{"query": "Free fall: how far in two seconds", "count": 20, "results": [{"id": "card_works_free_fall", "title": "Free fall: how far in two seconds", "shelf": "the-works", "surface": "secular", "snippet": "Drop something from rest near Earth. Constant g = 9.8 m/s² carries it 19.6 m in two seconds — s = ½·a·t².  Worked & sealed by the engine — s = ½·g·t² = ½·9.8·2² = 19.6 m.  [HOLDS; open the seal to re-", "authority_tier": "verified", "source": "The Works — worked & sealed", "generated": false}, {"id": "card_theory_systems_engineering", "title": "Systems engineering (requirements, interfaces, and emergent failure)", "shelf": "theories", "surface": "secular", "snippet": "Systems engineering (requirements, interfaces, and emergent failure) — an engine domain that can touch it: operations_research. Calibration: map-only — a discipline of practice; reliability and margin", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_statistical_mechanics", "title": "Statistical mechanics (Boltzmann — why the second law is a counting argument)", "shelf": "theories", "surface": "secular", "snippet": "Statistical mechanics (Boltzmann — why the second law is a counting argument) — an engine domain that can touch it: thermodynamics. Calibration: seals — Boltzmann distributions, partition functions an", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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)", "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)", "generated": false}, {"id": "card_theory_second_law_of_thermodynamics", "title": "Second law of thermodynamics (entropy)", "shelf": "theories", "surface": "secular", "snippet": "Second law of thermodynamics (entropy) — an engine domain that can touch it: thermodynamics. Calibration: partial — efficiency and entropy changes compute; the arrow of time is map-only. The entropy o", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_landauer", "title": "Landauer's principle (erasing information costs heat)", "shelf": "theories", "surface": "secular", "snippet": "Landauer's principle (erasing information costs heat) — an engine domain that can touch it: information_theory. Calibration: seals — the energy bound computes exactly. ERASING one bit must dissipate a", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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)", "generated": false}, {"id": "card_theory_error_correcting_codes", "title": "Error-correcting codes (Hamming, Reed–Solomon)", "shelf": "theories", "surface": "secular", "snippet": "Error-correcting codes (Hamming, Reed–Solomon) — an engine domain that can touch it: information_theory. Calibration: seals — code distances, correctable error counts and parity all compute exactly. A", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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)", "generated": false}, {"id": "card_theory_mechanism_design___auction_theory", "title": "Mechanism design & auction theory", "shelf": "theories", "surface": "secular", "snippet": "Mechanism design & auction theory — an engine domain that can touch it: economics. Calibration: partial — auction outcomes and incentive conditions compute. Game theory run BACKWARDS: instead of askin", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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)", "generated": false}, {"id": "card_theory_exercise_physiology", "title": "Exercise physiology (VO₂max, HR zones)", "shelf": "theories", "surface": "secular", "snippet": "Exercise physiology (VO₂max, HR zones) — an engine domain that can touch it: exercise_science. Calibration: seals — max HR estimates, zones and work rates compute. VO₂max is the maximum rate of oxygen", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_special_relativity", "title": "Special relativity", "shelf": "theories", "surface": "secular", "snippet": "Special relativity — an engine domain that can touch it: physics. Calibration: partial — Lorentz and E = mc² relations verify; the postulates are map-only. Two postulates (Einstein, 1905): the laws of", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_conservation_of_energy", "title": "Conservation of energy (1st law of thermodynamics)", "shelf": "theories", "surface": "secular", "snippet": "Conservation of energy (1st law of thermodynamics) — an engine domain that can touch it: thermodynamics. Calibration: seals. Energy is neither created nor destroyed, only converted. ΔU = Q - W: the ch", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_carnot_efficiency", "title": "The Carnot limit (the ceiling on every engine ever built)", "shelf": "theories", "surface": "secular", "snippet": "The Carnot limit (the ceiling on every engine ever built) — an engine domain that can touch it: thermodynamics. Calibration: seals — the efficiency bound computes from two temperatures. No heat engine", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_differential_equations", "title": "Differential equations (the language every physical law is written in)", "shelf": "theories", "surface": "secular", "snippet": "Differential equations (the language every physical law is written in) — an engine domain that can touch it: mathematics. Calibration: seals — solutions verify by substitution; specific integrations c", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_peano_arithmetic_axioms", "title": "Peano arithmetic axioms", "shelf": "theories", "surface": "secular", "snippet": "Peano arithmetic axioms — an engine domain that can touch it: number_theory. Calibration: seals. Five axioms generating the natural numbers: zero is a number, every number has a successor, zero succee", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_g_del_s_incompleteness_theorems", "title": "Gödel's incompleteness theorems", "shelf": "theories", "surface": "secular", "snippet": "Gödel's incompleteness theorems — an engine domain that can touch it: formal_logic. Calibration: map-only — a meta-theorem about systems, not a sealable computation. FIRST (1931): any consistent forma", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_vaccination_immunity", "title": "Vaccination & immune memory (Jenner to eradication)", "shelf": "theories", "surface": "secular", "snippet": "Vaccination & immune memory (Jenner to eradication) — an engine domain that can touch it: medicine. Calibration: map-only — herd-immunity thresholds compute; efficacy is empirical. Show the immune sys", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}]}