{"id": "card_v_06eca966d113", "kind": "verified", "title": "[1,2,3]·[4,5,6] = 4+10+18 = 32 · det [[1,2],[3,4]] = 1·4 − 2·3 = −2", "body": "Verdict: HOLDS.\n• vector.dot_product: [1.0, 2.0, 3.0] · [4.0, 5.0, 6.0] = 32.0\n• matrix.determinant: det = -2\nSealed and independently re-checkable: https://narrowhighway.com/s/5a497c248aa2ecb6cdbbda77103315c3ed6927d599fcffa323446bfe95db0af7", "source": {"label": "Verified by the engine — linear_algebra", "url": "https://narrowhighway.com/s/5a497c248aa2ecb6cdbbda77103315c3ed6927d599fcffa323446bfe95db0af7", "ref": "", "domain": "linear_algebra", "authority_tier": "engine"}, "shelf": "linear_algebra", "box": "verified", "bands": ["verified", "linear_algebra", "HOLDS"], "connections": [{"to_card_id": "card_k_spine_created_order", "relationship": "part_of", "evidence": "a verified seed of the created order (linear_algebra)"}, {"to_card_id": "card_works_linear_algebra", "relationship": "demonstrates", "evidence": "A worked demonstration in the same field (linear_algebra)."}], "author": "engine", "created_at": 1784892567.929683, "updated_at": 1784892567.9296837, "visibility": "public", "lifecycle_stage": "public", "volatility": "durable", "surface": "secular", "generated": false, "presentation": {"glyph": "•", "kind_label": "verified", "by": "Verified by the engine — linear_algebra", "authority": "engine", "posted": "1 month ago", "standing": "", "link": {"url": "https://narrowhighway.com/s/5a497c248aa2ecb6cdbbda77103315c3ed6927d599fcffa323446bfe95db0af7", "host": "narrowhighway.com", "provider": "", "titled": "[1,2,3]·[4,5,6] = 4+10+18 = 32 · det [[1,2],[3,4]] = 1·4 − 2·3 = −2", "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 (linear_algebra)", "href": "/card/card_k_spine_created_order", "resolved": true}, {"id": "card_works_linear_algebra", "title": "Vectors and matrices: a dot product and a determinant", "relationship": "demonstrates", "why": "A worked demonstration in the same field (linear_algebra).", "href": "/card/card_works_linear_algebra", "resolved": true}]}