{"query": "Radioactive decay — the exponential clock of matter", "count": 20, "results": [{"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", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_theory_chemical_kinetics_equilibrium", "title": "Chemical kinetics & equilibrium (Arrhenius, Le Chatelier)", "shelf": "theories", "surface": "secular", "snippet": "Chemical kinetics & equilibrium (Arrhenius, Le Chatelier) — an engine domain that can touch it: chemistry. Calibration: partial — rate constants and equilibrium shifts compute. KINETICS asks how fast,", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_theory_epidemiology_models", "title": "Compartmental epidemiology (SIR models and R₀)", "shelf": "theories", "surface": "secular", "snippet": "Compartmental epidemiology (SIR models and R₀) — an engine domain that can touch it: medicine. Calibration: seals — R0, herd-immunity thresholds and epidemic curves compute. Divide a population into S", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_c_01a2b706782a", "title": "Radioactive decay — the exponential clock of ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "The same exponential that discharges a capacitor empties a nucleus's odds — the bench's RC clock and the carbon clock are one curve wearing different constants.  — a concord the card itself states; mi", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_77ba6d7691ca", "title": "Pheromones — the molecule is the message ↔ Radioactive decay — the exponential clock of", "shelf": "connections", "surface": null, "snippet": "Pheromones DIFFUSE down a gradient (the continuity/diffusion equation) and DECAY (the exponential clock) — the fluid and the clock of this whole map, carried in a scent.  — a concord the card itself s", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_b71d6ddb4a46", "title": "Logarithms — multiplication made addition, a ↔ Radioactive decay — the exponential clock of", "shelf": "connections", "surface": null, "snippet": "it is the exact INVERSE of the exponential that is the spine of this whole map: the capacitor's RC clock, radioactive decay, compound interest, the diode's curve all rise by multiplying; the logarithm", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_n_770170ab1111", "title": "The linguistic clock — the comparative method dates the dispersal", "shelf": "science", "surface": "secular", "snippet": "The same history is written in the words. The comparative method reconstructs ancestral\ntongues from their daughters (sealed in the language-evolution wing), and glottochronology's\nexponential vocabul", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_c_27866e541925", "title": "The evolution of language — descent traced b ↔ Radioactive decay — the exponential clock of", "shelf": "connections", "surface": null, "snippet": "core vocabulary decays EXPONENTIALLY, ~86% retained per millennium, a ~4,595-year half-life; the linear-decay misconception sealed BROKEN  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_5592b5e8c1e7", "title": "Logarithms — multiplication made addition, a ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "it is the exact INVERSE of the exponential that is the spine of this whole map: the capacitor's RC clock, radioactive decay, compound interest, the diode's curve all rise by multiplying; the logarithm", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_c40ecb16eb60", "title": "The nucleus — the strongest glue and the slo ↔ Radioactive decay — the exponential clock of", "shelf": "connections", "surface": null, "snippet": "the decay constant λ = ln2/t½ for carbon-14 (3.833×10⁻¹² per second — a clock ticking in every living thing)  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_src_word_exponential", "title": "exponential", "shelf": "dictionary", "surface": "secular", "snippet": "exponential: (noun) a function in which an independent variable appears as an exponent — syn: exponential function · (adjective) of or involving exponents", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_c_059c5628759e", "title": "Tracing the peoples — genes and words, two c ↔ Radioactive decay — the exponential clock of", "shelf": "connections", "surface": null, "snippet": "shared basic vocabulary decays exponentially to 47% after five millennia — the linguistic half-life beside the genetic one  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "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", "readable": false, "generated": false}, {"id": "card_c_122ecae2ff8b", "title": "Glottochronology — carbon-dating the words ↔ Radioactive decay — the exponential clock of", "shelf": "connections", "surface": null, "snippet": "The identical decay math as carbon-14, which is why it is called linguistic dating.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_src_word_exponential_decay", "title": "exponential decay", "shelf": "dictionary", "surface": "secular", "snippet": "exponential decay: (noun) a decrease that follows an exponential function — syn: exponential return", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_n_36048aaa9a1b", "title": "Glottochronology — carbon-dating the words", "shelf": "science", "surface": "secular", "snippet": "Swadesh (1950s): a language's CORE vocabulary — the 100-200 most basic words (mother,\nwater, two, hand) — is replaced at a roughly constant rate, so its loss is EXPONENTIAL:\nretention r^t with r about", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_n_88ac7219a4a9", "title": "Laplace — the map's dynamics (decay/growth), beyond the steady spectrum", "shelf": "concepts", "surface": "secular", "snippet": "Matt: 'laplace transform ... missing.' Fourier gives the STEADY spectrum (the imaginary axis); Laplace adds the REAL axis s=sigma+i*omega — decay/growth RATES. The map's eigenvalue spectrum decays EXP", "authority_tier": "matt", "source": "Operator's seed (Matt) — honest grade: plausible", "readable": false, "generated": false}, {"id": "card_n_6f5aa0b22245", "title": "Capacitor — the exponential clock (RC time constant)", "shelf": "science", "surface": "secular", "snippet": "A capacitor charging through a resistor follows V(t) = V·(1 − e^(−t/RC)); after one\ntime constant τ = RC it holds exactly 1 − 1/e ≈ 63.2% of the supply — sealed in-domain\n(1000 Ω × 1000 µF = 1 s; 5 V ", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}]}