{"query": "Intervals — the harmonic series in small ratios", "count": 20, "results": [{"id": "card_music_intervals", "title": "Intervals — the harmonic series in small ratios", "shelf": "codex", "surface": "secular", "snippet": "The octave is the ratio 2:1, the perfect fifth 3:2, the fourth 4:3 — the consonant intervals are the low harmonics of a vibrating string or air column, sealed on the music-theory stick. A chord is sta", "authority_tier": "engine_derived", "source": "Narrow Highway — music", "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_music_theory", "title": "Music theory (harmonic series, equal temperament)", "shelf": "theories", "surface": "secular", "snippet": "Music theory (harmonic series, equal temperament) — an engine domain that can touch it: music_theory. Calibration: seals — frequencies, intervals and temperament errors compute exactly. A vibrating st", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_dalton_s_atomic_theory", "title": "Dalton's atomic theory", "shelf": "theories", "surface": "secular", "snippet": "Dalton's atomic theory — an engine domain that can touch it: chemistry. Calibration: partial — mass ratios verify. Matter is made of indivisible atoms; all atoms of an element share a mass; compounds ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_aperiodic_tiling", "title": "Aperiodic tiling (Penrose, and the 2023 monotile)", "shelf": "theories", "surface": "secular", "snippet": "Two tile shapes plus local edge-matching rules that cover the plane completely and CANNOT repeat. Penrose (1974) gave two forms: P2, the kite and dart; P3, a thin rhombus (36°) and a fat one (72°). Th", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_projective_geometry", "title": "Projective geometry (perspective & the cross-ratio)", "shelf": "theories", "surface": "secular", "snippet": "Projective geometry (perspective & the cross-ratio) — an engine domain that can touch it: geometry. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, a", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_mendelian_inheritance", "title": "Mendelian inheritance", "shelf": "theories", "surface": "secular", "snippet": "Mendelian inheritance — an engine domain that can touch it: genetics. Calibration: seals — ratios and Punnett squares compute exactly. Traits are carried by discrete factors, one inherited from each p", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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_law_of_the_minimum", "title": "Liebig's law of the minimum (what actually limits growth)", "shelf": "theories", "surface": "secular", "snippet": "Liebig's law of the minimum (what actually limits growth) — an engine domain that can touch it: soil_science. Calibration: seals — nutrient ratios and deficiency thresholds compute. Growth is limited ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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_stoichiometry_the_mole_concept", "title": "Stoichiometry & the mole concept", "shelf": "theories", "surface": "secular", "snippet": "Stoichiometry & the mole concept — an engine domain that can touch it: chemistry. Calibration: seals — molar masses, yields and limiting reagents compute exactly. A mole is 6.022×10²³ particles, chose", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_radiometric_dating_uniformitarianism", "title": "Radiometric dating & uniformitarianism", "shelf": "theories", "surface": "secular", "snippet": "Radiometric dating & uniformitarianism — an engine domain that can touch it: geology. Calibration: partial — the decay arithmetic seals; the assumptions are map-only. A radioactive isotope decays at a", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_third_law_of_thermodynamics", "title": "Third law of thermodynamics", "shelf": "theories", "surface": "secular", "snippet": "Third law of thermodynamics — an engine domain that can touch it: thermodynamics. Calibration: map-only — a limiting statement, not a computation. As temperature approaches absolute zero, the entropy ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_real_estate_valuation", "title": "Real-estate valuation (cap rate, DCF)", "shelf": "theories", "surface": "secular", "snippet": "Real-estate valuation (cap rate, DCF) — an engine domain that can touch it: real_estate. Calibration: seals — cap rate, NOI and discounted cash flows compute. CAP RATE = net operating income ÷ price. ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_sabermetrics_sports_analytics", "title": "Sabermetrics / sports analytics (Pythagorean expectation, Elo)", "shelf": "theories", "surface": "secular", "snippet": "Sabermetrics / sports analytics (Pythagorean expectation, Elo) — an engine domain that can touch it: sports_analytics. Calibration: seals — expected win ratios and Elo updates compute. Bill James's Py", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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_structural_statics", "title": "Structural statics (load, moment, floor-area ratio)", "shelf": "theories", "surface": "secular", "snippet": "Structural statics (load, moment, floor-area ratio) — an engine domain that can touch it: architecture. Calibration: seals — reactions, moments and load paths compute. Nothing accelerates, so forces a", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_ac_polyphase_power", "title": "AC & the polyphase system (Tesla, and why the grid is alternating)", "shelf": "theories", "surface": "secular", "snippet": "AC & the polyphase system (Tesla, and why the grid is alternating) — an engine domain that can touch it: electrical. Calibration: seals — transmission loss, turns ratio and phase relations compute. Ni", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_electromagnetic_induction", "title": "Electromagnetic induction (Faraday's law — how all electricity is made)", "shelf": "theories", "surface": "secular", "snippet": "Electromagnetic induction (Faraday's law — how all electricity is made) — an engine domain that can touch it: electrical. Calibration: seals — EMF, turns ratio and flux relations compute. A CHANGING m", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_dna_structure", "title": "The double helix (structure that explains its own copying)", "shelf": "theories", "surface": "secular", "snippet": "The double helix (structure that explains its own copying) — an engine domain that can touch it: genetics. Calibration: seals — base-pair ratios, melting temperatures and complement sequences compute.", "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_music_intervals"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}