{"query": "Boltzmann constant = 1.380649e-23 J/K", "count": 20, "results": [{"id": "card_ref_pc_boltzmann_constant", "title": "Boltzmann constant = 1.380649e-23 J/K", "shelf": "physics", "surface": "secular", "snippet": "The boltzmann constant is 1.380649e-23 J/K (exact by definition) — exact since 2019 SI. Verified physical constant.", "authority_tier": "reference", "source": "Verified reference — physical_constants", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_theory_heat_transfer", "title": "Heat transfer (conduction, convection, radiation)", "shelf": "theories", "surface": "secular", "snippet": "Heat transfer (conduction, convection, radiation) — an engine domain that can touch it: thermodynamics. Calibration: seals — Fourier's law, R-values and Stefan–Boltzmann all compute. Heat moves three ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_theory_category_theory", "title": "Category theory (the mathematics of structure-preserving maps)", "shelf": "theories", "surface": "secular", "snippet": "Category theory (the mathematics of structure-preserving maps) — an engine domain that can touch it: mathematics. Calibration: map-only — an organising framework rather than a computation. Study objec", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_n_041763374eca", "title": "Fokker–Planck & Liouville — probability flow in statistical mechanics", "shelf": "science", "surface": "secular", "snippet": "The stochastic instantiation of probability-as-fluid. Fokker–Planck sets the current\nJ = μρ − D∇ρ (drift + diffusion); its steady state is the Boltzmann distribution ρ ∝ e^(−U/kT),\nwhich makes the cur", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "readable": false, "generated": false}, {"id": "card_bridge_master_boltzmann_factor", "title": "Master equation: n ~ e^(-E / kT)", "shelf": "bridges", "surface": "secular", "snippet": "the fraction of a system with energy E falls off exponentially against thermal energy kT. ONE equation, 5 domains, connected by a change of variable: meteorology [E = m g h — the barometric formula is", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_statistical_mechanics__shannon_information_theory", "title": "Bridge: Statistical mechanics (Boltzmann — why the second law is a counting argument)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Statistical mechanics (Boltzmann — why the second law is a counting argument) and Shannon information theory (entropy, channel capacity) are the same form in different domains. Boltzmann's log W and S", "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_thermo_entropy_information", "title": "Entropy is information — Boltzmann, Shannon, Landauer", "shelf": "codex", "surface": "secular", "snippet": "Entropy in joules-per-kelvin and entropy in bits are the same quantity. Landauer's limit - erasing one bit costs at least k_B T ln2 - is the bridge, and where Maxwell's demon is exorcised (sealed on s", "authority_tier": "engine_derived", "source": "Narrow Highway — thermodynamics", "readable": false, "generated": false}, {"id": "card_bridge_theory_heat_transfer__electromagnetic_spectrum", "title": "Bridge: Heat transfer (conduction, convection, radiation)  ↔  The electromagnetic spectrum & modulation (radio to gamma, one axis)", "shelf": "bridges", "surface": "secular", "snippet": "Heat transfer (conduction, convection, radiation) and The electromagnetic spectrum & modulation (radio to gamma, one axis) are the same form in different domains. thermal radiation is not a fourth kin", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_category_theory__group_theory", "title": "Bridge: Category theory (the mathematics of structure-preserving maps)  ↔  Group theory & symmetry (the mathematics of what stays the same)", "shelf": "bridges", "surface": "secular", "snippet": "Category theory (the mathematics of structure-preserving maps) and Group theory & symmetry (the mathematics of what stays the same) are the same form in different domains. a group IS a category with o", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_floor_logarithm", "title": "The logarithm - the instrument the joints share", "shelf": "codex", "surface": "secular", "snippet": "Two trees: Napier's table (1614) and Saint-Vincent's hyperbola (1647) - a number's logarithm as a tabulated count, and as an area. They become one function in Euler's Introductio (1748): e, and exp an", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_floor_thermodynamics", "title": "Thermodynamics — the arrow and the one end", "shelf": "codex", "surface": "secular", "snippet": "The four laws. The first law is energy conservation (Noether's energy, now counting heat and work). The second law - entropy never decreases - is the one place physics is not time-reversible: the arro", "authority_tier": "engine_derived", "source": "Narrow Highway — thermodynamics", "readable": false, "generated": false}, {"id": "card_n_8530c72a2201", "title": "Fluid probability dynamics — one continuity equation across physics, geometry, and ML", "shelf": "science", "surface": "secular", "snippet": "One equation wears many clothes. Probability is a conserved fluid: the continuity equation\ndρ/dt + ∇·J = 0 (current J = ρv) says density is never created or destroyed — it only flows. The\nsame skeleto", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "readable": false, "generated": false}, {"id": "card_sys_entropy_arrow", "title": "The arrow of time — the root of every one-way form", "shelf": "systems", "surface": "secular", "snippet": "Why can any path run one way and not the other? Because the world itself does. The second law of thermodynamics: in an isolated system entropy does not spontaneously decrease (dS ≥ 0) — heat flows hot", "authority_tier": "reference", "source": "The recurring form — the system analogies (standard engineering) + the design they witness to", "readable": false, "generated": false}, {"id": "card_bridge_hub_statistical_mechanics", "title": "Hub: Statistical mechanics (Boltzmann — why the second law is a counting argument) carries 3 domains", "shelf": "bridges", "surface": "secular", "snippet": "Calculations from 3 different domains (physics, statistics, thermodynamics) all rest on Statistical mechanics (Boltzmann — why the second law is a counting argument) — one theory holding up many field", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_law_of_large_numbers__statistical_mechanics", "title": "Bridge: Law of large numbers  ↔  Statistical mechanics (Boltzmann — why the second law is a counting argument)", "shelf": "bridges", "surface": "secular", "snippet": "Law of large numbers and Statistical mechanics (Boltzmann — why the second law is a counting argument) are the same form in different domains. both say the same thing at different scales: averages ove", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_calc_boltzmann_distribution", "title": "Boltzmann distribution", "shelf": "calculations", "surface": "secular", "snippet": "Boltzmann distribution — thermodynamics. Formula: p_i = e^(-E_i/kT) / Z. Canonical FORM: decay (y = y0 e^(-kt)) — the probability of a state falls exponentially with its energy, normalized by the part", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_softmax", "title": "Softmax", "shelf": "calculations", "surface": "secular", "snippet": "Softmax — computer_science. Formula: p_i = e^(z_i) / sum_j e^(z_j). Canonical FORM: decay (y = y0 e^(-kt)) — a network's class probabilities ARE a Boltzmann distribution over scores (temperature = 1).", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "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_ref_pc_boltzmann_constant"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}