{"query": "Diffusion models — the probability-flow ODE behind generativ", "count": 20, "results": [{"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_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)", "generated": false}, {"id": "card_theory_fluid_mechanics", "title": "Fluid mechanics (Bernoulli, Reynolds, Navier–Stokes)", "shelf": "theories", "surface": "secular", "snippet": "Fluid mechanics (Bernoulli, Reynolds, Navier–Stokes) — an engine domain that can touch it: hydrology. Calibration: seals — continuity, Bernoulli and Reynolds number compute directly. CONTINUITY first:", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_n_2be7f1c3f6e9", "title": "Diffusion models — the probability-flow ODE behind generative AI", "shelf": "science", "surface": "secular", "snippet": "Score-based generative models noise data toward a Gaussian and learn to reverse it. The\n'probability-flow ODE' is the deterministic fluid whose time-marginals match the noising SDE — the\nsame continui", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_theory_hydrologic_cycle_open_channel_flow", "title": "Hydrologic cycle & open-channel flow (Manning, Darcy)", "shelf": "theories", "surface": "secular", "snippet": "Hydrologic cycle & open-channel flow (Manning, Darcy) — an engine domain that can touch it: hydrology. Calibration: seals — Manning velocity, Darcy flow and catchment volumes compute. Water circulates", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_null_hypothesis_significance_testing", "title": "Null-hypothesis significance testing (Fisher / Neyman–Pearson)", "shelf": "theories", "surface": "secular", "snippet": "Null-hypothesis significance testing (Fisher / Neyman–Pearson) — an engine domain that can touch it: statistics. Calibration: seals — a p-value recomputes exactly. Assume the null hypothesis, compute ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_c_d7daafda1482", "title": "Fluid probability dynamics — one continuity  ↔ Diffusion models — the probability-flow ODE ", "shelf": "connections", "surface": null, "snippet": "machine learning (the probability-flow ODE under diffusion models)  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_theory_dimensional_analysis", "title": "Dimensional analysis & similarity (Buckingham Π)", "shelf": "theories", "surface": "secular", "snippet": "Dimensional analysis & similarity (Buckingham Π) — an engine domain that can touch it: physics. Calibration: seals — dimensional consistency and Π-group counts check exactly. Any true physical equatio", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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", "generated": false}, {"id": "card_theory_bohr_quantum_model_of_the_atom", "title": "Bohr / quantum model of the atom", "shelf": "theories", "surface": "secular", "snippet": "Bohr / quantum model of the atom — an engine domain that can touch it: atomic. Calibration: seals — energy levels and shell capacities compute. Electrons occupy discrete orbits with QUANTISED energies", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_statistical_learning_theory__bias_variance__generali", "title": "Statistical learning theory (bias-variance, generalization)", "shelf": "theories", "surface": "secular", "snippet": "Statistical learning theory (bias-variance, generalization) — an engine domain that can touch it: statistics. Calibration: map-only — bounds are asymptotic and assumption-laden. Why fitting the data y", "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_src_book_78905", "title": "Model yachts and model yacht sailing — James E. Walton", "shelf": "gutenberg", "surface": "secular", "snippet": "Model yachts and model yacht sailing, by James E. Walton. Subjects: Ship models; Yachts -- Models. Read the full text (public domain): https://www.gutenberg.org/ebooks/78905", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_theory_bayes_theorem", "title": "Bayes' theorem", "shelf": "theories", "surface": "secular", "snippet": "Bayes' theorem — an engine domain that can touch it: probability. Calibration: seals. P(H|E) = P(E|H)·P(H) / P(E). How to update a belief when evidence arrives: posterior ∝ likelihood × prior. A trivi", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_domchk_probability_claimed_binomial_probability", "title": "Probability: binomial probability", "shelf": "probability", "surface": "secular", "snippet": "A worked check in probability: binomial probability.\n\nGIVEN\n  binomial_k = 5\n  binomial_n = 10\n  binomial_p = 0.5\n\nCLAIMED\n  claimed_binomial_probability = 0.246094\n\nTHE ENGINE'S VERDICT\n  probability", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "generated": false}, {"id": "card_src_book_68100", "title": "Model aeroplanes The building of model monoplanes, biplanes, etc., together with a chapter on building a model airship — F. J. (Frederick James) Camm", "shelf": "gutenberg", "surface": "secular", "snippet": "Model aeroplanes The building of model monoplanes, biplanes, etc., together with a chapter on building a model airship, by F. J. (Frederick James) Camm. Subjects: Airplanes -- Models. Read the full te", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "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)", "generated": false}, {"id": "card_c_e510a4e8b7f4", "title": "Diffusion models instantiate Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "The probability-flow ODE is the same continuity equation with a learned velocity.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_theory_differential_equations", "title": "Differential equations (the language every physical law is written in)", "shelf": "theories", "surface": "secular", "snippet": "Differential equations (the language every physical law is written in) — an engine domain that can touch it: mathematics. Calibration: seals — solutions verify by substitution; specific integrations c", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_src_word_horatian_ode", "title": "horatian ode", "shelf": "dictionary", "surface": "secular", "snippet": "horatian ode: (noun) an ode with several stanzas — syn: Sapphic ode", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}]}