{"query": "Madelung hydrodynamics — quantum mechanics as a probability", "count": 20, "results": [{"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_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_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_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", "readable": false, "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", "readable": false, "generated": false}, {"id": "card_theory_kolmogorov_probability_axioms", "title": "Kolmogorov probability axioms", "shelf": "theories", "surface": "secular", "snippet": "Kolmogorov probability axioms — an engine domain that can touch it: probability. Calibration: seals. Three axioms (1933): probabilities are non-negative, the whole sample space has probability 1, and ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_quantum_gravity_problem", "title": "Spacetime & the quantum-gravity problem (where physics ends)", "shelf": "theories", "surface": "secular", "snippet": "Spacetime & the quantum-gravity problem (where physics ends) — an engine domain that can touch it: physics. Calibration: map-only — the Planck quantities compute, but there is no accepted theory here ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_topological_quantum_computation", "title": "Topological quantum computation (non-Abelian / Fibonacci anyons)", "shelf": "theories", "surface": "secular", "snippet": "Topological quantum computation (non-Abelian / Fibonacci anyons) — an engine domain that can touch it: quantum_computing. Calibration: partial — specific relations verify; the theory as a whole is not", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_quantum_mechanics", "title": "Quantum mechanics (Schrödinger equation)", "shelf": "theories", "surface": "secular", "snippet": "Quantum mechanics (Schrödinger equation) — an engine domain that can touch it: physics. Calibration: partial — energy levels and specific relations verify; interpretation is map-only. A system is desc", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_quantum_information___entanglement__von_neumann_entr", "title": "Quantum information & entanglement (von Neumann entropy)", "shelf": "theories", "surface": "secular", "snippet": "Quantum information & entanglement (von Neumann entropy) — an engine domain that can touch it: information_theory. Calibration: seals. S = -Tr(ρ log ρ), the entropy of a density matrix, which reduces ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_quantum_error_correction", "title": "Quantum error correction & the threshold theorem", "shelf": "theories", "surface": "secular", "snippet": "Quantum error correction & the threshold theorem — an engine domain that can touch it: quantum_computing. Calibration: partial — specific relations verify; the theory as a whole is not a sealable comp", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_bohr_quantum_model_of_the_atom", "title": "Bohr / quantum model of the atom", "shelf": "theories", "surface": "secular", "snippet": "Bohr / quantum model of the atom — an engine domain that can touch it: atomic. Calibration: seals — energy levels and shell capacities compute. Electrons occupy discrete orbits with QUANTISED energies", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_casimir_effect", "title": "The Casimir effect (structured energy of the quantum vacuum)", "shelf": "theories", "surface": "secular", "snippet": "The Casimir effect (structured energy of the quantum vacuum) — an engine domain that can touch it: physics. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn fr", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_newton_s_three_laws_of_motion", "title": "Newton's three laws of motion", "shelf": "theories", "surface": "secular", "snippet": "Newton's three laws of motion — an engine domain that can touch it: physics. Calibration: seals. (1) A body keeps its velocity unless a force acts — which contradicts everyday experience only because ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_domchk_atomic_claimed_valid_quantum_numbers", "title": "Atomic: valid quantum numbers", "shelf": "atomic", "surface": "secular", "snippet": "A worked check in atomic: valid quantum numbers.\n\nGIVEN\n  l = 2\n  n = 3\n\nCLAIMED\n  claimed_valid_quantum_numbers = True\n\nTHE ENGINE'S VERDICT\n  atomic.quantum_numbers: CONFIRMED — validity True matche", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_theory_quantization", "title": "Quantization (why nature comes in whole units)", "shelf": "theories", "surface": "secular", "snippet": "Quantization (why nature comes in whole units) — an engine domain that can touch it: physics. Calibration: seals — energy levels, photon energies and charge multiples compute exactly. Certain physical", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_superfluid_vacuum_theory", "title": "Superfluid vacuum theory (the vacuum as a quantum liquid)", "shelf": "theories", "surface": "secular", "snippet": "Superfluid vacuum theory (the vacuum as a quantum liquid) — an engine domain that can touch it: physics. Calibration: map-only — out of scope for sealing — foundational, empirical or interpretive (RES", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_3_introduction_018ccaf5", "title": "Introduction — University Physics Volume 3", "shelf": "physics", "surface": "secular", "snippet": "Figure\n7.1\n\nA D-wave qubit processor: The brain of a quantum computer that encodes information in quantum bits to perform complex calculations. (credit: modification of work by D-Wave Systems, Inc.)\n\n", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 3 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_bridge_theory_quantum_mechanics__game_theory", "title": "Bridge: Quantum mechanics (Schrödinger equation)  ↔  Game theory (Nash equilibrium)", "shelf": "bridges", "surface": "secular", "snippet": "Quantum mechanics (Schrödinger equation) and Game theory (Nash equilibrium) are the same form in different domains. a MIXED STRATEGY and a QUANTUM MIXED STATE are the same object: a probability distri", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_theory_pauli_exclusion_principle", "title": "Pauli exclusion principle", "shelf": "theories", "surface": "secular", "snippet": "Pauli exclusion principle — an engine domain that can touch it: atomic. Calibration: seals — electron configurations and shell capacities compute. No two identical fermions may occupy the same quantum", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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_n_8530c72a2201"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}