SIGNIFICANCE

Checked 2026-08-16 · source current · v2

Claim from Rafikzeraoulia2025

The paper proves Problem #726 conditionally on an explicitly stated reciprocal-prime equidistribution hypothesis.

Quoted from the source · rafikzeraoulia2025 · 2026-08-11 · View source

Problem link

ErdősProblems.com #726 · open the original problem page

Quoted from the source · Significance editor · 2026-08-16 · View source

Author involvement

Rafik Zeraoulia reviewed and approved the claim description, source version, hash, and reviewer map by correspondence on 2026-08-18.

Record note · rafikzeraoulia2025 · 2026-08-18

Summary · for readers

In one sentence
The public proof-claim page says that the submission addresses Problem #726 conditionally and links to a Zenodo manuscript. The page classifies it as a full proof claim, while a public commenter suggested calling it a partial proof; Rafik confirms that it should remain clearly conditional.

Reader summary · Significance · 2026-08-16

Start here · for reviewers

Main deduction

Follow the conditional deduction from Hypothesis 3.1 to the asymptotic in Theorem 1.1.

Theorem 1.1 and Section 6 · Trace the small, intermediate, and large-prime ranges through Lemma 6.1. · Stated by the author · rafikzeraoulia2025 · 2026-08-18

Risk points

  • Hypothesis 3.1 is the main dependency: its range, smoothness norm, and error term must be read exactly and kept separate from known theorems.

    Hypothesis 3.1 and Remark 3.2 · Stated by the author · rafikzeraoulia2025 · 2026-08-18

  • The final estimate depends on the continuum cancellation and on all three prime ranges contributing only the claimed error.

    Lemma 6.1 and the proof of Theorem 1.1 · Stated by the author · rafikzeraoulia2025 · 2026-08-18

Useful background

  • Basic Mertens estimates for reciprocal primes, dyadic decomposition, and smooth partial summation.

    Sections 3–6; compare the cited prime-equidistribution result separately. · Stated by the author · rafikzeraoulia2025 · 2026-08-18

Needs checking

  • First compare Hypothesis 3.1 with the cited literature before reading the conditional deduction. — The paper itself says the required range is presently unproved.

    Hypothesis 3.1 and the cited proposition · Stated by the author · rafikzeraoulia2025 · 2026-08-18

  • Suggest another focused check

Review activity

Independent reruns
0
Math assessments
0
Written reviews
0
Open checks
4

What Significance checked: Significance fetched the proof-claim page and its linked Zenodo PDF, checked the Zenodo version metadata, and computed the PDF SHA-256 hash recorded here.

Still open: Significance has not independently checked the stated hypothesis against the literature or checked the conditional deduction and error accumulation. Independent verification remains open.

Copy for sharing

Copy and paste this summary.

The public proof-claim page says that the submission addresses Problem #726
conditionally and links to a Zenodo manuscript. The page classifies it as a
full proof claim, while a public commenter suggested calling it a partial
proof; Rafik confirms that it should remain clearly conditional.

Checked: Significance fetched the proof-claim page and its linked Zenodo
PDF, checked the Zenodo version metadata, and computed the PDF SHA-256 hash
recorded here.

Not checked: Significance has not independently checked the stated
hypothesis against the literature or checked the conditional deduction and
error accumulation. Independent verification remains open.

As of 2026-08-16T15:19:21Z (freshness: current)
Full record: https://hjyuh.github.io/significance/2026-rafikzeraoulia-erdos-726/
Significance records evidence. It does not judge the mathematics.
Scope
The proof-claim page labels this submission as a full proof claim and its notes call it conditional. Quoted from the source · rafikzeraoulia2025 · 2026-08-11 · View source
Source
A Conditional Resolution of an Erdős-Graham-Ruzsa-Straus Conjecture on Reciprocal Sums over Primes · zenodo-21882603-v1.0 · retrieved 2026-08-16T15:19:21Z
sha256 dae18ee07e2b…

Evidence — 2 entries

  1. Source inspection

    ev-source-inspection

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

    Significance fetched the queued proof-claim page, followed its direct Zenodo manuscript link, confirmed the public v1.0 metadata, and computed the PDF hash above. The page exposed no formal artifact and no substantive review comment about this claim.

    Automated result · Significance editor · 2026-08-16 · View source

  2. Source inspection

    ev-community-classification

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

    A public commenter suggested that this conditional submission be called a partial proof. This records the comment as a public classification, not as Significance's verdict.

    Quoted from the source · robsneiderman · 2026-08-12 · View source

Plain-language explanation

This record is a review map, not a substitute for the manuscript: it identifies the exact claim, source version, and bounded open tasks so a reader can decide whether to inspect a particular passage. The result is conditional, not an unconditional resolution.

Explanation · Significance

Plain-language explanation

This page records what the author claims and what Significance checked about the source file. It does not explain or judge the proof.

Explanation · Significance

Limits

  • 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.