{
  "annotation_id": "c7e6deaa-f8ab-4d1b-94e8-6fe0b322e65a",
  "date_created": "2026-02-17T05:53:12.444000Z",
  "date_modified": "2026-02-17T05:53:12.444000Z",
  "file_hash": "dcb4dcbfa25cd654e9d78c0cd2647eb175d0941cd3aed34e1ab2a5aa7deffa95",
  "private": false,
  "record": {
    "abstract": "We introduce \\emph{patterned numbers}, a digit--divisor-based classification of integers motivated by recreational mathematics. A number is defined to be patterned if at least one of its positive divisors appears as a digit in its base-10 representation. We study the first hundred natural numbers under this definition, analyze frequency and density, compare prime and composite behavior, and propose a generation rule. Visual ``shape diagrams\u0027\u0027 along the number line illustrate transitions between patterned numbers. Finally, we comment on potential relevance to sequence-based operators and algebraic intuition in quantum and combinatorial contexts.",
    "arxiv_id": "2601.07846",
    "authors": [
      "John TM Campbell"
    ],
    "categories": [
      "math.HO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Patterned Numbers: A Novel Number Classification with Structural and Quantum Algebraic Perspectives",
    "url": "https://arxiv.org/abs/2601.07846",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "960ab9e4-31e7-4735-b147-b2b425749ee3",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}