SIGNIFICANCE

Checked 2026-09-08 · source current · v1

Zeraoulia Rafik · ErdősProblems.com #719

What is claimed?

For every 3-graph G on n ≤ 9 vertices, |E(G)| − 3ν(G) ≤ ex₃(n, K₄³). Equivalently, every such G admits an edge-disjoint decomposition into at most ex₃(n, K₄³) single triples and tetrahedra.

Quoted from the source · Significance editor · 2026-09-08 §Theorem 1.1, p.2 · View source

Component dates
Preprint
2026-09-07
Exposition
Not recorded
Formalization
Not recorded

Component dates (preprint / exposition / formalization). “Not recorded” means no dated source is recorded for that component. Preprint dates refer to the pinned manuscript version.

Reader summary

Claimed
Zeraoulia Rafik's public claim reports the r = 3 bound for hypergraphs on at most nine vertices, plus structural sufficient conditions. The claim page explicitly excludes a solution of the general r = 3 conjecture.

Reader summary · Significance · 2026-09-08

What has been checked?

Significance inspected the problem and claim pages, followed the linked Zenodo note, checked its version 1.1 metadata, and computed the downloaded manuscript PDF SHA-256.

Reader summary · Significance · 2026-09-08

Independent reruns
0
Math assessments
0
Written reviews
0

Where is help needed?

The mathematics has not been independently assessed. The author-supplied first-pass task remains open, including matching hypotheses, quantifiers, cases, and cited-result assumptions, and listing what was checked and what remains.

Reader summary · Significance · 2026-09-08

Open questions contributed by Zeraoulia Rafik.

  • First pass statement comparison: Compare the note’s main result with Problem 719, explicitly recording the restriction to r = 3 and n ≤ 9 and any differences from the general problem.

    Check hypotheses, quantifiers, coverage of cases, and assumptions needed by cited results using the pinned Zenodo version 1.1. Record checked passages, gaps, and remaining dependencies. Allow an...

See 1 open check →

Problem link

ErdősProblems.com #719 · open the original problem page

Quoted from the source · Significance editor · 2026-09-08 · View source

Author involvement

The author contributed a suggested review task. Private correspondence is not reproduced.

Record note · rafikzeraoulia2025 · 2026-09-07

Start here · for reviewers

Main deduction

First pass: compare the note's main result with the full Problem 719 statement, recording the hypotheses, quantifiers, cases, and cited results examined and what remains.

Exact problem statement and note's main result · Significance’s interpretation · Significance editor · 2026-09-08 §Private correspondence; message text withheld.

Risk points

  • Match the requested full-statement comparison against the claim page's explicit r = 3 and n <= 9 scope; record the difference without expanding the author's public claim.

    Claim page: Summary and Notes · Significance’s interpretation · Significance editor · 2026-09-08 · View source

  • Check that hypotheses and quantifiers match, that no cases within the stated scope are untreated, and that cited results apply under the assumptions actually available.

    Main result and its cited results · Significance’s interpretation · Significance editor · 2026-09-08 §Private correspondence; message text withheld.

Useful background

  • The exact Problem 719 statement, the linked note pinned here as version 1.1, and the references it cites.

    Significance’s interpretation · Significance editor · 2026-09-08 §Private correspondence; message text withheld.

Needs checking

  • Produce a first-pass list of what was checked and what remains, including explicit remaining dependencies and any gap or additional assumption encountered; this is not a verdict.

    First pass: full-statement comparison · Significance’s interpretation · Significance editor · 2026-09-08 §Private correspondence; message text withheld.

  • Suggest another focused check
Copy for sharing

Copy and paste this summary.

Zeraoulia Rafik's public claim reports the r = 3 bound for hypergraphs on at
most nine vertices, plus structural sufficient conditions. The claim page
explicitly excludes a solution of the general r = 3 conjecture.

Checked: Significance inspected the problem and claim pages, followed the
linked Zenodo note, checked its version 1.1 metadata, and computed the
downloaded manuscript PDF SHA-256.

Not checked: The mathematics has not been independently assessed. The
author-supplied first-pass task remains open, including matching hypotheses,
quantifiers, cases, and cited-result assumptions, and listing what was
checked and what remains.

As of 2026-09-08T14:30:26Z (freshness: current)
Full record: https://hjyuh.github.io/significance/2026-rafikzeraoulia-erdos-719/
Significance records evidence. It does not judge the mathematics.
Scope
The note also develops structural sufficient conditions around a maximum tetrahedron packing, but does not claim a proof of the general r = 3 conjecture. Significance’s interpretation · Significance editor · 2026-09-08 §Notes · View source
Source
The Erdős–Sauer Clique Decomposition Problem for 3-Graphs: Verification through Nine Vertices and Local Packing Reductions · zenodo-22568303-v1.1 · retrieved 2026-09-08T14:25:08Z
sha256 c4a5fbe38c62…

Evidence: 6 entries

  1. Source inspection

    ev-source-inspection

    Public-source and version check only. This is not a mathematical review.

    Significance inspected the public problem and proof-claim pages and their source links, located the pinned manuscript version, and computed its SHA-256 from the downloaded PDF bytes. The mathematics has not been independently assessed; the author-supplied task remains open.

    Significance’s interpretation · Significance editor · 2026-09-08 · View source

  2. Source inspection

    ev-ai-claim-disclosure

    Public-source and version check only. This is not a mathematical review.

    A partial proof claimed by Rafik Zeraoulia (using OpenAI GPT-5.6 Thinking).

    Quoted from the source · Significance editor · 2026-09-08 · View source

  3. Source inspection

    ev-version-pin

    Public-source and version check only. This is not a mathematical review.

    The proof-claim page links Zenodo record 22568303, whose metadata identifies Version 1.1. manuscript.url names its PDF; the SHA-256 is c4a5fbe38c62…, computed from 302451 downloaded bytes at 2026-09-08T14:25:08Z. The file MD5 also matches Zenodo's displayed 3a9283706296b3704a643347dfc67ba4.

    Significance’s interpretation · Significance editor · 2026-09-08 · View source

  4. Source inspection

    ev-author-first-task

    Public-source and version check only. This is not a mathematical review.

    Editorial summary of the author-suggested task: Compare the note’s main result with Problem 719, explicitly recording the restriction to r = 3 and n ≤ 9 and any differences from the general problem. Check hypotheses, quantifiers, coverage of cases, and assumptions needed by cited results using the pinned Zenodo version 1.1. Record checked passages, gaps, and remaining dependencies. Allow an initial 2–3 hours; full verification may require more work.

    Significance’s interpretation · Significance editor · 2026-09-07 §Private correspondence; message text withheld.

  5. Source inspection

    ev-first-pass-scope

    Public-source and version check only. This is not a mathematical review.

    The author asks for a full-statement first pass, while the linked public claim explicitly limits its result to r = 3 and n <= 9. Preserve the requested comparison as an open task: its deliverable is a list of passages, hypotheses, quantifiers, cases, and references checked, with remaining dependencies and scope differences listed. No whole-proof verdict is requested.

    Significance’s interpretation · Significance editor · 2026-09-08 · View source

  6. Source inspection

    ev-publication-date

    Public-source and version check only. This is not a mathematical review.

    The DOI registry records an Issued date of 2026-09-07 for Zenodo 22568303.

    Significance’s interpretation · Significance editor · 2026-09-09 · View source

Limits of this record
  • This record does not issue a whole-paper correctness judgement.
  • Open invitations identify work not yet represented by a completed evidence entry.
  • No independent reproduction or mathematical assessment is represented unless an evidence entry above says otherwise.