A machine-checked proof of the Dong-Yang classification of optimal (n,4) binary codes for BSCs — Paper

Abstract

We present a machine-checked Lean~4 formalization of Dong and Yang's classification of optimal finite-length $(n,4)$ binary block codes for binary symmetric channels. The formalization was developed mainly by feeding the paper's proofs to an AI tool. To establish correctness, the authors verified the main theorem statements in Lean and the accepted axioms. This note discusses the corrections and simplifications made to the AI-generated formalization, and records discrepancies found in the paper during the formalization. The Lean code is available at https://github.com/shhyang/n4code_lean.

Authors 2

Shenghao Yang, Yanyan Dong

Specification

Official page: arxiv.org/abs/2609.10579
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
Arxiv announce type: cross
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
arXiv id: 2609.10579
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
Categories: cs.AI, cs.IT, math.HO, math.IT
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
PDF: arxiv.org/pdf/2609.10579
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
Primary category: math.HO
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
Published: 12 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh

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9

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T19

Freshest observation

1 h ago

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Authors: Shenghao Yang, Yanyan Dong

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Claim history · Abstract

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Claim history for Abstract
Value	Valid from → to	Status	Source	Confidence	Extractor
We present a machine-checked Lean~4 formalization of Dong and Yang's classification of optimal finite-length $(n,4)$ binary block codes for binary symmetric channels. The formalization was developed mainly by feeding the paper's proofs to an AI tool. To establish correctness, the authors verified the main theorem statements in Lean and the accepted axioms. This note discusses the corrections and simplifications made to the AI-generated formalization, and records discrepancies found in the paper during the formalization. The Lean code is available at https://github.com/shhyang/n4code_lean.	12 Sept 2026 04:12 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

12 Sept 2026
New paperPaperA machine-checked proof of the Dong-Yang classification of optimal (n,4) binary codes for BSCs
New paper: A machine-checked proof of the Dong-Yang classification of optimal (n,4) binary codes for BSCs
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Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.AI	feed	T1· Official	1 h ago	2

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