{"query": "Density from mass and volume", "count": 20, "results": [{"id": "card_works_density", "title": "Density from mass and volume", "shelf": "the-works", "surface": "secular", "snippet": "Ten kilograms in five litres is a density of 2,000 kg/m³ — ρ = m/V, the property that tells iron from aluminium and floats a ship of steel.  Worked & sealed by the engine — ρ = 10 / 0.005 = 2000 kg/m³", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_theory_thermohaline_circulation", "title": "Thermohaline circulation (the ocean conveyor)", "shelf": "theories", "surface": "secular", "snippet": "Thermohaline circulation (the ocean conveyor) — an engine domain that can touch it: oceanography. Calibration: partial — specific relations verify; the theory as a whole is not a sealable computation.", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "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_periodic_law", "title": "Periodic law (Mendeleev)", "shelf": "theories", "surface": "secular", "snippet": "Periodic law (Mendeleev) — an engine domain that can touch it: periodic_table. Calibration: seals — element properties and group trends look up and compute. Arrange elements by atomic number and their", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_physical_oceanography", "title": "Physical oceanography (hydrostatics, tides)", "shelf": "theories", "surface": "secular", "snippet": "Physical oceanography (hydrostatics, tides) — an engine domain that can touch it: oceanography. Calibration: seals — pressure with depth and tidal periods compute. Pressure rises about one atmosphere ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_category_theory", "title": "Category theory (the mathematics of structure-preserving maps)", "shelf": "theories", "surface": "secular", "snippet": "Category theory (the mathematics of structure-preserving maps) — an engine domain that can touch it: mathematics. Calibration: map-only — an organising framework rather than a computation. Study objec", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_n_bbecbbc24fb6", "title": "The nucleus — the strongest glue and the slowest clocks", "shelf": "science", "surface": "secular", "snippet": "Past gamma rays the spectrum ends and the nucleus itself begins. One chain,\neight steps, sealed — four of them IN-DOMAIN by the nuclear fleet: https://narrowhighway.com/s/8a5e89ab13bc499f39240c64360d9", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_bridge_theory_elasticity__acoustic_wave_theory", "title": "Bridge: Elasticity (Hooke's law, stress–strain)  ↔  Acoustic wave theory (harmonics, Doppler)", "shelf": "bridges", "surface": "secular", "snippet": "Elasticity (Hooke's law, stress–strain) and Acoustic wave theory (harmonics, Doppler) are the same form in different domains. Hooke's linear restoring force gives the harmonic oscillator, and a contin", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_quantum_information___entanglement__von_neumann_entr__shannon_information_theory", "title": "Bridge: Quantum information & entanglement (von Neumann entropy)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Quantum information & entanglement (von Neumann entropy) and Shannon information theory (entropy, channel capacity) are the same form in different domains. von Neumann entropy S = -Tr(rho log rho) red", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_floor_oceanography", "title": "Oceanography — the salt sea in motion", "shelf": "codex", "surface": "secular", "snippet": "Pressure rises with depth; seawater is 3.5 percent salt; density differences drive the thermohaline conveyor. Three pillars rest on earth science (the basins), chemistry (dissolved salts) and thermody", "authority_tier": "engine_derived", "source": "Narrow Highway — oceanography", "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_domchk_quantum_computing_claimed_normalized", "title": "Quantum Computing: normalized", "shelf": "quantum_computing", "surface": "secular", "snippet": "A worked check in quantum computing: normalized.\n\nGIVEN\n  amplitudes = [0.6, 0.8]\n  density_eigenvalues = [0.5, 0.5]\n  inner_product = 0.707\n  n_items = 64\n  qber = 0.09\n  qber_threshold = 0.11\n  shor", "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_bridge_theory_category_theory__group_theory", "title": "Bridge: Category theory (the mathematics of structure-preserving maps)  ↔  Group theory & symmetry (the mathematics of what stays the same)", "shelf": "bridges", "surface": "secular", "snippet": "Category theory (the mathematics of structure-preserving maps) and Group theory & symmetry (the mathematics of what stays the same) are the same form in different domains. a group IS a category with o", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "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_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_n_b04a994d0276", "title": "X-rays — shadows cast by 12-picometer light", "shelf": "science", "surface": "secular", "snippet": "Sealed: a 100 keV medical X-ray photon has a wavelength of 12.3 pm — smaller than an\natom: https://narrowhighway.com/s/2e10f3cd833c0da8ed1973eeb517c9de779e8956cd7d04eeee423aab280c4455 . That is why X-", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_bridge_master_entropy_log", "title": "Master equation: S = -k * sum(p_i log p_i)", "shelf": "bridges", "surface": "secular", "snippet": "disorder and information are one quantity — Boltzmann's S and Shannon's H are the same sum. ONE equation, 4 domains, connected by a change of variable: information_theory [k = 1/ln2 (bits), p = symbol", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_c_9e6d4c83f9bf", "title": "The nucleus — the strongest glue and the slo ↔ Fission — 82 terajoules in a kilogram", "shelf": "connections", "surface": null, "snippet": "uranium-235's fission energy density — 82 TJ/kg, sealed as 2.737 million times coal  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_n_22f6cb5bf619", "title": "Fission — 82 terajoules in a kilogram", "shelf": "science", "surface": "secular", "snippet": "Split uranium-235 and each atom yields ~200 MeV. Scaled by Avogadro's number (exact\nsince 2019), sealed: 82 TJ per kilogram — 2.737 million times coal at 30 MJ/kg: https://narrowhighway.com/s/8a5e89ab", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_bridge_master_diffusion_equation", "title": "Master equation: du/dt = D * laplacian(u)", "shelf": "bridges", "surface": "secular", "snippet": "spreading by random walk — first in time, second in space. ONE equation, 8 domains, connected by a change of variable: thermodynamics [u = temperature, D = thermal diffusivity]; chemistry [u = concent", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "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_works_density"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}