Wiki
Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
source_snapshot.json
json
{
"schema_version": 1,
"source": {
"authors": [
"Kenneth Moore"
],
"title": "A pyramid with a Ramsey base is Ramsey",
"arxiv_version": "2608.09649v1",
"version_record_url": "https://arxiv.org/abs/2608.09649v1",
"pdf_url": "https://arxiv.org/pdf/2608.09649v1",
"submission_utc": "2026-08-10T14:26:02Z",
"acquired_utc": "2026-09-05T11:56:46.442966+00:00",
"canonical_pdf": "moore_2026_pyramid_ramsey_base.pdf",
"bytes": 328018,
"physical_pages": 5,
"version_qualification": "Exact arXiv v1 only; no journal-version equivalence or acceptance claimed."
},
"reading": {
"all_source_pages_visually_read": [
1,
2,
3,
4,
5
],
"method": "pdftoppm 150 dpi PNG, viewed at original detail; no OCR",
"native_text_extraction": "Navigation and formula cross-checking only; no OCR.",
"scope": "All five pages visually inspected, including all statements, every same-paper proof, figures if any, notes and references."
},
"proof_scope": {
"same_paper_coverage": {
"theorem_1_2": "Complete relative proof",
"lemma_2_3": "Complete relative compactness application, added explicitly",
"theorem_2_1": "Exact external statement",
"theorem_2_2": "Exact external statement plus elementary consequence explanation",
"conjecture_1_1": "Historical context only; neither competing classification is proved",
"figure_1": "Visually checked; no deduction depends on visual measurement",
"acknowledgments_and_references": "Read; AI brainstorming acknowledgment is provenance only"
},
"complete_proof_pages": [
"lemma_2_3",
"theorem_1_2"
],
"external_statement_pages": {
"theorem_2_1": {
"classification": "exact_external_statement_only",
"scope": "Ordinary finite Cartesian product theorem; original Paper I Theorem 20 on printed p.357.",
"proof_included": false
},
"theorem_2_2": {
"classification": "exact_external_statement_with_elementary_consequence",
"scope": "Every finite affinely independent configuration is Ramsey, from Frankl-Rodl Theorem5.1 and Definition2.1.",
"proof_included": false,
"qualification": "The elementary super-Ramsey-to-Ramsey pigeonhole implication is explained, but the external simplex proof is not counted."
}
},
"external_inputs": {
"paper_i": {
"physical_pages_visually_read": [
3,
17
],
"reading_role": "Original Proposition4 and Theorem20 interfaces; no complete original-paper proof audit."
},
"frankl_rodl": {
"physical_pages_visually_read": [
1,
2,
5
],
"reading_role": "Title/publication and exact Definition2.1/Theorem5.1 input; full theorem proof remains external."
},
"rado_quoted_1951": {
"physical_pages_visually_read": [
1
],
"reading_role": "Exact Rado selection theorem quoted as Theorem2; the original 1949 proof is not acquired or reviewed here."
}
},
"source_precision": [
{
"source_location": "Moore p.2, Lemma2.3",
"issue": "The source states finite-witness compactness and cites hypergraph compactness without proving that application.",
"treatment": "A complete application of the exact existing Rado selection statement is supplied; Rado itself remains external.",
"classification": "compilation expansion, not a source erratum"
},
{
"source_location": "Moore p.4, ambient-embedding sentence",
"issue": "The sentence names P and C, whereas the auxiliary apices to be transported form A.",
"treatment": "Embed P and A explicitly in the common R^N, and fully justify the ambient isometry extension.",
"classification": "explanatory precision, no changed theorem"
},
{
"source_location": "Main theorem and proof conventions",
"issue": "The constructive proof uses a nonempty base and finite witness.",
"treatment": "The optional empty-base case is a singleton; all nonempty cases include affine dimension zero.",
"classification": "endpoint clarification"
}
],
"unresolved_same_paper_obligations": [],
"independent_final_review": "Not asserted by this author snapshot."
},
"provenance": {
"dated_search": "2026-09-05",
"journal_acceptance": "No acceptance or journal version located in the bounded search; absence is not proof of nonacceptance.",
"formal_evidence": "No formal proof artifact identified in the primary records; no exhaustive formalization search or local build performed.",
"later_primary_citation": {
"source": "Palvolgyi arXiv:2608.10865v2, p.24",
"url": "https://arxiv.org/pdf/2608.10865v2#page=24",
"scope": "Citation of Moore/Mirabi for pyramid closure only; no adoption of the later paper's unverified appendix."
},
"chronology": {
"moore_public_submission": "2026-08-10T14:26:02Z",
"mirabi_public_submission": "2026-08-12T07:23:39Z",
"mirabi_private_account": "Mirabi v1 p.1 says both partial and full arguments were privately circulated to Ivan, Leader and Walters in June2026 and obtained independently of Moore.",
"qualification": "Private circulation and independence are the author's account, not an independently established priority determination."
},
"moore_ai_acknowledgment": "Moore v1 p.5 acknowledges ChatGPT5.6 in brainstorming; provenance only, not mathematical validation.",
"mirabi_acknowledgments": "Mirabi v1 p.5 thanks Ivan and Leader for discussions and earlier-version reading; no acceptance is inferred."
}
}
Graph