source_record.json

{
  "title": "On Representatives of Subsets",
  "author_as_published": "P. Hall",
  "author": "Philip Hall",
  "journal": "Journal of the London Mathematical Society",
  "series": "first",
  "volume": 10,
  "publisher_volume_identifier": "s1-10",
  "issue": 1,
  "year": 1935,
  "issue_date": "1935-01",
  "printed_pages": "26–30",
  "physical_pages": 5,
  "doi": "10.1112/jlms/s1-10.37.26",
  "received_date_as_printed": "1934-04-23",
  "read_date_as_printed": "1934-04-26",
  "read_date_is_not_asserted_to_be_revision_or_acceptance": true,
  "crossref_online_date": "2016-12-23",
  "digital_dates_are_not_new_mathematical_versions": true,
  "canonical_version": "Published original page scan retained unchanged from Dartmouth institutional course archive",
  "pdf_file": "hall_1935_representatives_subsets.pdf",
  "pdf_bytes": 273318,
  "institutional_pdf_url": "https://math.dartmouth.edu/archive/m38s12/public_html/sources/Hall1935.pdf",
  "institutional_index_url": "https://math.dartmouth.edu/archive/m38s12/public_html/",
  "institutional_index_description": "Dartmouth Mathematics 38, Spring 2012, explicitly links P Hall 1935 separately from M Hall 1948",
  "publisher_article_url": "https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/s1-10.37.26",
  "publisher_pdf_url": "https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/jlms/s1-10.37.26",
  "publisher_pdf_binary_acquired": false,
  "publisher_pdf_byte_equivalence_claimed": false,
  "crossref_url": "https://api.crossref.org/works/10.1112%2Fjlms%2Fs1-10.37.26",
  "oxford_metadata_url": "https://academic.oup.com/jlms/article-abstract/s1-10/1/26/2194138",
  "acquired_date": "2026-09-05",
  "page_map": [
    {
      "physical": 1,
      "printed": 26
    },
    {
      "physical": 2,
      "printed": 27
    },
    {
      "physical": 3,
      "printed": 28
    },
    {
      "physical": 4,
      "printed": 29
    },
    {
      "physical": 5,
      "printed": 30
    }
  ],
  "last_page_boundary": "Hall text ends above the Davenport title; Hall Rado footnote remains below. The opening Davenport material is preserved in the PDF but is outside this source proof scope.",
  "visual_reading": "All five original pages inspected at original image detail from 200 dpi renders; printed p.29 also checked at 350 dpi. Existing text layer used only for navigation; no new OCR.",
  "proof_scope": "Five complete elementary components: forced-intersection lemma, Theorems 1–3, and equal positive finite block corollary. The Rado 1933 ancillary remark remains an unproved historical pointer.",
  "essential_external_theorem_inputs": [],
  "background_inputs": [
    "Finite counting",
    "Induction on a finite integer",
    "Finite selection from nonempty sets"
  ],
  "source_corrections": [
    {
      "printed_page": 29,
      "kind": "notation mismatch",
      "detail": "Theorem 2 display names its indexed intersection M, then prose uses M_i; the reconstruction consistently defines M_i."
    },
    {
      "kind": "metadata source priority",
      "detail": "The original identifies 26 April 1934 as read, although Oxford metadata calls it revision received."
    }
  ],
  "compilation_expansions": [
    "Shortest simple index chain and complete injectivity check for the source exchange.",
    "Explicit separation of indexed assignments from their underlying ranges.",
    "The printed rho>=0 endpoint is retained; m=0 is the elementary empty-system extension.",
    "Necessity of Theorems 2 and 3 and symmetry of Theorem 3 are made explicit.",
    "The graph formulation is translated directly inside the Theorem 1 proof.",
    "The equal-block counting step requires and uses positive finite block size."
  ],
  "author_erratum_claimed": false,
  "formalization_scope": "No formal-source audit or local Lean build.",
  "status_scope": "No new problem-status, current-best or contemporary acceptance claim."
}