{
  "schema_version": "26.0-internal",
  "paper_id": "PFT:THE_PATTERN_FIELD_THEORY_INFINITY_FRAMEWORK_INCREMENTAL_BOUNDARY_AND_FRAME_RELATIVE_INFINI",
  "entity_type": "paper",
  "slug": "the-pattern-field-theory-infinity-framework-incremental-boundary-and-frame-relative-infini",
  "title": "The Pattern Field Theory Infinity Framework: - Incremental, Boundary, and Frame-Relative Infinity",
  "visibility": {
    "approved_public": false,
    "scope": "internal",
    "approval_state": "unreviewed"
  },
  "publication": {
    "published": null,
    "verification_status": "unchecked",
    "last_checked": null,
    "locations": [
      {
        "provider": "patternfieldtheory",
        "url": "https://patternfieldtheory.com/papers/the-pattern-field-theory-infinity-framework-incremental-boundary-and-frame-relative-infini/",
        "verification_status": "discovered-unverified"
      },
      {
        "provider": "zenodo",
        "url": "https://zenodo.org/communities/pft",
        "verification_status": "discovered-unverified"
      },
      {
        "provider": "academia",
        "url": "https://independent.academia.edu/JamesAllen375",
        "verification_status": "discovered-unverified"
      }
    ]
  },
  "representations": {
    "html": {
      "available": true,
      "path": "index.html",
      "canonical": true
    },
    "json": {
      "available": true,
      "path": "paper.json"
    },
    "pdf": {
      "available": true,
      "path": "paper.pdf"
    },
    "latex": {
      "available": false,
      "path": null,
      "original_filename": "infinity.tex"
    },
    "timestamp": {
      "available": false,
      "path": null
    }
  },
  "sections": [
    {
      "level": 1,
      "title": "The Pattern Field Theory Infinity Framework: - Incremental, Boundary, and Frame-Relative Infinity",
      "anchor": null
    },
    {
      "level": 2,
      "title": "Repository Files",
      "anchor": null
    },
    {
      "level": 1,
      "title": "The Pattern Field Theory Infinity Framework: - Incremental, Boundary, and Frame-Relative Infinity",
      "anchor": null
    },
    {
      "level": 1,
      "title": "Introduction",
      "anchor": "#introduction"
    },
    {
      "level": 1,
      "title": "Incremental Infinity",
      "anchor": "#incremental-infinity"
    },
    {
      "level": 1,
      "title": "Boundary Infinity",
      "anchor": "#boundary-infinity"
    },
    {
      "level": 1,
      "title": "Horizon Limitation",
      "anchor": "#horizon-limitation"
    },
    {
      "level": 1,
      "title": "Frame-Relative Infinity",
      "anchor": "#frame-relative-infinity"
    },
    {
      "level": 1,
      "title": "External Non-Metricity",
      "anchor": "#external-non-metricity"
    },
    {
      "level": 1,
      "title": "Structural Consequences",
      "anchor": "#structural-consequences"
    },
    {
      "level": 2,
      "title": "Infinity is not a number",
      "anchor": "#infinity-is-not-a-number"
    },
    {
      "level": 2,
      "title": "Infinity is always finite from the outside",
      "anchor": "#infinity-is-always-finite-from-the-outside"
    },
    {
      "level": 2,
      "title": "Infinity expands internally but never externally",
      "anchor": "#infinity-expands-internally-but-never-externally"
    },
    {
      "level": 2,
      "title": "Expansion does not increase infinity",
      "anchor": "#expansion-does-not-increase-infinity"
    },
    {
      "level": 1,
      "title": "Position in Historical Context and Originality",
      "anchor": "#position-in-historical-context-and-originality"
    },
    {
      "level": 2,
      "title": "Set Theory",
      "anchor": "#set-theory"
    },
    {
      "level": 2,
      "title": "Philosophy",
      "anchor": "#philosophy"
    },
    {
      "level": 2,
      "title": "Physics",
      "anchor": "#physics"
    },
    {
      "level": 2,
      "title": "Computation",
      "anchor": "#computation"
    },
    {
      "level": 2,
      "title": "Fractal Geometry",
      "anchor": "#fractal-geometry"
    },
    {
      "level": 2,
      "title": "Cosmology",
      "anchor": "#cosmology"
    },
    {
      "level": 2,
      "title": "Discrete Mathematics",
      "anchor": "#discrete-mathematics"
    },
    {
      "level": 2,
      "title": "Category Theory and Type Theory",
      "anchor": "#category-theory-and-type-theory"
    },
    {
      "level": 2,
      "title": "Summary",
      "anchor": "#summary"
    },
    {
      "level": 1,
      "title": "Conclusion",
      "anchor": "#conclusion"
    },
    {
      "level": 1,
      "title": "Meaning of the Pattern Field Theory Infinity Framework",
      "anchor": "#meaning-of-the-pattern-field-theory-infinity-framework"
    }
  ],
  "external_locations": [
    {
      "provider": "patternfieldtheory",
      "url": "https://patternfieldtheory.com/papers/the-pattern-field-theory-infinity-framework-incremental-boundary-and-frame-relative-infini/",
      "verification_status": "discovered-unverified"
    },
    {
      "provider": "zenodo",
      "url": "https://zenodo.org/communities/pft",
      "verification_status": "discovered-unverified"
    },
    {
      "provider": "academia",
      "url": "https://independent.academia.edu/JamesAllen375",
      "verification_status": "discovered-unverified"
    }
  ],
  "software": [],
  "data_files": [],
  "legacy_metadata": {
    "title": "The Pattern Field Theory Infinity Framework: - Incremental, Boundary, and Frame-Relative Infinity",
    "slug": "the-pattern-field-theory-infinity-framework-incremental-boundary-and-frame-relative-infini",
    "canonical_html": "https://patternfieldtheory.com/papers/the-pattern-field-theory-infinity-framework-incremental-boundary-and-frame-relative-infini/",
    "pdf": "https://patternfieldtheory.com/papers/the-pattern-field-theory-infinity-framework-incremental-boundary-and-frame-relative-infini/paper.pdf",
    "ots": null,
    "ots_file_date": null,
    "original_folder": "infinity",
    "original_tex_filename": "infinity.tex",
    "original_pdf_filename": "infinity.pdf",
    "original_ots_filename": null,
    "images_folder_copied": [
      "images"
    ],
    "csv_files_copied": [],
    "pandoc_status": "success",
    "source_last_write_utc": "2025-11-30T22:01:24Z",
    "generated_utc": "2026-05-08T11:01:47Z",
    "status": "canonical_html_export"
  },
  "migration": {
    "source": "papers(1).zip",
    "content_policy": "existing scientific HTML preserved; v26 shell and resource controls injected",
    "formula_status": "not rewritten during structural migration",
    "requires_source_formula_audit": true,
    "source_html_sha256": "80533ba78bff7af3c94610349ab04f72e3e099e7568ecf3b638ce9fdd5e99789"
  }
}