{"query": "A gate closes against a number, an owner, and a fallback", "count": 20, "results": [{"id": "card_doctrine_gate_closure", "title": "A gate closes against a number, an owner, and a fallback", "shelf": "doctrine", "surface": "secular", "snippet": "\"Symmetry of rigor… every gate closes against a number, an owner and a fallback.\" Gate Zero is feasibility BEFORE form: the architecture is not permitted to proceed on enthusiasm, only on a first-orde", "authority_tier": "author", "source": "Project Prism — The Architecture of Time, Design Bible v2.3 — Matt Harris", "generated": false}, {"id": "card_history_the_witness_gate", "title": "The witness gate — how the events of history are established", "shelf": "history", "surface": "secular", "snippet": "History cannot go through the same gate as mathematics and physics: you cannot SEAL that the Battle of Hastings occurred the way you seal 2+2=4. History has two layers. Its SKELETON — the dates and th", "authority_tier": "reference", "source": "The witness gate — the historical method + Deuteronomy 19:15", "generated": false}, {"id": "card_n_6b8ba3914b09", "title": "1 Clement III", "shelf": "patristics", "surface": "witness", "snippet": "in it from envy and emulation._ Every kind of honour and happiness was bestowed upon you, and then was fulfilled that which is written, “My beloved did eat and drink, and was enlarged and became fat, ", "authority_tier": "father", "source": "First Epistle of Clement to the Corinthians (trans. Roberts-Donaldson, 1885)", "generated": false}, {"id": "card_domchk_number_theory_claimed_factorial", "title": "Number Theory: factorial", "shelf": "number_theory", "surface": "secular", "snippet": "A worked check in number theory: factorial.\n\nGIVEN\n  factorial_n = 5\n  gcd_a = 12\n\nCLAIMED\n  claimed_factorial = 120\n\nTHE ENGINE'S VERDICT\n  number_theory.factorial: CONFIRMED — 5! = 120 (matches clai", "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_domchk_number_theory_claimed_gcd", "title": "Number Theory: gcd", "shelf": "number_theory", "surface": "secular", "snippet": "A worked check in number theory: gcd.\n\nGIVEN\n  gcd_a = 12\n  gcd_b = 18\n\nCLAIMED\n  claimed_gcd = 6\n\nTHE ENGINE'S VERDICT\n  number_theory.gcd: CONFIRMED — gcd(12, 18) = 6 (matches claim)\n\nAND THE FALSEH", "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_alm_connection_chinese_remainder_is_residue_reconstruction", "title": "Almanac: The Chinese Remainder Theorem: a number is uniquely its residues", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  A number can be cut into its remainders against several coprime moduli and then rebuilt exactly from those pieces -- the Chinese Remainder Theorem, known since the 3rd-century Sunzi Suanji", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "generated": false}, {"id": "card_domchk_number_theory_claimed_prime", "title": "Number Theory: prime", "shelf": "number_theory", "surface": "secular", "snippet": "A worked check in number theory: prime.\n\nGIVEN\n  n_prime = 17\n\nCLAIMED\n  claimed_prime = True\n\nTHE ENGINE'S VERDICT\n  number_theory.primality: CONFIRMED — 17 is prime (matches claim)\n\nAND THE FALSEHOO", "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_domchk_number_theory_claimed_inverse", "title": "Number Theory: inverse", "shelf": "number_theory", "surface": "secular", "snippet": "A worked check in number theory: inverse.\n\nGIVEN\n  mod_a = 3\n  mod_m = 11\n\nCLAIMED\n  claimed_inverse = 4\n\nTHE ENGINE'S VERDICT\n  number_theory.modular_inverse: CONFIRMED — 3·4 mod 11 = 1; 4 is the mod", "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_domchk_periodic_table_claimed_atomic_number", "title": "Periodic Table: atomic number", "shelf": "periodic_table", "surface": "secular", "snippet": "A worked check in periodic table: atomic number.\n\nGIVEN\n  symbol = Fe\n\nCLAIMED\n  claimed_atomic_number = 26\n\nTHE ENGINE'S VERDICT\n  periodic_table.element: CONFIRMED — Fe (iron, Z=26) — definitional c", "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_spine_domain_number_theory", "title": "Number Theory — what this engine can check", "shelf": "number_theory", "surface": "secular", "snippet": "The number theory shelf of the keeping. This engine holds a deterministic verifier for number theory: hand it a claim in the NUM_VERIFY shape and it returns a verdict, the worked trail, and a re-check", "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_oeis_a000372", "title": "A000372 — Dedekind numbers or Dedekind's problem: number of monotone Boolean functions of n variables, number of antichains of subsets of an n-set, number of elements in a free dis", "shelf": "oeis", "surface": "secular", "snippet": "Dedekind numbers or Dedekind's problem: number of monotone Boolean functions of n variables, number of antichains of subsets of an n-set, number of elements in a free distributive lattice on n generat", "authority_tier": "reference", "source": "OEIS — On-Line Encyclopedia of Integer Sequences (oeis.org)", "generated": false}, {"id": "card_src_oeis_a000262", "title": "A000262 — Number of \"sets of lists\": number of partitions of {1,...,n} into any number of lists, where a list means an ordered subset.", "shelf": "oeis", "surface": "secular", "snippet": "Number of \"sets of lists\": number of partitions of {1,...,n} into any number of lists, where a list means an ordered subset.  