ScalingStacks

Proposition 11.4 (05VR)

Source history

Charles Rezk

Original source: arXiv:math/9811037v3

Detailed backend records are private. Public author/source status appears above.

The permanent identity and original source provenance are retained below.

{
  "key": "work:W000062:pdf:67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6:page:25:bbox:126.72,410.7,311.699,420.931",
  "first_source_version": "math/9811037v3",
  "chapter": "work-w000062",
  "work": "W000062",
  "kind": "Proposition",
  "number": "11.4",
  "title": "Proposition 11.4 .",
  "source_version": "math/9811037v3",
  "source": {
    "pdf_sha256": "67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6",
    "page": 25,
    "bbox": [
      126.72,
      410.7,
      311.699,
      420.931
    ]
  },
  "target": "/chapters/work-w000062.html",
  "identity_basis": "pinned original PDF hash and exact page/bbox; never display number",
  "status": "active",
  "source_span_sha256": "220dcaefabab1e9b3aa0005f49b8208dc74cf0e8aa5d4375d67d0395b53f9f4e",
  "source_label": "prop-homotopic-maps-and-equiv-compositions",
  "source_label_occurrences": 1,
  "display_source": {
    "url": "https://arxiv.org/html/math/9811037v3",
    "sha256": "0278fe7a29d291fcbf711513ebb8f91c2e74663d596c74bef57726c82d566169",
    "element_id": "S11.SS4",
    "alignment_status": "verified_pdf_author_occurrence"
  },
  "author_source": {
    "file": "main.tex",
    "line": 2461,
    "file_sha256": "6c08cf3f6853a2c90d8dc23adcf397a8c0367e7f7dcfde71a55658c9b044f936",
    "byte_start": 102475,
    "byte_end": 102797
  },
  "identity_alignment": {
    "tag": "05VR",
    "registry_key": "work:W000062:pdf:67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6:page:25:bbox:126.72,410.7,311.699,420.931",
    "source_version": "math/9811037v3",
    "pdf_source": {
      "pdf_sha256": "67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6",
      "page": 25,
      "bbox": [
        126.72,
        410.7,
        311.699,
        420.931
      ]
    },
    "pdf_heading_sha256": "12b138edc805256b6393a9051d07e4c28795395644ef5ff7ada9f402c64798a5",
    "author_source": {
      "file": "main.tex",
      "line": 2461,
      "file_sha256": "6c08cf3f6853a2c90d8dc23adcf397a8c0367e7f7dcfde71a55658c9b044f936",
      "byte_start": 102475,
      "byte_end": 102797
    },
    "source_span_sha256": "220dcaefabab1e9b3aa0005f49b8208dc74cf0e8aa5d4375d67d0395b53f9f4e",
    "display_source": {
      "url": "https://arxiv.org/html/math/9811037v3",
      "sha256": "0278fe7a29d291fcbf711513ebb8f91c2e74663d596c74bef57726c82d566169",
      "element_id": "S11.SS4",
      "alignment_status": "verified_pdf_author_occurrence"
    },
    "basis": "unique_ordered_pinned_pdf_heading_body_prefix",
    "prefix_adapter": {
      "normalization": "unicode_nfkc_ascii_alphanumeric_prefix",
      "omitted_reference_kinds": []
    },
    "normalized_pdf_prefix_sha256": "cfb6ffd54e4d7819bc039e3e2401e2381c2950a92ca5b1870dcac4d42778c866"
  },
  "historical_entry_before_author_html_binding": {
    "key": "work:W000062:pdf:67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6:page:25:bbox:126.72,410.7,311.699,420.931",
    "first_source_version": "math/9811037v3",
    "chapter": "work-w000062",
    "work": "W000062",
    "kind": "Proposition",
    "number": "11.4",
    "title": "Proposition 11.4. Let f, g ∈map(x, y).",
    "source_version": "math/9811037v3",
    "source": {
      "pdf_sha256": "67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6",
      "page": 25,
      "bbox": [
        126.72,
        410.7,
        311.699,
        420.931
      ]
    },
    "target": "/chapters/work-w000062.html",
    "identity_basis": "pinned original PDF hash and exact page/bbox; never display number",
    "status": "active"
  }
}

Original mathematics by the credited authors. Source collection and HTML conversion remain in progress.