{"id": "card_joint_gue_statistics", "kind": "note", "title": "Zeta zeros and the lattice Dirac operator share GUE statistics", "body": "The nearest-neighbour spacings of the zeros of zeta follow the Gaussian Unitary Ensemble of random matrix theory (Montgomery's pair correlation, 1973; Odlyzko's computation, 1987), and so does the low-lying spectrum of the Dirac operator in lattice gauge theory (chiral random matrix theory, Verbaarschot 1994). Hilbert and Polya's reading - the zeros as eigenvalues of an operator - is the same sentence from the other side (Berry-Keating 1999). The Riemann stick sealed the GUE fit on Odlyzko's first 10,000 zeros.", "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", "random matrices", "gue", "spectral"], "subject": "Zeta zeros and the lattice Dirac operator share GUE statistics", "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": "Zeta zeros and the lattice Dirac operator share GUE statistics. montgomery 1973; odlyzko 1987; verbaarschot 1994; berry keating 1999. Sealed: the Riemann stick's spacing witness (seal deefbb6d)"}, {"to_card_id": "card_question_yang_mills", "relationship": "connects_at", "evidence": "Zeta zeros and the lattice Dirac operator share GUE statistics. montgomery 1973; odlyzko 1987; verbaarschot 1994; berry keating 1999. Sealed: the Riemann stick's spacing witness (seal deefbb6d)"}, {"to_card_id": "card_src_mill_montgomery_1973", "relationship": "cites", "evidence": "the record the joint stands on"}, {"to_card_id": "card_src_mill_odlyzko_1987", "relationship": "cites", "evidence": "the record the joint stands on"}, {"to_card_id": "card_src_mill_verbaarschot_1994", "relationship": "cites", "evidence": "the record the joint stands on"}, {"to_card_id": "card_src_mill_berry_keating_1999", "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": ["floor", "gue", "millennium", "random matrices", "spectral", "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": "Zeta zeros and the lattice Dirac operator share GUE statistics. montgomery 1973; odlyzko 1987; verbaarschot 1994; berry keating 1999. Sealed: the Riemann stick's spacing witness (seal deefbb6d)", "href": "/card/card_question_riemann", "resolved": true}, {"id": "card_question_yang_mills", "title": "Yang-Mills existence and the mass gap", "relationship": "connects at", "why": "Zeta zeros and the lattice Dirac operator share GUE statistics. montgomery 1973; odlyzko 1987; verbaarschot 1994; berry keating 1999. Sealed: the Riemann stick's spacing witness (seal deefbb6d)", "href": "/card/card_question_yang_mills", "resolved": true}, {"id": "card_src_mill_montgomery_1973", "title": "H. L. Montgomery 1973 — The pair correlation of zeros of the zeta function", "relationship": "cites", "why": "the record the joint stands on", "href": "/card/card_src_mill_montgomery_1973", "resolved": true}, {"id": "card_src_mill_odlyzko_1987", "title": "A. M. Odlyzko 1987 — On the distribution of spacings between zeros of the zeta function", "relationship": "cites", "why": "the record the joint stands on", "href": "/card/card_src_mill_odlyzko_1987", "resolved": true}, {"id": "card_src_mill_verbaarschot_1994", "title": "J. J. M. Verbaarschot 1994 — Spectrum of the QCD Dirac operator and chiral random matrix theory", "relationship": "cites", "why": "the record the joint stands on", "href": "/card/card_src_mill_verbaarschot_1994", "resolved": true}, {"id": "card_src_mill_berry_keating_1999", "title": "M. V. Berry 1999 — The Riemann zeros and eigenvalue asymptotics", "relationship": "cites", "why": "the record the joint stands on", "href": "/card/card_src_mill_berry_keating_1999", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_joint_gue_statistics", "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_gue_statistics"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}