{"id": "card_floor_yang_mills", "kind": "note", "title": "The Yang-Mills chain - from the gauge field and the axioms to the mass gap", "body": "Two trees. The gauge field: Maxwell, Weyl's gauge principle (1929), Yang and Mills' non-abelian field (1954). The axioms: Wightman's (1956) and Osterwalder-Schrader's Euclidean ones (1973) - what it means for the theory to exist. They become one in the problem as Jaffe and Witten state it (2000). Along the gauge tree: asymptotic freedom (Gross-Wilczek, Politzer 1973), Wilson's lattice (1974), the gap proven at strong coupling (Osterwalder-Seiler 1978), the glueball spectrum measured (Morningstar-Peardon 1999). The open end: existence on R^4 and the continuum limit.", "source": {"label": "Narrow Highway - a chain on the one map (operator seed)", "url": "", "ref": "docs/MILLENNIUM_PREPAREDNESS.md", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "floor", "bands": ["floor", "chain", "two trees", "gauge theory", "yang-mills", "mass gap", "lattice"], "subject": "The Yang-Mills chain - from the gauge field and the axioms to the mass gap", "connections": [{"to_card_id": "card_k_floor_of_discovery", "relationship": "part_of", "evidence": "the yang mills chain rests on the one Floor of Discovery"}, {"to_card_id": "card_builder_james_clerk_maxwell", "relationship": "has_part", "evidence": "a root of this chain - one of the two trees it began from"}, {"to_card_id": "card_chain_wightman_1956", "relationship": "has_part", "evidence": "a root of this chain - one of the two trees it began from"}, {"to_card_id": "card_question_yang_mills", "relationship": "has_open_end", "evidence": "the open question this chain reaches"}], "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", "gauge theory", "lattice", "mass gap", "two trees", "yang-mills"]}, "presentation": {"glyph": "•", "kind_label": "floor", "by": "Narrow Highway - a chain on the one map (operator seed)", "authority": "engine_derived", "posted": "", "standing": ""}, "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 yang mills chain rests on the one Floor of Discovery", "href": "/card/card_k_floor_of_discovery", "resolved": true}, {"id": "card_builder_james_clerk_maxwell", "title": "James Clerk Maxwell", "relationship": "has part", "why": "a root of this chain - one of the two trees it began from", "href": "/card/card_builder_james_clerk_maxwell", "resolved": true}, {"id": "card_chain_wightman_1956", "title": "Wightman 1956 — Quantum field theory in terms of vacuum expectation values", "relationship": "has part", "why": "a root of this chain - one of the two trees it began from", "href": "/card/card_chain_wightman_1956", "resolved": true}, {"id": "card_question_yang_mills", "title": "Yang-Mills existence and the mass gap", "relationship": "has open end", "why": "the open question this chain reaches", "href": "/card/card_question_yang_mills", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_floor_yang_mills", "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_yang_mills"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}