{"query": "Turing 1936 — On computable numbers, with an application to", "count": 20, "results": [{"id": "card_theory_digital_analog", "title": "Digital versus analog (why discreteness survives copying)", "shelf": "theories", "surface": "secular", "snippet": "Digital versus analog (why discreteness survives copying) — an engine domain that can touch it: computer_science. Calibration: map-only — sampling rates and bit depth are ordinary arithmetic, and THIS", "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_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_turing_1936", "title": "Turing 1936 — On computable numbers, with an application to the Entscheidungsproblem", "shelf": "codex", "surface": "secular", "snippet": "A. M. Turing (1936). On computable numbers, with an application to the Entscheidungsproblem. Proc. London Math. Soc. (2) 42 (1937) 230–265. DOI 10.1112/plms/s2-42.1.230. Canonical: https://doi.org/10.", "authority_tier": "reference", "source": "A. M. Turing (1936), Proc. London Math. Soc. (2) 42 (1937) 230–265", "readable": false, "generated": false}, {"id": "card_src_mill_silverman_1988", "title": "J. H. Silverman 1988 — Computing heights on elliptic curves", "shelf": "millennium", "surface": "secular", "snippet": "J. H. Silverman (1988). Computing heights on elliptic curves. Math. Comp. 51 (1988) 339–358. DOI 10.1090/S0025-5718-1988-0942161-4. Canonical: https://doi.org/10.1090/S0025-5718-1988-0942161-4. Free c", "authority_tier": "reference", "source": "J. H. Silverman (1988), Math. Comp. 51 (1988) 339–358", "readable": false, "generated": false}, {"id": "card_src_mill_manin_1971", "title": "Yu. I. Manin 1971 — Cyclotomic fields and modular curves", "shelf": "millennium", "surface": "secular", "snippet": "Yu. I. Manin (1971). Cyclotomic fields and modular curves. Russian Math. Surveys 26:6 (1971) 7–78. DOI 10.1070/RM1971v026n06ABEH001272. Canonical: https://doi.org/10.1070/RM1971v026n06ABEH001272. No f", "authority_tier": "reference", "source": "Yu. I. Manin (1971), Russian Math. Surveys 26:6 (1971) 7–78", "readable": false, "generated": false}, {"id": "card_src_etym_computable", "title": "computable", "shelf": "etymology", "surface": "secular", "snippet": "computable: etymology (Webster 1913) — a.: [L. computabilis.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_joint_manin_algorithm", "title": "If Sha is finite, the rank is computable", "shelf": "codex", "surface": "secular", "snippet": "Manin (1971): if the Tate-Shafarevich group is finite - part of what BSD asserts - then the rank of an elliptic curve over Q is effectively computable by descent. Without it, no algorithm is known. A ", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "readable": false, "generated": false}, {"id": "card_builder_gottfried_wilhelm_leibniz", "title": "Gottfried Wilhelm Leibniz", "shelf": "builders", "surface": "secular", "snippet": "Gottfried Wilhelm Leibniz (1646–1716 AD) — mathematics. The gift: the calculus (independently, with the notation we still use), binary arithmetic, and the dream of a universal calculus of reasoning. W", "authority_tier": "reference", "source": "The builders of the Floor — credited with love, calibrated to the plumb-line", "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_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_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_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_chemical_engineering", "title": "Chemical engineering (unit operations, balances, and scale-up)", "shelf": "theories", "surface": "secular", "snippet": "Chemical engineering (unit operations, balances, and scale-up) — an engine domain that can touch it: manufacturing. Calibration: seals — mass and energy balances and residence times compute exactly. T", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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}, {"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_domchk_atomic_claimed_configuration", "title": "Atomic: configuration", "shelf": "atomic", "surface": "secular", "snippet": "A worked check in atomic: configuration.\n\nGIVEN\n  atomic_number = 24\n  l = 2\n  n = 3\n  shell_n = 3\n  subshell_l = 2\n\nCLAIMED\n  claimed_configuration = [Ar] 3d5 4s1\n\nTHE ENGINE'S VERDICT\n  atomic.quant", "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_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_src_word_turing", "title": "turing", "shelf": "dictionary", "surface": "secular", "snippet": "turing: (noun) English mathematician who conceived of the Turing machine and broke German codes during World War II (1912-1954) — syn: Alan Turing, Alan Mathison Turing", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_openstax_anatomy_and_physiology_2e_chapter_review_6112a6f1", "title": "Chapter Review — Anatomy and Physiology 2e", "shelf": "medicine", "surface": "secular", "snippet": "Chapter Review\n\n2.1\n\nElements and Atoms: The Building Blocks of Matter\n\nThe human body is composed of elements, the most abundant of which are oxygen (O), carbon (C), hydrogen (H) and nitrogen (N). Yo", "authority_tier": "reference", "source": "OpenStax: Anatomy and Physiology 2e (CC-BY 4.0)", "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_theory_digital_analog"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}