{"query": "Griffiths 1968 — Periods of integrals on algebraic manifolds", "count": 20, "results": [{"id": "card_theory_differential_geometry", "title": "Differential geometry (curvature measured from inside)", "shelf": "theories", "surface": "secular", "snippet": "Differential geometry (curvature measured from inside) — an engine domain that can touch it: geometry. Calibration: map-only — specific curvature and geodesic computations verify; the framework is bro", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_topology", "title": "Topology (what survives stretching)", "shelf": "theories", "surface": "secular", "snippet": "Topology (what survives stretching) — an engine domain that can touch it: mathematics. Calibration: map-only — specific invariants compute; the classification results are proofs, not computations. Geo", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_information_geometry", "title": "Information geometry (statistics as curved space)", "shelf": "theories", "surface": "secular", "snippet": "Information geometry (statistics as curved space) — an engine domain that can touch it: mathematics. Calibration: partial — specific relations verify; the theory as a whole is not a sealable computati", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_bridge_theory_noncommutative_geometry__general_relativity", "title": "Bridge: Noncommutative geometry & the spectral triple (Connes)  ↔  General relativity", "shelf": "bridges", "surface": "secular", "snippet": "Noncommutative geometry & the spectral triple (Connes) and General relativity are the same form in different domains. both encode geometry — GR as manifold curvature, NCG as the spectrum of the Dirac ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_floor_poincare", "title": "The Poincare chain - from the homology sphere and the heat flow to the closed question", "shelf": "codex", "surface": "secular", "snippet": "Two trees. Topology: Poincaré's homology sphere and the question (1904), Thurston's geometrization (1982). Geometric analysis: the heat-flow method of Eells and Sampson (1964), Hamilton's Ricci flow (", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_src_mill_perelman_2003a", "title": "G. Perelman 2003 — Ricci flow with surgery on three-manifolds", "shelf": "millennium", "surface": "secular", "snippet": "G. Perelman (2003). Ricci flow with surgery on three-manifolds. arXiv (2003). arXiv: math/0303109. Canonical: https://arxiv.org/abs/math/0303109. Free copy: https://arxiv.org/abs/math/0303109. License", "authority_tier": "reference", "source": "G. Perelman (2003), arXiv (2003)", "readable": false, "generated": false}, {"id": "card_src_mill_perelman_2003b", "title": "G. Perelman 2003 — Finite extinction time for the solutions to the Ricci flow on certain three-manifolds", "shelf": "millennium", "surface": "secular", "snippet": "G. Perelman (2003). Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. arXiv (2003). arXiv: math/0307245. Canonical: https://arxiv.org/abs/math/0307245. Free copy: ", "authority_tier": "reference", "source": "G. Perelman (2003), arXiv (2003)", "readable": false, "generated": false}, {"id": "card_question_poincare", "title": "The Poincare conjecture", "shelf": "millennium", "surface": "secular", "snippet": "The Poincare conjecture. Every simply connected closed three-manifold is homeomorphic to the three-sphere. Its chart is the tick stick stick_poincare_conjecture: what is sealed, what is cited and what", "authority_tier": "reference", "source": "Clay Mathematics Institute, the Millennium Prize Problems (2000)", "readable": false, "generated": false}, {"id": "card_k_ncs_validation", "title": "Nested Control Systems — a pre-registered falsification program (NHANES)", "shelf": "science", "surface": "secular", "snippet": "STATUS: pre-registered protocol, frozen 2026-03-04 — NOT yet executed. No verdict is claimed; this seed records the TEST, not a result.\nThe nested-control-systems framework (the autonomic spine) is bo", "authority_tier": "matt", "source": "Operator's artifact (Matt) — framework_validation_v3_final, frozen 2026-03-04", "readable": false, "generated": false}, {"id": "card_joint_arnold_geodesics", "title": "Euler flow is geodesic flow on the volume-preserving diffeomorphisms", "shelf": "codex", "surface": "secular", "snippet": "Arnold (1966): the Euler equations of an ideal fluid are the geodesic equations of the group of volume-preserving diffeomorphisms with the kinetic-energy metric - the fluid as a point moving on an inf", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "readable": false, "generated": false}, {"id": "card_src_mill_hamilton_1982", "title": "R. S. Hamilton 1982 — Three-manifolds with positive Ricci curvature", "shelf": "millennium", "surface": "secular", "snippet": "R. S. Hamilton (1982). Three-manifolds with positive Ricci curvature. J. Differential Geom. 17 (1982) 255–306. DOI 10.4310/jdg/1214436922. Canonical: https://doi.org/10.4310/jdg/1214436922. Free copy:", "authority_tier": "reference", "source": "R. S. Hamilton (1982), J. Differential Geom. 17 (1982) 255–306", "readable": false, "generated": false}, {"id": "card_src_mill_myers_1941", "title": "S. B. Myers 1941 — Riemannian manifolds with positive mean curvature", "shelf": "millennium", "surface": "secular", "snippet": "S. B. Myers (1941). Riemannian manifolds with positive mean curvature. Duke Math. J. 8 (1941) 401–404. DOI 10.1215/S0012-7094-41-00832-3. Canonical: https://doi.org/10.1215/S0012-7094-41-00832-3. No f", "authority_tier": "reference", "source": "S. B. Myers (1941), Duke Math. J. 8 (1941) 401–404", "readable": false, "generated": false}, {"id": "card_src_mill_atiyah_hirzebruch_1962", "title": "M. F. Atiyah 1962 — Analytic cycles on complex manifolds", "shelf": "millennium", "surface": "secular", "snippet": "M. F. Atiyah, F. Hirzebruch (1962). Analytic cycles on complex manifolds. Topology 1 (1962) 25–45. DOI 10.1016/0040-9383(62)90094-0. Canonical: https://doi.org/10.1016/0040-9383(62)90094-0. Free copy:", "authority_tier": "reference", "source": "M. F. Atiyah, F. Hirzebruch (1962), Topology 1 (1962) 25–45", "readable": false, "generated": false}, {"id": "card_ci_gradient_manifold", "title": "The gradient manifold — one form across the planes", "shelf": "science", "surface": "secular", "snippet": "This form is already kept here as doctrine (see 'the reservoir and the manifold', from Matt Harris's Universal Gradient Manifold): the enduring value in an energy system is the RESERVOIR that stores a", "authority_tier": "reference", "source": "Collective intelligence — measured natural systems, mapped to the engine", "readable": false, "generated": false}, {"id": "card_doctrine_reservoir_manifold", "title": "The reservoir and the manifold — value is in the routing layer, not the engine", "shelf": "doctrine", "surface": "secular", "snippet": "\"The most valuable asset in an energy system is not the fuel or the engine. 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Voisin (2002). A counterexample to the Hodge conjecture extended to Kähler varieties. Int. Math. Res. Not. 2002, no. 20, 1057–1075. DOI 10.1155/S1073792802111135. arXiv: math/0112247. Canonical: ht", "authority_tier": "reference", "source": "C. Voisin (2002), Int. Math. Res. Not. 2002, no. 20, 1057–1075", "readable": false, "generated": false}, {"id": "card_chain_eells_sampson_1964", "title": "Eells 1964 — Harmonic mappings of Riemannian manifolds", "shelf": "codex", "surface": "secular", "snippet": "J. Eells, J. H. Sampson (1964). Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86 (1964) 109–160. DOI 10.2307/2373037. Canonical: https://doi.org/10.2307/2373037. Cited by its record. Licen", "authority_tier": "reference", "source": "J. Eells, J. H. Sampson (1964), Amer. J. 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