swinnerton-Dyer conjecture", "relationship": "has open end", "why": "an open question hanging off the floor of what is proven", "href": "/card/card_question_bsd", "resolved": true}, {"id": "card_question_navier_stokes", "title": "Navier-Stokes existence and smoothness", "relationship": "has open end", "why": "an open question hanging off the floor of what is proven", "href": "/card/card_question_navier_stokes", "resolved": true}, {"id": "card_question_yang_mills", "title": "Yang-Mills existence and the mass gap", "relationship": "has open end", "why": "an open question hanging off the floor of what is proven", "href": "/card/card_question_yang_mills", "resolved": true}, {"id": "card_question_p_vs_np", "title": "P versus NP", "relationship": "has open end", "why": "an open question hanging off the floor of what is proven", "href": "/card/card_question_p_vs_np", "resolved": true}, {"id": "card_question_hodge", "title": "The Hodge conjecture", "relationship": "has open end", "why": "an open question hanging off the floor of what is proven", "href": "/card/card_question_hodge", "resolved": true}, {"id": "card_question_poincare", "title": "The Poincare conjecture", "relationship": "has open end", "why": "an open question hanging off the floor of what is proven", "href": "/card/card_question_poincare", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_floor_millennium", "next_step": {"do": "read the source itself", "door": "FIND", "web": "/reader.html?card=card_floor_millennium"}, "ends": "a verdict or a card · the trail · a seal · one next step"}}