{"query": "How fast water runs in an open channel", "count": 20, "results": [{"id": "card_works_manning", "title": "How fast water runs in an open channel", "shelf": "the-works", "surface": "secular", "snippet": "Manning's equation gives the velocity of water in a channel from its roughness, depth and slope — here 3.33 m/s. It sizes culverts, canals and storm drains.  Worked & sealed by the engine — V = (1/0.0", "authority_tier": "verified", "source": "The Works — worked & sealed", "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)", "generated": false}, {"id": "card_theory_shannon_information_theory", "title": "Shannon information theory (entropy, channel capacity)", "shelf": "theories", "surface": "secular", "snippet": "Shannon information theory (entropy, channel capacity) — an engine domain that can touch it: information_theory. Calibration: seals. H = -Σ p log p. Information is measured by how much UNCERTAINTY a m", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_haber_bosch", "title": "Haber–Bosch nitrogen fixation (bread from air)", "shelf": "theories", "surface": "secular", "snippet": "Haber–Bosch nitrogen fixation (bread from air) — an engine domain that can touch it: chemistry. Calibration: seals — stoichiometry, yield and equilibrium shifts compute. N₂ + 3H₂ ⇌ 2NH₃, run at roughl", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_general_relativity", "title": "General relativity", "shelf": "theories", "surface": "secular", "snippet": "General relativity — an engine domain that can touch it: physics. Calibration: partial — specific relations verify; the field equations as a whole are map-only. Gravity is not a force but the CURVATUR", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_biochemistry_enzymes", "title": "Biochemistry & enzymes (catalysis at body temperature)", "shelf": "theories", "surface": "secular", "snippet": "Biochemistry & enzymes (catalysis at body temperature) — an engine domain that can touch it: biology. Calibration: seals — reaction rates, Michaelis–Menten kinetics and energy budgets compute. An enzy", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_control_theory___cybernetics__feedback__stability", "title": "Control theory & cybernetics (feedback, stability)", "shelf": "theories", "surface": "secular", "snippet": "Control theory & cybernetics (feedback, stability) — an engine domain that can touch it: operations_research. Calibration: partial — stability criteria and PID responses compute. Steer a system by the", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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)", "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_cryptographic_security", "title": "Cryptographic security (hashing, checksums, PKI)", "shelf": "theories", "surface": "secular", "snippet": "Cryptographic security (hashing, checksums, PKI) — an engine domain that can touch it: cybersecurity. Calibration: seals — digests and signatures verify exactly. Three different things people routinel", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_time_value_of_money_discounting", "title": "Time value of money & discounting", "shelf": "theories", "surface": "secular", "snippet": "Time value of money & discounting — an engine domain that can touch it: finance. Calibration: seals — present value, annuities and amortisation compute exactly. A pound today is worth more than a poun", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_linear_programming_duality", "title": "Linear programming & duality", "shelf": "theories", "surface": "secular", "snippet": "Linear programming & duality — an engine domain that can touch it: operations_research. Calibration: seals — optimal values and shadow prices compute. Maximise or minimise a linear objective subject t", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_digital_analog", "title": "Digital versus analog (why discreteness survives copying)", "shelf": "theories", "surface": "secular", "snippet": "Digital versus analog (why discreteness survives copying) — an engine domain that can touch it: computer_science. Calibration: map-only — sampling rates and bit depth are ordinary arithmetic, and THIS", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_law_of_large_numbers", "title": "Law of large numbers", "shelf": "theories", "surface": "secular", "snippet": "Law of large numbers — an engine domain that can touch it: statistics. Calibration: partial — convergence checks verify; the limit statement is map-only. As a sample grows, its mean converges to the t", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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)", "generated": false}, {"id": "card_theory_homeostasis_physiological_regulation", "title": "Homeostasis & physiological regulation", "shelf": "theories", "surface": "secular", "snippet": "Homeostasis & physiological regulation — an engine domain that can touch it: medicine. Calibration: partial — specific indices compute; the framework is empirical. A body holds its internal conditions", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_dynamical_systems___deterministic_chaos", "title": "Dynamical systems & deterministic chaos", "shelf": "theories", "surface": "secular", "snippet": "Dynamical systems & deterministic chaos — an engine domain that can touch it: mathematics. Calibration: map-only — sensitivity is qualitative; specific trajectories compute. Deterministic rules whose ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_hess_s_law_thermochemistry", "title": "Hess's law / thermochemistry", "shelf": "theories", "surface": "secular", "snippet": "Hess's law / thermochemistry — an engine domain that can touch it: chemistry. Calibration: seals — enthalpy sums compute exactly. The total enthalpy change of a reaction is the same whatever route it ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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)", "generated": false}, {"id": "card_theory_queueing_theory", "title": "Queueing theory (Little's law)", "shelf": "theories", "surface": "secular", "snippet": "Queueing theory (Little's law) — an engine domain that can touch it: operations_research. Calibration: seals — Little's law and standard queue formulas compute. L = λW: the average number waiting equa", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}]}