{"query": "97 is prime · gcd(48, 36) = 12", "count": 20, "results": [{"id": "card_v_8abf65c1a315", "title": "97 is prime · gcd(48, 36) = 12", "shelf": "number_theory", "surface": "secular", "snippet": "Verdict: HOLDS.\n• number_theory.primality: 97 is prime (matches claim)\n• number_theory.gcd: gcd(48, 36) = 12 (matches claim)\nSealed and independently re-checkable: https://narrowhighway.com/s/e64527b1", "authority_tier": "engine", "source": "Verified by the engine — number_theory", "readable": false, "generated": false}, {"id": "card_alm_connection_reality_is_mappable", "title": "Almanac: Reality is mappable: the same verified structure recurs across every domain", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Across this whole moat -- physics, computer science, music, genetics -- the engine kept finding the SAME structures wearing different clothes, and this grand capstone confirms it by drawin", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_src_openstax_contemporary_mathematics_key_terms_746b90b5", "title": "Key Terms — Contemporary Mathematics", "shelf": "reference", "surface": "secular", "snippet": "Key Terms\n\n3.1\n\nPrime and Composite Numbers\n\nnatural numbers\n\nfactor of a number\n\nmultiple of a number\n\nprime number\n\ncomposite number\n\nprime factorization\n\ngreatest common divisor (GCD)\n\nleast common", "authority_tier": "reference", "source": "OpenStax: Contemporary Mathematics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_works_number_theory", "title": "The integers, examined: a prime, a divisor, a factorial", "shelf": "the-works", "surface": "secular", "snippet": "Exact facts about whole numbers, decided by algorithm, not by eye: 97 is prime; 48 and 36 share a greatest common divisor of 12; and 6! counts the orderings of six things.  Worked & sealed by the engi", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_src_openstax_contemporary_mathematics_key_concepts_7ea7697d", "title": "Key Concepts — Contemporary Mathematics", "shelf": "reference", "surface": "secular", "snippet": "Key Concepts\n\n3.1\n\nPrime and Composite Numbers\n\nThe natural numbers can be categorized as 1, prime numbers, and composite numbers.\n\nPrime numbers have as their only factors 1 and themselves.\n\nComposit", "authority_tier": "reference", "source": "OpenStax: Contemporary Mathematics (CC-BY 4.0)", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_calc_v_number_theory_gcd", "title": "Gcd", "shelf": "calculations", "surface": "secular", "snippet": "Gcd — number_theory. Formula: gcd(a,b)=gcd(b, a mod b). Canonical FORM: number_theoretic (a^x = 1 (mod m)) — engine verifier number_theory.gcd — the deterministic check the concordance runs. Same form", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_v_84e08f40a749", "title": "97 is prime · gcd(48, 36) = 12 · 6! = 720", "shelf": "number_theory", "surface": "secular", "snippet": "Verdict: HOLDS.\n• number_theory.primality: 97 is prime (matches claim)\n• number_theory.gcd: gcd(48, 36) = 12 (matches claim)\n• number_theory.factorial: 6! = 720 (matches claim)\nSealed and independentl", "authority_tier": "engine", "source": "Verified by the engine — number_theory", "readable": false, "generated": false}, {"id": "card_src_openstax_contemporary_mathematics_videos_ca2e47bb", "title": "Videos — Contemporary Mathematics", "shelf": "reference", "surface": "secular", "snippet": "Videos\n\n3.1\n\nPrime and Composite Numbers\n\nDivisibility Rules\n\nIllegal Prime Number\n\nUsing a Factor Tree to Find the Prime Factorization\n\nFinding the Prime Factorization of 168\n\nUsing Desmos to find th", "authority_tier": "reference", "source": "OpenStax: Contemporary Mathematics (CC-BY 4.0)", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_form_number_theoretic", "title": "Canonical form: number_theoretic  (a^x = 1 (mod m))", "shelf": "forms", "surface": "secular", "snippet": "A canonical mathematical FORM: a^x = 1 (mod m) — primes, gcd, modular inverse and exponentiation. Every calculation joined here is this same computation under a change of variable; the domains differ,", "authority_tier": "reference", "source": "The Calculation Map — canonical forms", "readable": false, "generated": false}, {"id": "card_src_lang_gang1267", "title": "Ganggalida (gcd) — Tangkic", "shelf": "languages", "surface": "secular", "snippet": "Ganggalida, a language of the Tangkic family, spoken in Australia. ISO 639-3: gcd. Glottocode gang1267.", "authority_tier": "reference", "source": "Glottolog (CC-BY 4.0)", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_enc_easton_haman", "title": "Haman", "shelf": "encyclopedia", "surface": "witness", "snippet": "(of Persian origin), magnificent, the name of the vizier (i.e., the prime minister) of the Persian king Ahasuerus (Esther 3:1, etc.). He is called an “Agagite,” which seems to denote that he was desce", "authority_tier": "reference", "source": "Easton's Bible Dictionary (1897, public domain)", "readable": false, "generated": false}, {"id": "card_n_1f0a211c571e", "title": "Easton: Haman", "shelf": "dictionary", "surface": "secular", "snippet": "(of Persian origin), magnificent, the name of the vizier (i.e., the prime minister) of the Persian king Ahasuerus (Esther 3:1, etc.). He is called an “Agagite,” which seems to denote that he was desce", "authority_tier": "external_aligned", "source": "Matthew Easton, Illustrated Bible Dictionary (1897)", "readable": false, "generated": false}, {"id": "card_c_0d224da54cbf", "title": "Easton: Bigthan references Ahasuerus", "shelf": "connections", "surface": null, "snippet": "Mentions Ahasuerus (person) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a person.", "authority_tier": "engine_derived", "source": "Name mention (Easton's Bible Dictionary, PD)", "readable": false, "generated": false}, {"id": "card_c_8e225a3d7f01", "title": "Easton: Darius references Ahasuerus", "shelf": "connections", "surface": null, "snippet": "Mentions Ahasuerus (person) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a person.", "authority_tier": "engine_derived", "source": "Name mention (Easton's Bible Dictionary, PD)", "readable": false, "generated": false}, {"id": "card_c_b5f59611cc3c", "title": "Easton: Haman references Ahasuerus", "shelf": "connections", "surface": null, "snippet": "Mentions Ahasuerus (person) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a person.", "authority_tier": "engine_derived", "source": "Name mention (Easton's Bible Dictionary, PD)", "readable": false, "generated": false}, {"id": "card_c_e28e7794b013", "title": "Easton: Esther references Ahasuerus", "shelf": "connections", "surface": null, "snippet": "Mentions Ahasuerus (person) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a person.", "authority_tier": "engine_derived", "source": "Name mention (Easton's Bible Dictionary, PD)", "readable": false, "generated": false}, {"id": "card_c_e501cbea6237", "title": "Easton: Vashti references Ahasuerus", "shelf": "connections", "surface": null, "snippet": "Mentions Ahasuerus (person) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a person.", "authority_tier": "engine_derived", "source": "Name mention (Easton's Bible Dictionary, PD)", "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_v_8abf65c1a315"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}