First terms: 1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553, 58941091,", "authority_tier": "reference", "source": "OEIS — On-Line Encyclopedia of Integer Sequences (oeis.org)", "generated": false}, {"id": "card_n_8b107410efcc", "title": "Aurelius, Meditations §aur_07_xviii: An angry countenance is much against nature, and it is oftentimes the proper ...", "shelf": "classics", "surface": "secular", "snippet": "An angry countenance is much against nature, and it is oftentimes the proper countenance of them that are at the point of death. But were it so, that all anger and passion were so thoroughly quenched ", "authority_tier": "external_aligned", "source": "Marcus Aurelius, Meditations (c. AD 170)", "generated": false}, {"id": "card_alm_assessment_pythagoras_number_is_the_language_not_the_god", "title": "Almanac: Pythagoras -- 'all is number' is the root of the whole map; making number itself a god is the fork", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  The first of the missed-thinkers list, and a deep root. THE KERNEL -- true and sealed. Pythagoras was the first to see that hidden NUMBER and RATIO govern the world. Music's sweetness is a", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "generated": false}, {"id": "card_n_17f4f305d575", "title": "1 Clement XLVIII", "shelf": "patristics", "surface": "witness", "snippet": "Let us therefore, with all haste, put an end to this [state of things]; and let us fall down before the Lord, and beseech Him with tears, that He would mercifully be reconciled to us, and restore us t", "authority_tier": "father", "source": "First Epistle of Clement to the Corinthians (trans. Roberts-Donaldson, 1885)", "generated": false}, {"id": "card_src_oeis_a001205", "title": "A001205 — Number of clouds with n points; number of undirected 2-regular labeled graphs; or number of n X n symmetric matrices with (0,1) entries, trace 0 and all row sums 2.", "shelf": "oeis", "surface": "secular", "snippet": "Number of clouds with n points; number of undirected 2-regular labeled graphs; or number of n X n symmetric matrices with (0,1) entries, trace 0 and all row sums 2.  First terms: 1, 0, 0, 1, 3, 12, 70", "authority_tier": "reference", "source": "OEIS — On-Line Encyclopedia of Integer Sequences (oeis.org)", "generated": false}, {"id": "card_src_book_36656", "title": "A Seasonable Warning and Caution against the Insinuations of Papists and Jacobites in favour of the Pretender Being a Letter from an Englishman at the Court of Hanover — Daniel Def", "shelf": "gutenberg", "surface": "secular", "snippet": "A Seasonable Warning and Caution against the Insinuations of Papists and Jacobites in favour of the Pretender Being a Letter from an Englishman at the Court of Hanover, by Daniel Defoe. Subjects: Jame", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_book_37696", "title": "Arguments of Celsus, Porphyry, and the Emperor Julian, Against the Christians Also Extracts from Diodorus Siculus, Josephus, and Tacitus, Relating to the Jews, Together with an App", "shelf": "gutenberg", "surface": "secular", "snippet": "Arguments of Celsus, Porphyry, and the Emperor Julian, Against the Christians Also Extracts from Diodorus Siculus, Josephus, and Tacitus, Relating to the Jews, Together with an Appendix, by Thomas, 17", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_book_58555", "title": "Religion & Morality Vindicated, Against Hypocrisy and Pollution Or, an Account of the Life and Character of John Church the Obelisk Preacher, Who Was Formerly a Frequenter of Vere-", "shelf": "gutenberg", "surface": "secular", "snippet": "Religion & Morality Vindicated, Against Hypocrisy and Pollution Or, an Account of the Life and Character of John Church the Obelisk Preacher, Who Was Formerly a Frequenter of Vere-street, and Who Has ", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_oeis_a002720", "title": "A002720 — Number of partial permutations of an n-set; number of n X n binary matrices with at most one 1 in each row and column.", "shelf": "oeis", "surface": "secular", "snippet": "Number of partial permutations of an n-set; number of n X n binary matrices with at most one 1 in each row and column.  First terms: 1, 2, 7, 34, 209, 1546, 13327, 130922, 1441729, 17572114, 234662231", "authority_tier": "reference", "source": "OEIS — On-Line Encyclopedia of Integer Sequences (oeis.org)", "generated": false}]}