{"query": "Weil 1949 — Numbers of solutions of equations in finite fiel", "count": 20, "results": [{"id": "card_src_pron_fiel", "title": "fiel", "shelf": "pronunciation", "surface": "secular", "snippet": "fiel: pronounced (ARPABET) F IY1 L. 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_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_law_of_conservation_of_mass", "title": "Law of conservation of mass (Lavoisier)", "shelf": "theories", "surface": "secular", "snippet": "Law of conservation of mass (Lavoisier) — an engine domain that can touch it: chemistry. Calibration: seals — balanced equations verify exactly. Mass is neither created nor destroyed in a chemical rea", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_stellar_nucleosynthesis_the_hr_diagram", "title": "Stellar nucleosynthesis & the HR diagram", "shelf": "theories", "surface": "secular", "snippet": "Stellar nucleosynthesis & the HR diagram — an engine domain that can touch it: astronomy. Calibration: partial — specific relations verify; the theory as a whole is not a sealable computation. Where t", "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_src_openstax_algebra_1_2_7_5_practice_9983b6b2", "title": "2.7.5 Practice — Algebra 1", "shelf": "mathematics", "surface": "secular", "snippet": "2.7.5\n\nPractice\n\n2.7.5 • Practice\n\nComplete the following questions to practice the skills you have learned in this lesson.\n\nFor questions 1 – 8, solve each system of equations to determine if there i", "authority_tier": "reference", "source": "OpenStax: Algebra 1 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_theory_nuclear_decay_binding_energy", "title": "Nuclear decay & binding energy", "shelf": "theories", "surface": "secular", "snippet": "Nuclear decay & binding energy — an engine domain that can touch it: nuclear_physics. Calibration: seals — half-lives, decay chains and mass-energy conversions compute. An unstable nucleus decays with", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_maxwell_s_equations_classical_electromagnetism", "title": "Maxwell's equations / classical electromagnetism", "shelf": "theories", "surface": "secular", "snippet": "Maxwell's equations / classical electromagnetism — an engine domain that can touch it: electrical. Calibration: partial — circuit and field relations verify; the full field theory is map-only. Four eq", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_quantum_mechanics", "title": "Quantum mechanics (Schrödinger equation)", "shelf": "theories", "surface": "secular", "snippet": "Quantum mechanics (Schrödinger equation) — an engine domain that can touch it: physics. Calibration: partial — energy levels and specific relations verify; interpretation is map-only. A system is desc", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_fundamental_theorem_of_algebra", "title": "Fundamental theorem of algebra", "shelf": "theories", "surface": "secular", "snippet": "Fundamental theorem of algebra — an engine domain that can touch it: mathematics. Calibration: partial — root counts verify; the existence proof is map-only. Every non-constant polynomial with complex", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_algebraic_geometry", "title": "Algebraic geometry (solution sets as shapes)", "shelf": "theories", "surface": "secular", "snippet": "Algebraic geometry (solution sets as shapes) — an engine domain that can touch it: mathematics. Calibration: map-only — specific curve computations verify; the theory is abstract. The study of the sha", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_periodic_law", "title": "Periodic law (Mendeleev)", "shelf": "theories", "surface": "secular", "snippet": "Periodic law (Mendeleev) — an engine domain that can touch it: periodic_table. Calibration: seals — element properties and group trends look up and compute. Arrange elements by atomic number and their", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_src_openstax_algebra_1_2_7_1_systems_of_linear_equations_with_i_01c2afb7", "title": "2.7.1 Systems of Linear Equations with Infinitely Many Solutions — Algebra 1", "shelf": "mathematics", "surface": "secular", "snippet": "2.7.1\n\nSystems of Linear Equations with Infinitely Many Solutions\n\n2.7.1 • Systems of Linear Equations with Infinitely Many Solutions\n\nWarm Up\n\nAndre is trying to solve this system of equations:\n\nLook", "authority_tier": "reference", "source": "OpenStax: Algebra 1 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_chart_weil_rh", "title": "The finite-field (Weil) Riemann hypothesis", "shelf": "codex", "surface": "secular", "snippet": "The finite-field (Weil) Riemann hypothesis. A chart on the one map: this is the tick stick stick_finite_field_the_weil_riemann_hypothesis, placed at the node it charts. Basis: the stick seals |alpha|^", "authority_tier": "engine_derived", "source": "Narrow Highway - a chart: a tick stick placed on the one map", "readable": false, "generated": false}, {"id": "card_domchk_periodic_table_claimed_atomic_mass", "title": "Periodic Table: atomic mass", "shelf": "periodic_table", "surface": "secular", "snippet": "A worked check in periodic table: atomic mass.\n\nGIVEN\n  isotopes = [{'abundance': 5.845, 'mass': 53.9396}, {'abundance': 91.754, 'mass': 55.9349}, {'abundance': 2.119, 'mass': 56.9354}, {'abundance': ", "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)", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_src_openstax_algebra_1_2_7_3_sorting_systems_of_equations_based_a63b9950", "title": "2.7.3 Sorting Systems of Equations Based on Number of Solutions — Algebra 1", "shelf": "mathematics", "surface": "secular", "snippet": "2.7.3\n\nSorting Systems of Equations Based on Number of Solutions\n\n2.7.3 • Sorting Systems of Equations Based on Number of Solutions\n\nActivity\n\nYour teacher will give you a set\nof cards. Each card cont", "authority_tier": "reference", "source": "OpenStax: Algebra 1 (CC-BY 4.0)", "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_chain_weil_1949", "title": "Weil 1949 — Numbers of solutions of equations in finite fields", "shelf": "codex", "surface": "secular", "snippet": "A. Weil (1949). Numbers of solutions of equations in finite fields. Bull. Amer. Math. Soc. 55 (1949) 497–508. DOI 10.1090/S0002-9904-1949-09219-4. Canonical: https://doi.org/10.1090/S0002-9904-1949-09", "authority_tier": "reference", "source": "A. Weil (1949), Bull. Amer. Math. Soc. 55 (1949) 497–508", "readable": false, "generated": false}, {"id": "card_domchk_atomic_claimed_valid_quantum_numbers", "title": "Atomic: valid quantum numbers", "shelf": "atomic", "surface": "secular", "snippet": "A worked check in atomic: valid quantum numbers.\n\nGIVEN\n  l = 2\n  n = 3\n\nCLAIMED\n  claimed_valid_quantum_numbers = True\n\nTHE ENGINE'S VERDICT\n  atomic.quantum_numbers: CONFIRMED — validity True matche", "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)", "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_src_pron_fiel"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}