{"id": "card_v_3f924f5023bc", "kind": "verified", "title": "cos(π) = −1 · sin(π) = 0 · e^{iπ} + 1 = 0", "body": "Verdict: HOLDS.\n• cos(pi) = -1; both sides reduce to -1\n• sin(pi) = 0; both sides reduce to 0\n• exp(I*pi)+1 = 0; both sides reduce to 0\nSealed and independently re-checkable: https://narrowhighway.com/s/809fbaa9498918cf30444c3e16a63c6be7eb2c2026d944d08c467ecc0a305421", "source": {"label": "Verified by the engine — mathematics", "url": "https://narrowhighway.com/s/809fbaa9498918cf30444c3e16a63c6be7eb2c2026d944d08c467ecc0a305421", "ref": "", "domain": "mathematics", "authority_tier": "engine"}, "shelf": "mathematics", "box": "verified", "bands": ["verified", "mathematics", "HOLDS"], "connections": [{"to_card_id": "card_k_spine_created_order", "relationship": "part_of", "evidence": "a verified seed of the created order (mathematics)"}, {"to_card_id": "card_works_euler_identity", "relationship": "demonstrates", "evidence": "A worked demonstration in the same field (mathematics)."}, {"to_card_id": "card_works_calculus_chain", "relationship": "demonstrates", "evidence": "A worked demonstration in the same field (mathematics)."}, {"to_card_id": "card_works_trig_identities", "relationship": "demonstrates", "evidence": "A worked demonstration in the same field (mathematics)."}], "author": "engine", "created_at": 1784862230.0619233, "updated_at": 1784862230.0619245, "visibility": "public", "lifecycle_stage": "public", "volatility": "durable", "surface": "secular", "generated": false, "presentation": {"glyph": "•", "kind_label": "verified", "by": "Verified by the engine — mathematics", "authority": "engine", "posted": "1 month ago", "standing": "", "link": {"url": "https://narrowhighway.com/s/809fbaa9498918cf30444c3e16a63c6be7eb2c2026d944d08c467ecc0a305421", "host": "narrowhighway.com", "provider": "", "titled": "cos(π) = −1 · sin(π) = 0 · e^{iπ} + 1 = 0", "waybill_line": "", "reach": "", "embed": ""}}, "neighbors": [{"id": "card_k_spine_created_order", "title": "The created order — the science of the floor", "relationship": "part of", "why": "a verified seed of the created order (mathematics)", "href": "/card/card_k_spine_created_order", "resolved": true}, {"id": "card_works_euler_identity", "title": "Euler's identity, assembled from its parts", "relationship": "demonstrates", "why": "A worked demonstration in the same field (mathematics).", "href": "/card/card_works_euler_identity", "resolved": true}, {"id": "card_works_calculus_chain", "title": "Differentiate twice: position → velocity → acceleration", "relationship": "demonstrates", "why": "A worked demonstration in the same field (mathematics).", "href": "/card/card_works_calculus_chain", "resolved": true}, {"id": "card_works_trig_identities", "title": "From the unit circle to the double-angle law", "relationship": "demonstrates", "why": "A worked demonstration in the same field (mathematics).", "href": "/card/card_works_trig_identities", "resolved": true}]}