{"query": "97 is prime · gcd(48, 36) = 12", "count": 7, "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", "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_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", "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", "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_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_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)", "generated": false}]}