{"query": "Light bends: Snell's law at a glass surface", "count": 20, "results": [{"id": "card_works_snell", "title": "Light bends: Snell's law at a glass surface", "shelf": "the-works", "surface": "secular", "snippet": "Passing from air into glass (n = 1.5) at 30°, a ray refracts to 19.47° — n₁ sin θ₁ = n₂ sin θ₂. The same law bends every lens and every rainbow.  Worked & sealed by the engine — sin θ₂ = (1·sin30)/1.5", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_theory_wave_optics", "title": "Wave optics (Huygens, Snell's law, diffraction)", "shelf": "theories", "surface": "secular", "snippet": "Wave optics (Huygens, Snell's law, diffraction) — an engine domain that can touch it: optics. Calibration: seals — refraction, lens and diffraction relations compute. Light behaves as a wave: it refra", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_bridge_theory_acoustic_wave_theory__wave_optics", "title": "Bridge: Acoustic wave theory (harmonics, Doppler)  ↔  Wave optics (Huygens, Snell's law, diffraction)", "shelf": "bridges", "surface": "secular", "snippet": "Acoustic wave theory (harmonics, Doppler) and Wave optics (Huygens, Snell's law, diffraction) are the same form in different domains. both are the wave equation in different media: Huygens' constructi", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_hub_wave_optics", "title": "Hub: Wave optics (Huygens, Snell's law, diffraction) carries 3 domains", "shelf": "bridges", "surface": "secular", "snippet": "Calculations from 3 different domains (materials_science, optics, photonics) all rest on Wave optics (Huygens, Snell's law, diffraction) — one theory holding up many fields.", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_depth_of_field__wave_optics", "title": "Bridge: Depth of field & hyperfocal distance  ↔  Wave optics (Huygens, Snell's law, diffraction)", "shelf": "bridges", "surface": "secular", "snippet": "Depth of field & hyperfocal distance and Wave optics (Huygens, Snell's law, diffraction) are the same form in different domains. focus and the circle of confusion are optics — the lens equation on a s", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_calc_fermat_time", "title": "Fermat's least time", "shelf": "calculations", "surface": "secular", "snippet": "Fermat's least time — optics. Formula: delta (path time) = 0. Canonical FORM: optimization (d/dx f = 0) — light takes the path of least time — Snell's law falls out. Same form, different domain: this ", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_bridge_master_stationary_action", "title": "Master equation: delta(integral L) = 0", "shelf": "bridges", "surface": "secular", "snippet": "nature takes the extremal path — physics as optimization over functions. ONE equation, 5 domains, connected by a change of variable: physics [L = kinetic - potential; the path extremizes the action]; ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_theory_scaling_laws", "title": "Scaling laws & allometry (Kleiber's law, the square-cube)", "shelf": "theories", "surface": "secular", "snippet": "Scaling laws & allometry (Kleiber's law, the square-cube) — an engine domain that can touch it: biology. Calibration: seals — scaling exponents and ratios compute exactly. Size is not neutral: when a ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_newton_s_law_of_universal_gravitation", "title": "Newton's law of universal gravitation", "shelf": "theories", "surface": "secular", "snippet": "Newton's law of universal gravitation — an engine domain that can touch it: physics. Calibration: seals. F = G·m₁m₂/r². Every mass attracts every other, with a force falling as the SQUARE of the dista", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_heat_transfer", "title": "Heat transfer (conduction, convection, radiation)", "shelf": "theories", "surface": "secular", "snippet": "Heat transfer (conduction, convection, radiation) — an engine domain that can touch it: thermodynamics. Calibration: seals — Fourier's law, R-values and Stefan–Boltzmann all compute. Heat moves three ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_sanitation_clean_water", "title": "Sanitation, clean water & oral rehydration (Snow's pump handle)", "shelf": "theories", "surface": "secular", "snippet": "Sanitation, clean water & oral rehydration (Snow's pump handle) — an engine domain that can touch it: medicine. Calibration: seals — ORS composition and dilution compute exactly. In the 1854 Soho chol", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_renormalization_group", "title": "The renormalization group (physics across scales)", "shelf": "theories", "surface": "secular", "snippet": "The renormalization group (physics across scales) — an engine domain that can touch it: physics. 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_fundamental_theorem_of_calculus", "title": "Fundamental theorem of calculus", "shelf": "theories", "surface": "secular", "snippet": "Fundamental theorem of calculus — an engine domain that can touch it: mathematics. Calibration: seals. Differentiation and integration are inverse operations. Part one: the derivative of the accumulat", "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_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_acoustic_wave_theory", "title": "Acoustic wave theory (harmonics, Doppler)", "shelf": "theories", "surface": "secular", "snippet": "Acoustic wave theory (harmonics, Doppler) — an engine domain that can touch it: acoustics. Calibration: seals — frequencies, harmonics and Doppler shifts compute. Sound is a PRESSURE wave in a medium,", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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_geostrophic_balance", "title": "Geostrophic balance & Coriolis dynamics", "shelf": "theories", "surface": "secular", "snippet": "Geostrophic balance & Coriolis dynamics — an engine domain that can touch it: meteorology. Calibration: partial — specific relations verify; the theory as a whole is not a sealable computation. In lar", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_tuning_systems_comma", "title": "Tuning systems & the Pythagorean comma", "shelf": "theories", "surface": "secular", "snippet": "Tuning systems & the Pythagorean comma — an engine domain that can touch it: music_theory. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, and seal t", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_chemical_bonding", "title": "Chemical bonding (valence-bond / molecular-orbital)", "shelf": "theories", "surface": "secular", "snippet": "Chemical bonding (valence-bond / molecular-orbital) — an engine domain that can touch it: chemistry. Calibration: partial — some relations verify; the full theory is map-only. Atoms bond to lower thei", "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_works_snell"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}