{"query": "Number theory", "count": 20, "results": [{"id": "card_instr_number_theory", "title": "Number theory", "shelf": "codex", "surface": "secular", "snippet": "The Number theory verifier (src/concordance/verifiers/number_theory.py). Builds on: The Riemann-Siegel acceleration. On the one map it instruments: card_question_riemann. Found from the code's own imp", "authority_tier": "engine_derived", "source": "verifier: number_theory", "readable": false, "generated": false}, {"id": "card_theory_peano_arithmetic_axioms", "title": "Peano arithmetic axioms", "shelf": "theories", "surface": "secular", "snippet": "Peano arithmetic axioms — an engine domain that can touch it: number_theory. Calibration: seals. Five axioms generating the natural numbers: zero is a number, every number has a successor, zero succee", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_integers_counting", "title": "Counting & the integers (the first abstraction)", "shelf": "theories", "surface": "secular", "snippet": "Counting & the integers (the first abstraction) — an engine domain that can touch it: number_theory. Calibration: seals — arithmetic on the integers verifies exactly. Counting is the recognition that ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_fundamental_theorem_of_arithmetic", "title": "Fundamental theorem of arithmetic (unique factorization)", "shelf": "theories", "surface": "secular", "snippet": "Fundamental theorem of arithmetic (unique factorization) — an engine domain that can touch it: number_theory. Calibration: seals. Every integer greater than 1 is a product of primes in exactly one way", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "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)", "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_theory_julian_day_number", "title": "Julian Day Number (continuous astronomical time)", "shelf": "theories", "surface": "secular", "snippet": "Julian Day Number (continuous astronomical time) — an engine domain that can touch it: calendar_time. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it,", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "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_theory_shannon_information_theory", "title": "Shannon information theory (entropy, channel capacity)", "shelf": "theories", "surface": "secular", "snippet": "Shannon information theory (entropy, channel capacity) — an engine domain that can touch it: information_theory. Calibration: seals. H = -Σ p log p. Information is measured by how much UNCERTAINTY a m", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_music_theory", "title": "Music theory (harmonic series, equal temperament)", "shelf": "theories", "surface": "secular", "snippet": "Music theory (harmonic series, equal temperament) — an engine domain that can touch it: music_theory. Calibration: seals — frequencies, intervals and temperament errors compute exactly. A vibrating st", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_numerical_analysis", "title": "Numerical analysis (why the computer's answer is not the answer)", "shelf": "theories", "surface": "secular", "snippet": "Numerical analysis (why the computer's answer is not the answer) — an engine domain that can touch it: computer_science. Calibration: map-only — error bounds and condition numbers are computable in pr", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_dalton_s_atomic_theory", "title": "Dalton's atomic theory", "shelf": "theories", "surface": "secular", "snippet": "Dalton's atomic theory — an engine domain that can touch it: chemistry. Calibration: partial — mass ratios verify. Matter is made of indivisible atoms; all atoms of an element share a mass; compounds ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_seq_catalan_numbers", "title": "Catalan numbers", "shelf": "sequences", "surface": "secular", "snippet": "Catalan numbers: 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, … — C(2n,n)/(n+1) — countless combinatorial families.", "authority_tier": "reference", "source": "Computed — classical number theory (public domain)", "readable": false, "generated": false}, {"id": "card_theory_measure_theory__lebesgue_integration", "title": "Measure theory (Lebesgue integration)", "shelf": "theories", "surface": "secular", "snippet": "Measure theory (Lebesgue integration) — an engine domain that can touch it: mathematics. Calibration: map-only — a foundation, not a computation. What it means for a set to have a SIZE, done carefully", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_prospect_theory", "title": "Prospect theory & bounded rationality (Kahneman, Simon)", "shelf": "theories", "surface": "secular", "snippet": "Prospect theory & bounded rationality (Kahneman, Simon) — an engine domain that can touch it: economics. Calibration: map-only — empirical and interpretive; specific experiments replicate. People do n", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_mechanism_design___auction_theory", "title": "Mechanism design & auction theory", "shelf": "theories", "surface": "secular", "snippet": "Mechanism design & auction theory — an engine domain that can touch it: economics. Calibration: partial — auction outcomes and incentive conditions compute. Game theory run BACKWARDS: instead of askin", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_quantum_gravity_problem", "title": "Spacetime & the quantum-gravity problem (where physics ends)", "shelf": "theories", "surface": "secular", "snippet": "Spacetime & the quantum-gravity problem (where physics ends) — an engine domain that can touch it: physics. Calibration: map-only — the Planck quantities compute, but there is no accepted theory here ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_kinetic_theory_of_gases", "title": "Kinetic theory of gases", "shelf": "theories", "surface": "secular", "snippet": "Kinetic theory of gases — an engine domain that can touch it: thermodynamics. Calibration: partial — RMS speeds and mean free paths compute; the microscopic picture is a model. A gas is a swarm of mol", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_graph_theory", "title": "Graph theory (Euler, connectivity)", "shelf": "theories", "surface": "secular", "snippet": "Graph theory (Euler, connectivity) — an engine domain that can touch it: combinatorics. Calibration: seals. Dots and lines — vertices and edges — and everything that follows from which dots are joined", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_chemical_bonding", "title": "Chemical bonding (valence-bond / molecular-orbital)", "shelf": "theories", "surface": "secular", "snippet": "Chemical bonding (valence-bond / molecular-orbital) — an engine domain that can touch it: chemistry. Calibration: partial — some relations verify; the full theory is map-only. Atoms bond to lower thei", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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_instr_number_theory"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}