Claim from Significance editor

$| A | \leq ⌊ \frac{N + 18}{25} ⌋$

Quoted from the source · Significance editor · 2026-08-22 · View source

Problem link

ErdősProblems.com #848 · open the original problem page

Quoted from the source · Significance editor · 2026-08-22 · View source

Author involvement

Alex Chengyu Li confirmed that the public paper, repository, and pinned release may be used for a Significance record, and confirmed that the three bounded task descriptions accurately reflect the public release. Published with the author's confirmed description; publication does not assert independent mathematical verification.

Record note · alexchengyuli · 2026-08-22

Summary · for readers

In one sentence: The public proof-claim page links a paper and Lean repository for a claimed solution of Erdős Problem #848. The author confirms that the public release is the intended material.

Reader summary · Significance · 2026-08-22

Start here · for reviewers

Main deduction

Begin with the paper's main theorem and the finite certificate-generation steps, then compare the stated theorem with the Lean target.

SSRN abstract; paper theorem; Erdos848.PaperGeneratedCertificateProvider.all_N · The author has confirmed the public release as the intended material. · Significance’s interpretation · Significance editor · 2026-08-22

Risk points

The finite certificate-generation and finite-range arguments are the first bounded reading targets.
Exact Hall reformulation; finite range N <= 5*10^6; uniform tail estimate · Significance’s interpretation · Significance editor · 2026-08-22
The formalized theorem and the paper's informal statement should be compared before treating the Lean result as correspondence.
Lean target and paper's main theorem · Significance’s interpretation · Significance editor · 2026-08-22

Useful background

The Erdos Problem #848 definitions, Hall reformulation, finite certificates, and the repository's Lean build instructions.
Paper abstract and repository README · Significance’s interpretation · Significance editor · 2026-08-22

Needs checking

Suggest another focused check

Formalization handoff

A compact map for someone who wants to formalize this claim. It records preparation and open work, not a mathematical verdict.

Target: The paper's exact all-N extremal statement and Erdos848.PaperGeneratedCertificateProvider.all_N. Significance’s interpretation · Significance editor · 2026-08-22
System: Lean 4 with the repository's pinned release and certificate checker. Quoted from the source · Significance editor · 2026-08-22 · View source
Work state: Artifact reported
Code: formalization repository · commit bb8e1b10b006…

Definitions

The squarefree-product condition, exact extremal bound, finite certificates, and the paper-to-Lean theorem map must be compared.
Significance’s interpretation · Significance editor · 2026-08-22

Prerequisites

Basic extremal number theory, squarefree integers, Hall's theorem, and the repository's Lean build instructions.
Significance’s interpretation · Significance editor · 2026-08-22

Open questions

Does the Lean declaration exactly match the paper's all-N theorem?
Significance’s interpretation · Significance editor · 2026-08-22
Can an independent build reproduce the reported kernel-checked result and certificate checks?
Stated by the author · alexchengyuli · 2026-08-22 · View source

Paper/code correspondence: The reported formal artifact is evidence about the pinned Lean files; correspondence with the paper's exact theorem remains a separate reading task. Significance’s interpretation · Significance editor · 2026-08-22

Significance’s interpretation · Significance editor · 2026-08-22

Review activity

Independent reruns: 0
Math assessments: 0
Written reviews: 0
Open checks: 3

What Significance checked: Significance inspected the public claim page, paper link, repository link, and the pinned v1.0.5-kernel release information.

Still open: Significance has not independently rebuilt the repository, audited the finite certificates, or assessed the mathematical argument. Verification tasks remain open.

Copy for sharing

Copy and paste this summary.

The public proof-claim page links a paper and Lean repository for a claimed
solution of Erdős Problem #848. The author confirms that the public release
is the intended material.

Checked: Significance inspected the public claim page, paper link,
repository link, and the pinned v1.0.5-kernel release information.

Not checked: Significance has not independently rebuilt the repository,
audited the finite certificates, or assessed the mathematical argument.
Verification tasks remain open.

As of 2026-08-22T15:00:00Z (freshness: current)
Full record: https://hjyuh.github.io/significance/records/2026-alexchengyuli-erdos-848/
Significance records evidence. It does not judge the mathematics.

Scope: The record concerns the paper and the v1.0.5-kernel Lean formalization release, not a conclusion that the mathematical claim is established. Stated by the author · alexchengyuli · 2026-08-22 · View source
Source: Pinned repository PDF (the public claim also links SSRN 7230480) · github-crabsatellite-erdos-848-bb8e1b10 · retrieved 2026-08-22T15:00:00Z
sha256 54a910e7bcda…

Evidence — 3 entries

Source inspection
ev-source-inspection

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

Significance inspected the public proof-claim page and the linked paper and repository references. This is a source-and-version check, not a mathematical review.

Significance’s interpretation · Significance editor · 2026-08-22 · View source
Formal code published by the source
ev-formalization-reported

Published by the source. Any independent rerun appears as a separate entry.

The author reports that the complete publication proof and finite certificates are incorporated into the public Lean project and kernel-checked. Significance has not independently reproduced that run.

Open link @ bb8e1b10b006… · Stated by the author · alexchengyuli · 2026-08-22 · View source
Source inspection
ev-ssrn-source

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

The public proof-claim page links the manuscript record at SSRN 7230480; the pinned repository PDF above is recorded separately as the byte-hashed artifact available for this draft.

Quoted from the source · Significance editor · 2026-08-22 · View source

Plain-language explanation

This private draft records where the public claim and formal artifact live, and turns the next reading into bounded tasks. It does not decide whether the mathematical claim holds.

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.

Source inspection

Formal code published by the source

Source inspection