{"query": "Equilibrium — Delta G = -RT ln K", "count": 20, "results": [{"id": "card_pchem_equilibrium", "title": "Equilibrium — Delta G = -RT ln K", "shelf": "codex", "surface": "secular", "snippet": "A reaction settles where the equilibrium constant K is fixed by the free energy: Delta G-naught = -RT ln K (sealed, -5.71 kJ/mol for K = 10 at 298 K). The bridge from thermodynamics to the measured ra", "authority_tier": "engine_derived", "source": "Narrow Highway — physical chemistry", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_n_cdb747a427d2", "title": "Electronics — the resonant chain, from Ohm's law to the radio wave", "shelf": "science", "surface": "secular", "snippet": "One sealed chain runs the whole bench: Ohm's law (V = I·R), the capacitor's\nexponential clock (one time constant → 63.2% charged), the diode's exponential gate (current\ndoubles every ln2·nVT ≈ 17.9 mV", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_bridge_theory_pharmacokinetics__chemical_kinetics_equilibrium", "title": "Bridge: Pharmacokinetics (dosing, clearance, half-life)  ↔  Chemical kinetics & equilibrium (Arrhenius, Le Chatelier)", "shelf": "bridges", "surface": "secular", "snippet": "Pharmacokinetics (dosing, clearance, half-life) and Chemical kinetics & equilibrium (Arrhenius, Le Chatelier) are the same form in different domains. first-order clearance and chemical first-order dec", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_alm_connection_entropy_is_thermodynamic", "title": "Almanac: Shannon entropy and thermodynamic entropy are the same quantity", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  The entropy of a message and the entropy of a gas are not analogies -- they are one formula. information_theory confirmed Shannon entropy numerically: a fair coin carries 1 bit, four equal", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_bridge_theory_shannon_information_theory__second_law_of_thermodynamics", "title": "Bridge: Shannon information theory (entropy, channel capacity)  ↔  Second law of thermodynamics (entropy)", "shelf": "bridges", "surface": "secular", "snippet": "Shannon information theory (entropy, channel capacity) and Second law of thermodynamics (entropy) are the same form in different domains. Shannon's H = -sum p log p and Boltzmann's S = k log W are the", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "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_alm_assessment_popper_falsifiability_is_the_method", "title": "Almanac: Falsifiability -- a theory must forbid something; the fork -- demarcation over-applied banishes the metaphysics it cannot test", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  THE KERNEL: Popper got the deep thing right, and it is the engine's own heartbeat. A claim with content forbids something; it sticks its neck out; it can be refuted by a single counterexam", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_bridge_master_nernst_potential", "title": "Master equation: V = (RT / zF) * ln(C_out / C_in)", "shelf": "bridges", "surface": "secular", "snippet": "a voltage from the log of a concentration ratio — the same equation in a battery and a neuron. ONE equation, 2 domains, connected by a change of variable: electrochemistry [the electrode potential of ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_n_0fa594da0bff", "title": "Diode — the exponential gate", "shelf": "science", "surface": "secular", "snippet": "The diode's current grows exponentially with voltage; sealed exactly: e^(x+ln2) = 2e^x —\ncurrent DOUBLES for every ln2·nVT of forward voltage, ≈ 17.9 mV at room temperature (sealed:\nfloor(10⁴·ln2·0.02", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "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", "readable": false, "generated": false}, {"id": "card_bridge_master_sigmoid", "title": "Master equation: y = 1 / (1 + e^(-x))", "shelf": "bridges", "surface": "secular", "snippet": "the S-curve — a soft switch between two states; a near-miss with logistic growth that IS a calculation. ONE equation, 7 domains, connected by a change of variable: economics [x = k(t - t0): the logist", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_calc_nernst", "title": "Nernst equation", "shelf": "calculations", "surface": "secular", "snippet": "Nernst equation — electrochemistry. Formula: E = E0 - (RT/nF) ln(Q). Canonical FORM: logarithmic (y = k * log(x / x0)) — a cell's voltage from the log of a concentration ratio. Same form, different do", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_bridge_master_logarithmic_scale", "title": "Master equation: L = k * log10(x / x_ref)", "shelf": "bridges", "surface": "secular", "snippet": "put a ratio on a log scale — the same operation, wherever a range spans many orders of magnitude. ONE equation, 8 domains, connected by a change of variable: acoustics [k = 10, x = intensity, x_ref = ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_thermo_statistical_mechanics", "title": "Statistical mechanics — many microstates, one macrostate", "shelf": "codex", "surface": "secular", "snippet": "The bridge from the reversible microscopic law to the irreversible macrostate: 10^23 particles, one temperature and one pressure. Boltzmann S = k_B ln W counts the microstates; the macrostate is what ", "authority_tier": "engine_derived", "source": "Narrow Highway — thermodynamics", "readable": false, "generated": false}, {"id": "card_calc_weber_fechner", "title": "Weber-Fechner law", "shelf": "calculations", "surface": "secular", "snippet": "Weber-Fechner law — neuroscience. Formula: S = k ln(I / I0). Canonical FORM: logarithmic (y = k * log(x / x0)) — perceived intensity is the log of the stimulus — loudness, brightness, weight. Same for", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_floor_physical_chemistry", "title": "Physical chemistry — rate, equilibrium, acid-base, redox", "shelf": "codex", "surface": "secular", "snippet": "Deeper in chemistry: the laws that make it predictive. Kinetics (how fast), equilibrium (the balance point, Delta G = -RT ln K), acid-base (pKa + pKb = 14), and electrochemistry (the cell potential). ", "authority_tier": "engine_derived", "source": "Narrow Highway — physical chemistry", "readable": false, "generated": false}, {"id": "card_src_pron_ln", "title": "ln", "shelf": "pronunciation", "surface": "secular", "snippet": "ln: pronounced (ARPABET) L EY1 N. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_src_lang_lamn1239", "title": "Lamnso' (lns) — Atlantic-Congo", "shelf": "languages", "surface": "secular", "snippet": "Lamnso', a language of the Atlantic-Congo family, spoken in Africa. ISO 639-3: lns. Glottocode lamn1239.", "authority_tier": "reference", "source": "Glottolog (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_c_547436596e63", "title": "Diode — the exponential gate ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "The diode's current grows exponentially with voltage; sealed exactly: e^(x+ln2) = 2e^x — current DOUBLES for every ln2·nVT of forward voltage  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "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_pchem_equilibrium"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}