{"query": "Primes — the raw material", "count": 20, "results": [{"id": "card_crypto_primes", "title": "Primes — the raw material", "shelf": "codex", "surface": "secular", "snippet": "Crypto runs on primes and on Fermat/Euler (a^(p-1) = 1 mod p, sealed) - the reason e and d are inverse modulo phi(n). The supply and distribution of primes is the zeta function's domain. Rests on Riem", "authority_tier": "engine_derived", "source": "Narrow Highway — cryptography", "readable": false, "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)", "readable": false, "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)", "readable": false, "generated": false}, {"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", "readable": false, "generated": false}, {"id": "card_sys_oneway_function", "title": "The one-way function — the computational rectifier", "shelf": "systems", "surface": "secular", "snippet": "Some computations are cheap one way and infeasible the reverse. A one-way function is easy to evaluate (polynomial time) but computationally infeasible to invert; a TRAPDOOR one-way function adds a se", "authority_tier": "reference", "source": "The recurring form — the system analogies (standard engineering) + the design they witness to", "readable": false, "generated": false}, {"id": "card_alm_located_goldbach_conjecture_verified", "title": "Almanac: Goldbach's conjecture — verified where we can reach, open where we cannot", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Goldbach conjectured in 1742 that every even number greater than 2 is the sum of two primes. It is still UNPROVEN. The engine verified it for a ladder of even numbers, each as a genuine pr", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_n_ebe4c25c22ae", "title": "The Riemann hypothesis — sealed all around, refused at the center", "shelf": "science", "surface": "secular", "snippet": "The deepest open question about the primes, and the cleanest demonstration of the engine's\nhonesty. The FACTS seal: zeta(2)=pi²/6 (Basel), zeta(4)=pi⁴/90, zeta(6)=pi⁶/945, zeta(-1)=-1/12,\nthe trivial ", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_floor_riemann", "title": "The Riemann chain - from Euler's product and Legendre's count to the critical line", "shelf": "codex", "surface": "secular", "snippet": "Two trees. The analytic: Euler's product over the primes (1737), Dirichlet's L-functions (1837). The arithmetic: Legendre's guess at the prime count (1798), Gauss's logarithmic integral (counted 1792,", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_alm_located_modular_exponentiation_trapdoor", "title": "Almanac: The modular-exponentiation trapdoor: fast one way, hard the other", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Public-key cryptography needs an operation that is easy to do and ruinous to undo -- and modular exponentiation is it. mathematics confirmed the FAST direction by square-and-multiply: beca", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_chain_vallee_poussin_1896", "title": "Poussin 1896 — Recherches analytiques sur la théorie des nombres premiers", "shelf": "codex", "surface": "secular", "snippet": "C.-J. de la Vallée Poussin (1896). Recherches analytiques sur la théorie des nombres premiers. Ann. Soc. Sci. Bruxelles 20 (1896) 183–256. Cited by its record. License as found: public domain (the aut", "authority_tier": "reference", "source": "C.-J. de la Vallée Poussin (1896), Ann. Soc. Sci. Bruxelles 20 (1896) 183–256", "readable": false, "generated": false}, {"id": "card_floor_cryptography", "title": "Cryptography — public keys and hard problems", "shelf": "codex", "surface": "secular", "snippet": "Secrecy built on number theory and computational hardness. RSA encrypts with a public key and decrypts with a private one (the round-trip sealed), its security the belief that factoring is hard; the o", "authority_tier": "engine_derived", "source": "Narrow Highway — cryptography", "readable": false, "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", "readable": false, "generated": false}, {"id": "card_form_combinatorial", "title": "Canonical form: combinatorial  (C(n,k) = n! / (k!(n-k)!))", "shelf": "forms", "surface": "secular", "snippet": "A canonical mathematical FORM: C(n,k) = n! / (k!(n-k)!) — counting arrangements and selections — factorials, permutations, primes. Every calculation joined here is this same computation under a change", "authority_tier": "reference", "source": "The Calculation Map — canonical forms", "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_crypto_hardness", "title": "Hardness — security is a hard problem", "shelf": "codex", "surface": "secular", "snippet": "RSA is secure only because factoring n into its primes is believed hard; break that (or prove P = NP, or run Shor's quantum algorithm) and it falls. Security IS a hardness assumption. Rests on the P v", "authority_tier": "engine_derived", "source": "Narrow Highway — cryptography", "readable": false, "generated": false}, {"id": "card_src_etym_primer", "title": "primer", "shelf": "etymology", "surface": "secular", "snippet": "primer: etymology (Webster 1913) — a.: [OF. primer, primier, premier, F. premier. See Premier.]; n.: [Originally, the book read at prime, the first canonical hour. LL. primae liber. See Prime, n., 4.]", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_etym_primary", "title": "primary", "shelf": "etymology", "surface": "secular", "snippet": "primary: etymology (Webster 1913) — a.: [L. primarius, fr. primus first: cf. F. primaire. See Prime, a., and cf. Premier, Primero.]. 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_src_etym_premier", "title": "premier", "shelf": "etymology", "surface": "secular", "snippet": "premier: etymology (Webster 1913) — a.: [F. premier, fr. L. primarius of the first rank, principal, fr. primus the first. See Primary, Prime, a.]. From Webster's Revised Unabridged Dictionary (1913), ", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_chain_hadamard_1896", "title": "Hadamard 1896 — Sur la distribution des zéros de la fonction zeta(s) et ses conséquences arithmétiques", "shelf": "codex", "surface": "secular", "snippet": "J. Hadamard (1896). Sur la distribution des zéros de la fonction zeta(s) et ses conséquences arithmétiques. Bull. Soc. Math. France 24 (1896) 199–220. DOI 10.24033/bsmf.545. Canonical: https://doi.org", "authority_tier": "reference", "source": "J. Hadamard (1896), Bull. Soc. Math. France 24 (1896) 199–220", "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_crypto_primes"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}