{
  "abstract": "I construct a self-unfolding combinatorial structure from a single integer seed nc0 ∈ Z≥0: a finite, bilaterally symmetric double-cone hierarchy whose total cell count equals the partition function p(nc0). The central contribution is the construction of a regular generative structure for integer partitions, a single object that deterministically generates all partitions of nc0 through its intrinsic geometry. The framework connects partition theory with mixed-radix systems, conical geometry, and signed partitions via a tunable non-decreasing constraint. For standard partitions, a digital root invariance theorem shows that every path label is congruent to the seed modulo 9, confining the generated universe to one of nine equivalence classes ED(nc0 ).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Masoud Akbarpour"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2ngpaepz0sqb.bib",
  "cited_by": 0,
  "doi": null,
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  "id": "f2ngpaepz0sqb",
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  "landing_url": "https://hal.science/hal-05776192v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
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  "native_subjects": [
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  "pdf_url": "https://hal.science/hal-05776192/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2ngpaepz0sqb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:46Z",
      "native_id": "hal-05776192",
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      "url": "https://hal.science/hal-05776192v1"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-nt",
      "subfield": "algebra-number-theory"
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    {
      "field": "mathematics",
      "origin": "hal:1.math.math-co",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "hal:0.phys",
      "subfield": "general"
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  "title": "Order, Structure and Reality: Hierarchical Shell Structure of Integer Partitions",
  "title_text": "Order, Structure and Reality: Hierarchical Shell Structure of Integer Partitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:46Z",
  "url": "https://research.draconitic.com/paper/f2ngpaepz0sqb",
  "venue": "HAL",
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}