{"query": "Fluid probability dynamics — one continuity equation across", "count": 20, "results": [{"id": "card_theory_translation_theory__formal_vs_dynamic_equivalence", "title": "Translation theory (formal vs dynamic equivalence)", "shelf": "theories", "surface": "secular", "snippet": "Translation theory (formal vs dynamic equivalence) — an engine domain that can touch it: linguistics. Calibration: map-only — out of scope for sealing — foundational, empirical or interpretive (RESONA", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_antibiotics_resistance", "title": "Antibiotics & antimicrobial resistance (Fleming's own warning)", "shelf": "theories", "surface": "secular", "snippet": "Antibiotics & antimicrobial resistance (Fleming's own warning) — an engine domain that can touch it: medicine. Calibration: map-only — dosing computes (see pharmacokinetics); resistance dynamics are e", "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_3cc9f3e8e74f", "title": "Fokker–Planck & Liouville instantiates Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "Statistical mechanics is the stochastic instance of the probability-continuity equation.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_c_e510a4e8b7f4", "title": "Diffusion models instantiate Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "The probability-flow ODE is the same continuity equation with a learned velocity.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_n_810d857d886e", "title": "Madelung hydrodynamics — quantum mechanics as a probability fluid", "shelf": "science", "surface": "secular", "snippet": "Write ψ = √ρ·e^(iS/ħ) and the Schrödinger equation becomes fluid dynamics of the probability\ndensity ρ = |ψ|²: a continuity equation with velocity v = ∇S/m, plus an Euler equation carrying a\n'quantum ", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_c_576d28632055", "title": "Madelung hydrodynamics instantiates Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "Quantum mechanics rewritten as the fluid dynamics of |ψ|².", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_c_c1d4f07c75cd", "title": "Fokker–Planck & Liouville — probability flow ↔ Fluid probability dynamics — one continuity ", "shelf": "connections", "surface": null, "snippet": "The stochastic instantiation of probability-as-fluid. ... In Hamiltonian phase space, Liouville's theorem gives dρ/dt = 0 — the probability fluid is incompressible.  — a concord the card itself states", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_c_108666f40f9f", "title": "Fluid probability dynamics resonates with Fluid dynamics of the axes", "shelf": "connections", "surface": null, "snippet": "Same conserved-flow skeleton, read on the map's own axes — RESONANCE, a map-aid not a proof.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_c_37abe9676328", "title": "Fluid probability dynamics — one continuity  ↔ Balancing equations — nothing is created or ", "shelf": "connections", "surface": null, "snippet": "the continuity equation dρ/dt + ∇·J = 0 (current J = ρv) says density is never created or destroyed — it only flows  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_c_41cd8b933961", "title": "Fluid probability dynamics — one continuity  ↔ Madelung hydrodynamics — quantum mechanics a", "shelf": "connections", "surface": null, "snippet": "quantum mechanics (Madelung: v = ∇S/m plus a quantum potential — the Schrödinger equation rewritten as fluid dynamics of |ψ|²)  — a concord the card itself states; mined + verified.", "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_n_ff27b07c4577", "title": "Fluid dynamics as the behavior of the axes", "shelf": "concepts", "surface": "secular", "snippet": "Matt: 'Fluid dynamics as behavior of axes? something along that line.' The axes are not static — they FLOW and redistribute as the map grows. Fluid dynamics may describe their behavior: a turbulent fl", "authority_tier": "matt", "source": "Operator's seed (Matt) — honest grade: resonance", "generated": false}, {"id": "card_c_3437884ad1bb", "title": "Fluid probability dynamics related to the spectral (Fourier) lens", "shelf": "connections", "surface": null, "snippet": "Fourier eigenmodes of the Laplacian are exactly how the diffusion/continuity operator is solved.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_c_1650c345cc7d", "title": "Pheromones — the molecule is the message ↔ Fluid probability dynamics — one continuity ", "shelf": "connections", "surface": null, "snippet": "Pheromones DIFFUSE down a gradient (the continuity/diffusion equation) and DECAY (the exponential clock) — the fluid and the clock of this whole map, carried in a scent.  — a concord the card itself s", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_c_d7daafda1482", "title": "Fluid probability dynamics — one continuity  ↔ Diffusion models — the probability-flow ODE ", "shelf": "connections", "surface": null, "snippet": "machine learning (the probability-flow ODE under diffusion models)  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "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_src_port_tcp_2150_dynamic3d", "title": "Port 2150/tcp — dynamic3d", "shelf": "networking", "surface": "secular", "snippet": "Port 2150/tcp is assigned to dynamic3d: DYNAMIC3D.", "authority_tier": "reference", "source": "IANA Service Name and Port Number Registry (public domain)", "generated": false}, {"id": "card_src_port_udp_2150_dynamic3d", "title": "Port 2150/udp — dynamic3d", "shelf": "networking", "surface": "secular", "snippet": "Port 2150/udp is assigned to dynamic3d: DYNAMIC3D.", "authority_tier": "reference", "source": "IANA Service Name and Port Number Registry (public domain)", "generated": false}, {"id": "card_src_word_dynamic_viscosity", "title": "dynamic viscosity", "shelf": "dictionary", "surface": "secular", "snippet": "dynamic viscosity: (noun) a measure of the resistance to flow of a fluid under an applied force — syn: coefficient of viscosity, absolute viscosity", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}]}