{"query": "N = 100·½¹ = 50 after one half-life", "count": 20, "results": [{"id": "card_v_ba246361cb43", "title": "N = 100·½¹ = 50 after one half-life", "shelf": "geology", "surface": "secular", "snippet": "Verdict: HOLDS.\n• geology.radiometric_decay: 100.0 · 2^(−5730.0/5730.0) = 50 after 1 half-lives (matches claim 50.0)\nSealed and independently re-checkable: https://narrowhighway.com/s/f1ed7b8e8b7b481a", "authority_tier": "engine", "source": "Verified by the engine — geology", "generated": false}, {"id": "card_theory_pharmacokinetics", "title": "Pharmacokinetics (dosing, clearance, half-life)", "shelf": "theories", "surface": "secular", "snippet": "Pharmacokinetics (dosing, clearance, half-life) — an engine domain that can touch it: medicine. Calibration: seals — half-lives, steady state and loading doses compute exactly. What the body does to a", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_discrete_vs_continuous", "title": "Discrete versus continuous (the oldest dividing line)", "shelf": "theories", "surface": "secular", "snippet": "Discrete versus continuous (the oldest dividing line) — an engine domain that can touch it: number_theory. Calibration: map-only — a foundational distinction; specific cardinality results compute. Som", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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)", "generated": false}, {"id": "card_theory_nuclear_decay_binding_energy", "title": "Nuclear decay & binding energy", "shelf": "theories", "surface": "secular", "snippet": "Nuclear decay & binding energy — an engine domain that can touch it: nuclear_physics. Calibration: seals — half-lives, decay chains and mass-energy conversions compute. An unstable nucleus decays with", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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)", "generated": false}, {"id": "card_theory_atomism", "title": "Atomism (the idea that matter is not infinitely divisible)", "shelf": "theories", "surface": "secular", "snippet": "Atomism (the idea that matter is not infinitely divisible) — an engine domain that can touch it: chemistry. Calibration: map-only — historical and foundational; mole arithmetic computes. Cut a thing i", "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_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_electrochemistry", "title": "Electrochemistry & the battery (Volta, Faraday, and stored charge)", "shelf": "theories", "surface": "secular", "snippet": "Electrochemistry & the battery (Volta, Faraday, and stored charge) — an engine domain that can touch it: chemistry. Calibration: seals — cell voltages, Faraday's laws of electrolysis and Nernst shifts", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_population_ecology", "title": "Population ecology (Lotka–Volterra, carrying capacity)", "shelf": "theories", "surface": "secular", "snippet": "Population ecology (Lotka–Volterra, carrying capacity) — an engine domain that can touch it: ecology. Calibration: seals — logistic and predator-prey models compute. Unlimited resources give exponenti", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_works_radiometric", "title": "One half-life of a radioactive clock", "shelf": "the-works", "surface": "secular", "snippet": "After one half-life — 5,730 years for carbon-14 — exactly half the original atoms remain. This is how charcoal, bone and shell are dated.  Worked & sealed by the engine — N = 100·½¹ = 50 after one hal", "authority_tier": "verified", "source": "The Works — worked & sealed", "generated": false}, {"id": "card_src_word_half", "title": "half", "shelf": "dictionary", "surface": "secular", "snippet": "half: (noun) one of two equal parts of a divisible whole — syn: one-half · (noun) one of two divisions into which some games or performances are divided: the two divisions are separated by an interval", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_half_and_half", "title": "half-and-half", "shelf": "dictionary", "surface": "secular", "snippet": "half-and-half: (noun) half milk and half light cream; contains 10% to 18% butterfat · (adjective) in equal parts · (adverb) in equal parts", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_n_cfb57dd6b005", "title": "Radioactive decay — the exponential clock of matter", "shelf": "science", "surface": "secular", "snippet": "Sealed in-domain: after one half-life exactly half remains; after two, exactly one\nquarter (2^(−2) = 1/4, exact); carbon-14's decay constant is ln2/5730 years = 3.833×10⁻¹²\nper second: https://narrowh", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}, {"id": "card_src_word_half_and_half_dressing", "title": "half-and-half dressing", "shelf": "dictionary", "surface": "secular", "snippet": "half-and-half dressing: (noun) half mayonnaise and half vinaigrette seasoned with minced garlic and mashed anchovies and grated Parmesan cheese; especially good for combination salads", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_half_life", "title": "half-life", "shelf": "dictionary", "surface": "secular", "snippet": "half-life: (noun) the time required for something to fall to half its initial value (in particular, the time for half the atoms in a radioactive substance to disintegrate) — syn: half life", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "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", "generated": false}, {"id": "card_src_lex_g2255", "title": "G2255 — ἥμισυς (hēmisus): half", "shelf": "lexicon", "surface": "secular", "snippet": "ἥμισυς (hēmisus), Strong's G2255: half. ἥμισυς , -εια, -υ genitive, -ους (late, as in π., for cl., -εος Bl., § 8, 4; Mayser, 294), n. p1., ἡμίσια (Rec., cl., -εια), [in LXX for חֵצִי, מַחֲצִית ;] half", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "generated": false}, {"id": "card_src_food_171255", "title": "Cream, Fluid, Half And Half", "shelf": "nutrition", "surface": "secular", "snippet": "Cream, fluid, half and half — a food in the USDA FoodData Central reference. Per 100 g: 131 kcal, 3.13 g protein, 11.5 g fat, 4.3 g carbohydrate.", "authority_tier": "reference", "source": "USDA FoodData Central (public domain)", "generated": false}]}