{"query": "Madelung hydrodynamics — quantum mechanics as a probability", "count": 5, "results": [{"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_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_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_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_b0dd29a6dbce", "title": "The periodic table — the map of the elements ↔ Madelung hydrodynamics — quantum mechanics a", "shelf": "connections", "surface": null, "snippet": "its periodicity is the fingerprint of the quantum shells beneath  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}]}