{"query": "The primes and the nucleus — one statistical fingerprint", "count": 20, "results": [{"id": "card_n_ea9e3f380756", "title": "The primes and the nucleus — one statistical fingerprint", "shelf": "science", "surface": "secular", "snippet": "The night's deepest rhyme, and it is real, published, and unexplained. Montgomery (1973)\nand Dyson noticed that the SPACINGS between the Riemann zeta zeros follow the same distribution\nas the eigenval", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}, {"id": "card_theory_fundamental_theorem_of_arithmetic", "title": "Fundamental theorem of arithmetic (unique factorization)", "shelf": "theories", "surface": "secular", "snippet": "Fundamental theorem of arithmetic (unique factorization) — an engine domain that can touch it: number_theory. Calibration: seals. Every integer greater than 1 is a product of primes in exactly one way", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_theory_signal_detection", "title": "Signal detection theory (sensitivity, criterion, ROC)", "shelf": "theories", "surface": "secular", "snippet": "Signal detection theory (sensitivity, criterion, ROC) — an engine domain that can touch it: statistics. Calibration: seals — sensitivity, specificity, predictive values and ROC areas compute exactly. ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_n_639fcf317634", "title": "Primes and zeta — Euler's bridge and the prime number theorem", "shelf": "science", "surface": "secular", "snippet": "Euler tied the primes to the continuum: zeta(s) = product over primes of 1/(1-p^-s), so a\nstatement about ALL integers becomes a statement about the primes. Sealed: there are exactly 25\nprimes below 1", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}, {"id": "card_c_741715d501d0", "title": "The primes and the nucleus — one statistical ↔ Primes and zeta — Euler's bridge and the pri", "shelf": "connections", "surface": null, "snippet": "A prime number and a uranium nucleus carry the same deep statistical signature.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_src_word_prim", "title": "prim", "shelf": "dictionary", "surface": "secular", "snippet": "prim: (verb) assume a prim appearance · (verb) contract one's lips · (verb) dress primly — syn: prim up, prim out · (adjective) affectedly dainty or refined — syn: mincing, niminy-piminy, twee · (adje", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_c_59abe461b1af", "title": "The primes and the nucleus — one statistical ↔ The nucleus — the strongest glue and the slo", "shelf": "connections", "surface": null, "snippet": "the very statistics that describe the ENERGY LEVELS of heavy nuclei and quantum chaos ... A prime number and a uranium nucleus carry the same deep statistical signature.  — a concord the card itself s", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_src_word_prim_out", "title": "prim out", "shelf": "dictionary", "surface": "secular", "snippet": "prim out: (verb) dress primly — syn: prim, prim up", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_prim_up", "title": "prim up", "shelf": "dictionary", "surface": "secular", "snippet": "prim up: (verb) dress primly — syn: prim, prim out", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "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_alm_connection_euclid_euler_perfect_numbers", "title": "Almanac: Euclid-Euler: every even perfect number is a Mersenne prime times a power of two", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  A perfect number equals the sum of its own proper divisors -- 6 = 1+2+3, 28 = 1+2+4+7+14 -- and Euclid (Book IX) plus Euler proved exactly where they come from: every even perfect number i", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "generated": false}, {"id": "card_alm_connection_riemann_hypothesis_open_zeta_facts", "title": "Almanac: The Riemann Hypothesis -- an open question about where the zeta function vanishes, with the established facts sealed and the conjecture marked honestly", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  The Riemann zeta function, zeta(s) = the sum of 1/k^s, is the deepest known bridge between the smooth world of analysis and the prime numbers. Several of its truths are firmly ESTABLISHED ", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "generated": false}, {"id": "card_alm_connection_fermat_little_theorem_and_primality", "title": "Almanac: Fermat little theorem and the primality test -- with its Carmichael blind spot", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Raise any base to the power one-less-than a prime and reduce modulo that prime, and you always land on 1 -- Fermat little theorem. number_theory confirmed 17 and 11 are prime; mathematics ", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "generated": false}, {"id": "card_src_word_prime_factor", "title": "prime factor", "shelf": "dictionary", "surface": "secular", "snippet": "prime factor: (noun) the prime factors of a quantity are all of the prime quantities that will exactly divide the given quantity", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_book_60179", "title": "The Prime Minister — Harold Spender", "shelf": "gutenberg", "surface": "secular", "snippet": "The Prime Minister, by Harold Spender. Subjects: Prime ministers -- Great Britain -- Biography; Lloyd George, David, 1863-1945. Read the full text (public domain): https://www.gutenberg.org/ebooks/601", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_book_69", "title": "The 32nd Mersenne Prime Predicted by Mersenne — David Slowinski", "shelf": "gutenberg", "surface": "secular", "snippet": "The 32nd Mersenne Prime Predicted by Mersenne, by David Slowinski. Subjects: Numbers, Prime; Number theory. Read the full text (public domain): https://www.gutenberg.org/ebooks/69", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_lex_g5230", "title": "G5230 — ὑπέρακμος (huperakmos): past one’s prime", "shelf": "lexicon", "surface": "secular", "snippet": "ὑπέρακμος (huperakmos), Strong's G5230: past one’s prime. ὑπέρακμος , -ον past the bloom of youth : 1Co.7:36 (Eustath.).† (AS)", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "generated": false}, {"id": "card_src_word_prime", "title": "prime", "shelf": "dictionary", "surface": "secular", "snippet": "prime: (noun) a natural number that has exactly two distinct natural number divisors: 1 and itself — syn: prime quantity · (noun) the period of greatest prosperity or productivity — syn: flower, peak,", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_prime_quantity", "title": "prime quantity", "shelf": "dictionary", "surface": "secular", "snippet": "prime quantity: (noun) a natural number that has exactly two distinct natural number divisors: 1 and itself — syn: prime", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_pron_primes", "title": "primes", "shelf": "pronunciation", "surface": "secular", "snippet": "primes: pronounced (ARPABET) P R AY1 M Z. 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", "generated": false}]}