ScalingStacks

Proof (05VZ)

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:27:bbox:126.72,444.05,485.396,455.371",
  "first_source_version": "math/9811037v3",
  "chapter": "work-w000062",
  "work": "W000062",
  "kind": "Proof",
  "number": "",
  "title": "Proof.",
  "source_version": "math/9811037v3",
  "source": {
    "pdf_sha256": "67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6",
    "page": 27,
    "bbox": [
      126.72,
      444.05,
      485.396,
      455.371
    ]
  },
  "target": "/chapters/work-w000062.html",
  "identity_basis": "pinned original PDF hash and exact page/bbox; never display number",
  "status": "active",
  "source_span_sha256": "902be02f0f91fea7836eb0337312751fb8f040131af20b23a938c79434f98fd2",
  "source_label": null,
  "source_label_occurrences": 0,
  "display_source": {
    "url": "https://arxiv.org/html/math/9811037v3",
    "sha256": "0278fe7a29d291fcbf711513ebb8f91c2e74663d596c74bef57726c82d566169",
    "element_id": "S11.SS7.2",
    "alignment_status": "verified_pdf_author_occurrence"
  },
  "author_source": {
    "file": "main.tex",
    "line": 2633,
    "file_sha256": "6c08cf3f6853a2c90d8dc23adcf397a8c0367e7f7dcfde71a55658c9b044f936",
    "byte_start": 108386,
    "byte_end": 109234
  },
  "identity_alignment": {
    "tag": "05VZ",
    "registry_key": "work:W000062:pdf:67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6:page:27:bbox:126.72,444.05,485.396,455.371",
    "source_version": "math/9811037v3",
    "pdf_source": {
      "pdf_sha256": "67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6",
      "page": 27,
      "bbox": [
        126.72,
        444.05,
        485.396,
        455.371
      ]
    },
    "pdf_heading_sha256": "6e9156891a6f56b898f44b120215dc29e9ad8213b2d19421911ab639e728212e",
    "author_source": {
      "file": "main.tex",
      "line": 2633,
      "file_sha256": "6c08cf3f6853a2c90d8dc23adcf397a8c0367e7f7dcfde71a55658c9b044f936",
      "byte_start": 108386,
      "byte_end": 109234
    },
    "source_span_sha256": "902be02f0f91fea7836eb0337312751fb8f040131af20b23a938c79434f98fd2",
    "display_source": {
      "url": "https://arxiv.org/html/math/9811037v3",
      "sha256": "0278fe7a29d291fcbf711513ebb8f91c2e74663d596c74bef57726c82d566169",
      "element_id": "S11.SS7.2",
      "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": "0f8e3543028673d830b2737312010a70bd10a49a8a3f66528fef808bb1aa0419"
  },
  "historical_entry_before_author_html_binding": {
    "key": "work:W000062:pdf:67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6:page:27:bbox:126.72,444.05,485.396,455.371",
    "first_source_version": "math/9811037v3",
    "chapter": "work-w000062",
    "work": "W000062",
    "kind": "Proof",
    "number": "",
    "title": "Proof. Let d0H(k −1) ⊂C(k) denote the image of H(k −1) in C(k) induced by",
    "source_version": "math/9811037v3",
    "source": {
      "pdf_sha256": "67ad8eef47b7aba409bbcc80c59d5e34d0a3978869cfbafc1e39eba6f05049c6",
      "page": 27,
      "bbox": [
        126.72,
        444.05,
        485.396,
        455.371
      ]
    },
    "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.