{"query": "Flow - discharge and the continuity equation", "count": 20, "results": [{"id": "card_hydrology_flow", "title": "Flow - discharge and the continuity equation", "shelf": "codex", "surface": "secular", "snippet": "Q = v A governs every river and flood (sealed); conservation of mass is the continuity equation. Rests on earth science.", "authority_tier": "engine_derived", "source": "Narrow Highway — hydrology", "readable": false, "generated": false}, {"id": "card_theory_fluid_mechanics", "title": "Fluid mechanics (Bernoulli, Reynolds, Navier–Stokes)", "shelf": "theories", "surface": "secular", "snippet": "Fluid mechanics (Bernoulli, Reynolds, Navier–Stokes) — an engine domain that can touch it: hydrology. Calibration: seals — continuity, Bernoulli and Reynolds number compute directly. CONTINUITY first:", "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_fundamental_theorem_of_algebra", "title": "Fundamental theorem of algebra", "shelf": "theories", "surface": "secular", "snippet": "Fundamental theorem of algebra — an engine domain that can touch it: mathematics. Calibration: partial — root counts verify; the existence proof is map-only. Every non-constant polynomial with complex", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "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", "readable": false, "generated": false}, {"id": "card_n_e5c0cda9157a", "title": "Belgic Art. 34: Holy Baptism", "shelf": "codex", "surface": "witness", "snippet": "We believe and confess that Jesus Christ, in whom the law is fulfilled, has by his shed blood put an end to every other shedding of blood. Therefore he has instituted in its place the sacrament of bap", "authority_tier": "creed", "source": "Belgic Confession (1561)", "readable": false, "generated": false}, {"id": "card_n_ae08bd563c6e", "title": "Balancing equations — nothing is created or destroyed", "shelf": "science", "surface": "secular", "snippet": "Lavoisier's law: matter is conserved, so a chemical equation must have equal atoms on\nboth sides. The engine balances in-domain — given CH4 + O2 -> CO2 + H2O it returns the true\ncoefficients CH4 + 2 O", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_n_0a41c0e3298d", "title": "Pheromones — the molecule is the message", "shelf": "science", "surface": "secular", "snippet": "A pheromone is chemistry acting as language: a molecule IS a signal. Sealed: a\n20-component blend encodes 2^20 = 1,048,576 distinguishable messages (~4.3 bits per component),\nand an ant's trail evapor", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_bridge_theory_circulation_harvey__fluid_mechanics", "title": "Bridge: Circulation of the blood (Harvey's quantitative argument)  ↔  Fluid mechanics (Bernoulli, Reynolds, Navier–Stokes)", "shelf": "bridges", "surface": "secular", "snippet": "Circulation of the blood (Harvey's quantitative argument) and Fluid mechanics (Bernoulli, Reynolds, Navier–Stokes) are the same form in different domains. Harvey's argument was ARITHMETIC -- ejected v", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_dual_conservation__linear_flux", "title": "Duality: conservation  ↔  linear_flux  (continuity equation)", "shelf": "bridges", "surface": "secular", "snippet": "A deep bridge between two forms — continuity equation. a conservation law in differential form is the continuity equation: the divergence of a flux equals the rate of change of what is stored", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_c_77ba6d7691ca", "title": "Pheromones — the molecule is the message ↔ Radioactive decay — the exponential clock of", "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", "readable": false, "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", "readable": false, "generated": false}, {"id": "card_maxwell_gauge_charge", "title": "U(1) gauge symmetry → conservation of charge", "shelf": "codex", "surface": "secular", "snippet": "Electromagnetism is the U(1) gauge theory, and by Noether its symmetry gives conservation of electric charge - the continuity equation d(rho)/dt + div J = 0 is built into Maxwell's equations. The symm", "authority_tier": "engine_derived", "source": "Narrow Highway — Maxwell's equations", "readable": false, "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", "readable": false, "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", "readable": false, "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", "readable": false, "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", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_introduction_to_fluid_dynamics_and_its_b_637c23e8", "title": "Introduction to Fluid Dynamics and Its Biological and Medical Applications — College Physics", "shelf": "physics", "surface": "secular", "snippet": "Figure\n12.1\n\nMany fluids are flowing in this scene. Water from the hose and smoke from the fire are visible flows. Less visible are the flow of air and the flow of fluids on the ground and within the ", "authority_tier": "reference", "source": "OpenStax: College Physics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_ap_courses_12_1_flow_rate_and_its_relation_to_veloc_18c425b0", "title": "12.1 Flow Rate and Its Relation to Velocity — College Physics for AP® Courses", "shelf": "physics", "surface": "secular", "snippet": "12.1\n\nFlow Rate and Its Relation to Velocity\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\nCalculate flow rate.\n\nDefine units of volume.\n\nDescribe incompressible fluids.\n\nExp", "authority_tier": "reference", "source": "OpenStax: College Physics for AP® Courses (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_calc_continuity", "title": "Continuity equation", "shelf": "calculations", "surface": "secular", "snippet": "Continuity equation — physics. Formula: d(rho)/dt + div(rho v) = 0. Canonical FORM: conservation (in = out + change_in_store) — the general law: what flows in must be stored or flow out. Same form, 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_hydrology_flow"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}