{"query": "Euler's identity, assembled from its parts", "count": 7, "results": [{"id": "card_works_euler_identity", "title": "Euler's identity, assembled from its parts", "shelf": "the-works", "surface": "secular", "snippet": "Often called the most beautiful equation in mathematics: it binds e, i, π, 1 and 0 in a single line. We hand the engine each piece and the whole, and it confirms every one.  Worked & sealed by the eng", "authority_tier": "verified", "source": "The Works — worked & sealed", "generated": false}, {"id": "card_c_d721087fe2f2", "title": "The Riemann hypothesis — sealed all around,  ↔ Primes and zeta — Euler's bridge and the pri", "shelf": "connections", "surface": null, "snippet": "zeta(2)=pi²/6 (Basel), zeta(4)=pi⁴/90, zeta(6)=pi⁶/945, zeta(-1)=-1/12, the trivial zero zeta(-2)=0, and Euler's bridge zeta(2)·6 = pi².  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "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", "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_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_c_9aaf105f7dd8", "title": "Primes and zeta — Euler's bridge and the pri ↔ The Riemann hypothesis — sealed all around, ", "shelf": "connections", "surface": null, "snippet": "the Riemann zeros control exactly how the actual count wobbles around the smooth estimate  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "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}]}