{"query": "Vectors and matrices: a dot product and a determinant", "count": 7, "results": [{"id": "card_works_linear_algebra", "title": "Vectors and matrices: a dot product and a determinant", "shelf": "the-works", "surface": "secular", "snippet": "The dot product of two 3-vectors measures how they align; the determinant of a 2×2 matrix measures the signed area it scales. Both computed exactly.  Worked & sealed by the engine — [1,2,3]·[4,5,6] = ", "authority_tier": "verified", "source": "The Works — worked & sealed", "generated": false}, {"id": "card_theory_linear_algebra", "title": "Linear algebra (vector spaces, eigenvalues)", "shelf": "theories", "surface": "secular", "snippet": "Linear algebra (vector spaces, eigenvalues) — an engine domain that can touch it: linear_algebra. Calibration: seals. Vectors, the linear maps between them, and matrices as those maps written down. Th", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_src_word_matric", "title": "matric", "shelf": "dictionary", "surface": "secular", "snippet": "matric: (noun) admission to a group (especially a college or university) — syn: matriculation", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_c_25f0eae28355", "title": "The primes and the nucleus — one statistical ↔ The Riemann hypothesis — sealed all around, ", "shelf": "connections", "surface": null, "snippet": "the SPACINGS between the Riemann zeta zeros follow the same distribution as the eigenvalue spacings of large random Hermitian matrices (the Gaussian Unitary Ensemble)  — a concord the card itself stat", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "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", "generated": false}, {"id": "card_src_pron_matrice", "title": "matrice", "shelf": "pronunciation", "surface": "secular", "snippet": "", "authority_tier": "", "source": "", "generated": false}, {"id": "card_src_pron_matrices", "title": "matrices", "shelf": "pronunciation", "surface": "secular", "snippet": "", "authority_tier": "", "source": "", "generated": false}]}