{"query": "The normal law — the central limit theorem", "count": 20, "results": [{"id": "card_stats_normal_law", "title": "The normal law — the central limit theorem", "shelf": "codex", "surface": "secular", "snippet": "Sum or average enough independent things, whatever their shapes, and the result tends to the SAME bell curve, and the standard error shrinks as sigma/sqrt(n) (sealed). Many possibilities converging to", "authority_tier": "engine_derived", "source": "Narrow Highway — statistics", "readable": false, "generated": false}, {"id": "card_theory_g_del_s_incompleteness_theorems", "title": "Gödel's incompleteness theorems", "shelf": "theories", "surface": "secular", "snippet": "Gödel's incompleteness theorems — an engine domain that can touch it: formal_logic. Calibration: map-only — a meta-theorem about systems, not a sealable computation. FIRST (1931): any consistent forma", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_requisite_variety", "title": "Ashby's law of requisite variety (the humility theorem)", "shelf": "theories", "surface": "secular", "snippet": "Ashby's law of requisite variety (the humility theorem) — an engine domain that can touch it: operations_research. Calibration: map-only — a structural bound, stated in variety counts rather than comp", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_theory_pythagorean_theorem", "title": "Pythagorean theorem", "shelf": "theories", "surface": "secular", "snippet": "Pythagorean theorem — an engine domain that can touch it: geometry. Calibration: seals. In a right triangle, a² + b² = c². Known in practice to Babylonian and Egyptian builders long before its Greek p", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_spectral_geometry", "title": "Spectral geometry (can one hear the shape of a drum?)", "shelf": "theories", "surface": "secular", "snippet": "Spectral geometry (can one hear the shape of a drum?) — an engine domain that can touch it: mathematics. Calibration: partial — specific relations verify; the theory as a whole is not a sealable compu", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_group_theory", "title": "Group theory & symmetry (the mathematics of what stays the same)", "shelf": "theories", "surface": "secular", "snippet": "Group theory & symmetry (the mathematics of what stays the same) — an engine domain that can touch it: mathematics. Calibration: seals — group orders, subgroup structure and symmetry counts compute. A", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_fixed_point_theorems__brouwer__kakutani", "title": "Fixed-point theorems (Brouwer, Kakutani)", "shelf": "theories", "surface": "secular", "snippet": "Fixed-point theorems (Brouwer, Kakutani) — an engine domain that can touch it: mathematics. Calibration: map-only — an existence proof, not a computation. Brouwer: any continuous map of a convex compa", "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_topology", "title": "Topology (what survives stretching)", "shelf": "theories", "surface": "secular", "snippet": "Topology (what survives stretching) — an engine domain that can touch it: mathematics. Calibration: map-only — specific invariants compute; the classification results are proofs, not computations. Geo", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_projective_geometry", "title": "Projective geometry (perspective & the cross-ratio)", "shelf": "theories", "surface": "secular", "snippet": "Projective geometry (perspective & the cross-ratio) — an engine domain that can touch it: geometry. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, a", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_quantum_information___entanglement__von_neumann_entr", "title": "Quantum information & entanglement (von Neumann entropy)", "shelf": "theories", "surface": "secular", "snippet": "Quantum information & entanglement (von Neumann entropy) — an engine domain that can touch it: information_theory. Calibration: seals. S = -Tr(ρ log ρ), the entropy of a density matrix, which reduces ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_theory_aperiodic_tiling", "title": "Aperiodic tiling (Penrose, and the 2023 monotile)", "shelf": "theories", "surface": "secular", "snippet": "Two tile shapes plus local edge-matching rules that cover the plane completely and CANNOT repeat. Penrose (1974) gave two forms: P2, the kite and dart; P3, a thin rhombus (36°) and a fat one (72°). Th", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_noether_s_theorem__symmetry_and_conservation", "title": "Noether's theorem (symmetry and conservation)", "shelf": "theories", "surface": "secular", "snippet": "Noether's theorem (symmetry and conservation) — an engine domain that can touch it: physics. Calibration: map-only — out of scope for sealing — foundational, empirical or interpretive (RESONANCE); for", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_heisenberg_uncertainty_principle", "title": "Heisenberg uncertainty principle", "shelf": "theories", "surface": "secular", "snippet": "Heisenberg uncertainty principle — an engine domain that can touch it: physics. Calibration: partial — the bound computes; the ontology is map-only. Δx·Δp ≥ ħ/2. Position and momentum cannot both be s", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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_church_turing_thesis_computability", "title": "Church–Turing thesis / computability", "shelf": "theories", "surface": "secular", "snippet": "Church–Turing thesis / computability — an engine domain that can touch it: computer_science. Calibration: map-only — a thesis, not a theorem. Everything effectively computable is computable by a Turin", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_power_laws", "title": "Power laws & heavy tails (Zipf, Pareto)", "shelf": "theories", "surface": "secular", "snippet": "Power laws & heavy tails (Zipf, Pareto) — an engine domain that can touch it: statistics. Calibration: seals — exponents, rank-frequency fits and tail probabilities compute. A distribution where P(x) ", "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}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_stats_normal_law"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}