A machine-checked proof of the Dong-Yang classification of optimal (n,4) binary codes for BSCs
Updated 2 h ago · first seen 12 Sept 2026
paper_01M29X34RE6CZR7K2Z07C1ZDC3
- Published
- 12 Sept 2026
- T1 · 2 h ago
- arXiv
- 2609.10579
- T1 · 2 h ago
- Category
- math.HO
- T1 · 2 h ago
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
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
- Arxiv announce type
- cross
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
- arXiv id
- 2609.10579
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
- Categories
- cs.AI, cs.IT, math.HO, math.IT
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
- Primary category
- math.HO
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
- Published
- 12 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Each value shows its source, tier and observation time. Conflicting claims are kept side by side and flagged — never averaged. How AI Atlas records facts →
Provenance
Attributed facts
9
Source tiers
T19
Freshest observation
2 h ago
Conflicts
None
No models linked to this paper yet.
- Authors
- Shenghao Yang, Yanyan Dong
As of
Rewind the record: see this entity's attributes exactly as AI Atlas knew them on a given day.
Claim history
Official pageofficial_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/abs/2609.10579 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Abstractabstract1
| 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. | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Arxiv announce typearxiv_announce_type1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cross | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
arXiv idarxiv_id1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 2609.10579 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Categoriescategories1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.AI, cs.IT, math.HO, math.IT | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
PDFpdf_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/pdf/2609.10579 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Primary categoryprimary_category1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| math.HO | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Publishedpublished_at1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 12 Sept 2026 | → 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 →
- 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
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.AI | feed | T1· Official | 2 h ago | 2 |
Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.