{
  "annotation_id": "f22cead8-4f03-413a-b136-411d60add6d3",
  "date_created": "2026-03-02T18:02:16.355000Z",
  "date_modified": "2026-03-02T18:02:16.355000Z",
  "file_hash": "bc8fb60ecc9e1245e6d031177ed32fda978968d8cd9e9ead65883d45ee76dfeb",
  "private": false,
  "record": {
    "abstract": "The N distinct prime numbers that make up a composite number M allow\n$2^{N-1}$ bi partioning into two relatively prime factors. Each such pair\ndefines a pair of conjugate representations. These pairs of conjugate\nrepresentations, each of which spans the M dimensional space are the familiar\ncomplete sets of Zak transforms (J. Zak, Phys. Rev. Let.{\\bf 19}, 1385 (1967))\nwhich are the most natural representations for periodic systems. Here we show\ntheir relevance to factorizations. An example is provided for the manifestation\nof the factorization.",
    "arxiv_id": "quant-ph/0503228",
    "authors": [
      "M. Revzen",
      "A. Mann",
      "J. Zak"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Physics of Factorization",
    "url": "https://arxiv.org/abs/quant-ph/0503228"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6e6f8cc5-c315-4c61-82e4-d08bb97ed0c6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}