{"query": "G. Perelman 2003 — Finite extinction time for the solutions", "count": 12, "results": [{"id": "card_floor_millennium", "title": "The Millennium floor - seven open questions, and where they connect", "shelf": "codex", "surface": "secular", "snippet": "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 ", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor (operator seed)", "readable": false, "generated": false}, {"id": "card_floor_logarithm", "title": "The logarithm - the instrument the joints share", "shelf": "codex", "surface": "secular", "snippet": "Two trees: Napier's table (1614) and Saint-Vincent's hyperbola (1647) - a number's logarithm as a tabulated count, and as an area. They become one function in Euler's Introductio (1748): e, and exp an", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "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_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_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_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_src_mill_cao_zhu_2006", "title": "H.-D. Cao 2006 — A complete proof of the Poincaré and geometrization conjectures — application of the Hamilton-Perelman theory of the Ricci flow", "shelf": "millennium", "surface": "secular", "snippet": "H.-D. Cao, X.-P. Zhu (2006). A complete proof of the Poincaré and geometrization conjectures — application of the Hamilton-Perelman theory of the Ricci flow. Asian J. Math. 10 (2006) 165–492. DOI 10.4", "authority_tier": "reference", "source": "H.-D. Cao, X.-P. Zhu (2006), Asian J. Math. 10 (2006) 165–492", "readable": false, "generated": false}, {"id": "card_src_mill_perelman_2002", "title": "G. Perelman 2002 — The entropy formula for the Ricci flow and its geometric applications", "shelf": "millennium", "surface": "secular", "snippet": "G. Perelman (2002). The entropy formula for the Ricci flow and its geometric applications. arXiv (2002). arXiv: math/0211159. Canonical: https://arxiv.org/abs/math/0211159. Free copy: https://arxiv.or", "authority_tier": "reference", "source": "G. Perelman (2002), arXiv (2002)", "readable": false, "generated": false}, {"id": "card_chain_hamilton_1995", "title": "Hamilton 1995 — The formation of singularities in the Ricci flow", "shelf": "codex", "surface": "secular", "snippet": "R. S. Hamilton (1995). The formation of singularities in the Ricci flow. Surveys in Differential Geometry 2 (1995) 7–136. DOI 10.4310/SDG.1993.v2.n1.a2. Canonical: https://doi.org/10.4310/SDG.1993.v2.", "authority_tier": "reference", "source": "R. S. Hamilton (1995), Surveys in Differential Geometry 2 (1995) 7–136", "readable": false, "generated": false}, {"id": "card_src_pron_perelman", "title": "perelman", "shelf": "pronunciation", "surface": "secular", "snippet": "perelman: pronounced (ARPABET) P EH1 R AH0 L M AH0 N. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_calc_black_scholes", "title": "Black-Scholes equation", "shelf": "calculations", "surface": "secular", "snippet": "Black-Scholes equation — finance. Formula: dV/dt + rS dV/dS + sigma^2 S^2/2 d2V/dS2 = rV. Canonical FORM: diffusion (du/dt = D * laplacian(u)) — an option price diffuses — the heat equation in disguis", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_kimura_diffusion", "title": "Kimura allele diffusion", "shelf": "calculations", "surface": "secular", "snippet": "Kimura allele diffusion — biology. Formula: dp/dt = drift + (1/2)V d2p/dp^2. Canonical FORM: diffusion (du/dt = D * laplacian(u)) — allele frequencies drift and diffuse in a finite population — the di", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_floor_millennium"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}