{"query": "Optimal transport — the geometry of moving probability", "count": 20, "results": [{"id": "card_n_d59ca677ea24", "title": "Optimal transport — the geometry of moving probability", "shelf": "science", "surface": "secular", "snippet": "Benamou–Brenier: the distance between two distributions is the least kinetic energy of a\nfluid that carries one to the other, subject to the continuity equation. Jordan–Kinderlehrer–Otto\n(1998): the F", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_theory_explore_exploit", "title": "Explore versus exploit (the multi-armed bandit)", "shelf": "theories", "surface": "secular", "snippet": "Explore versus exploit (the multi-armed bandit) — an engine domain that can touch it: operations_research. Calibration: map-only — regret bounds are asymptotic; specific policies compute. When you mus", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_honeycomb_conjecture", "title": "Optimal packing & the honeycomb conjecture (Hales)", "shelf": "theories", "surface": "secular", "snippet": "The hexagonal grid is the most efficient way to divide a surface into regions of equal area with the LEAST TOTAL PERIMETER. Stated by Pappus of Alexandria around 300 AD as an observation about bees, i", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_mechanism_design___auction_theory", "title": "Mechanism design & auction theory", "shelf": "theories", "surface": "secular", "snippet": "Mechanism design & auction theory — an engine domain that can touch it: economics. Calibration: partial — auction outcomes and incentive conditions compute. Game theory run BACKWARDS: instead of askin", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_linear_programming_duality", "title": "Linear programming & duality", "shelf": "theories", "surface": "secular", "snippet": "Linear programming & duality — an engine domain that can touch it: operations_research. Calibration: seals — optimal values and shadow prices compute. Maximise or minimise a linear objective subject t", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_n_8530c72a2201", "title": "Fluid probability dynamics — one continuity equation across physics, geometry, and ML", "shelf": "science", "surface": "secular", "snippet": "One equation wears many clothes. Probability is a conserved fluid: the continuity equation\ndρ/dt + ∇·J = 0 (current J = ρv) says density is never created or destroyed — it only flows. The\nsame skeleto", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_c_583b49254af6", "title": "Fluid probability dynamics — one continuity  ↔ Optimal transport — the geometry of moving p", "shelf": "connections", "surface": null, "snippet": "geometry (optimal transport: distance = least kinetic energy to carry one distribution to another; Fokker–Planck is the gradient flow of free energy in Wasserstein space)  — a concord the card itself ", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_c_e655b3fcef54", "title": "Optimal transport instantiates Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "The geometry of moving probability — Fokker–Planck as a Wasserstein gradient flow.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_src_word_optimal", "title": "optimal", "shelf": "dictionary", "surface": "secular", "snippet": "optimal: (adjective) most desirable possible under a restriction expressed or implied — syn: optimum", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_pron_optimal", "title": "optimal", "shelf": "pronunciation", "surface": "secular", "snippet": "optimal: pronounced (ARPABET) AA1 P T AH0 M AH0 L. 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", "generated": false}, {"id": "card_src_fed_nasa_techdoc_19620006857", "title": "APPLICATION OF STATISTICAL FILTER THEORY TO THE OPTIMAL ESTIMATION OF POSITION AND VELOCITY ON BOARD A CIRCUMLUNAR VEHICLE", "shelf": "science", "surface": "secular", "snippet": "APPLICATION OF STATISTICAL FILTER THEORY TO THE OPTIMAL ESTIMATION OF POSITION AND VELOCITY ON BOARD A CIRCUMLUNAR VEHICLE. A United States federal publication, public domain (17 USC 105). The full te", "authority_tier": "reference", "source": "NASA technical documents (PD, 17 USC 105)", "generated": false}, {"id": "card_alm_almanac_quantum_grover_search", "title": "Almanac: Grover's search -- square-root, not linear (and not magic)", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  To find one marked item among N with no structure to exploit, a classical search needs about N/2 looks on average. Grover's quantum algorithm (1996) needs about T = floor(pi*sqrt(N)/4) -- ", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "generated": false}, {"id": "card_src_rfc_9107", "title": "RFC9107 — BGP Optimal Route Reflection (BGP ORR)", "shelf": "rfcs", "surface": "secular", "snippet": "RFC9107: BGP Optimal Route Reflection (BGP ORR) (August 2021). Status: PROPOSED STANDARD.", "authority_tier": "reference", "source": "The RFC Index (RFC Editor / IETF) — public domain", "generated": false}, {"id": "card_v_03794e9aea45", "title": "0-1 knapsack (cap 5) → optimal value 7", "shelf": "operations_research", "surface": "secular", "snippet": "Verdict: HOLDS.\n• operations_research.knapsack_01: optimal_value=7.0 (matches claim)\nSealed and independently re-checkable: https://narrowhighway.com/s/146ec914dad0d44e177cd894b09742163848ac2508926d7b", "authority_tier": "engine", "source": "Verified by the engine — operations_research", "generated": false}, {"id": "card_works_knapsack", "title": "The best a knapsack can carry", "shelf": "the-works", "surface": "secular", "snippet": "Given items of weight and value and a fixed capacity, the 0-1 knapsack picks the most valuable subset that fits — here a total value of 7 within a weight of 5. The core of scheduling, budgeting and ca", "authority_tier": "verified", "source": "The Works — worked & sealed", "generated": false}, {"id": "card_n_bbd5dfda4135", "title": "The dwellings — cube to cube to city, and the ship that floats", "shelf": "science", "surface": "secular", "snippet": "The only cubic rooms in Scripture are where God dwells, and they scale: the\nTabernacle's Most Holy Place 10×10×10 cubits → the Temple's 20×20×20 (volume exactly ×8,\nsealed) → the New Jerusalem, 12,000", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}, {"id": "card_src_word_optimization", "title": "optimization", "shelf": "dictionary", "surface": "secular", "snippet": "optimization: (noun) the act of rendering optimal — syn: optimisation", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_optimally", "title": "optimally", "shelf": "dictionary", "surface": "secular", "snippet": "optimally: (adverb) in an optimal and most desirable way", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_optimise", "title": "optimise", "shelf": "dictionary", "surface": "secular", "snippet": "optimise: (verb) make optimal — syn: optimize · (verb) modify to achieve maximum efficiency in storage capacity or time or cost — syn: optimize · (verb) act as an optimist and take a sunny view of the", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_optimize", "title": "optimize", "shelf": "dictionary", "surface": "secular", "snippet": "optimize: (verb) make optimal — syn: optimise · (verb) modify to achieve maximum efficiency in storage capacity or time or cost — syn: optimise · (verb) act as an optimist and take a sunny view of the", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}]}