Chinese math paper

Chinese Mathematical Paper Writing & Translation

When to load: translating an English math paper to Chinese, formatting a Chinese math paper for submission/thesis, improving the narrative flow of a proof-heavy paper, or expanding a research paper into self-contained lecture notes.

Communication language

Discussion and strategy in Chinese. Lean code, lemma names, and mathematical notation stay in English. This is the user's strong preference and is recorded in their profile.

Translation Pre-Flight: English Compression Pass

Ou/KK style alignment — after compression, run the full style-alignment checklist at references/ou-kk-style-alignment.md. It covers 8 specific patterns: parenthetical removal, roadmap deletion, case-label flattening, global-declaration compression, coined-term replacement, pattern-language removal, sub-case merging, and transition cleanup. These are the patterns that make a paper read like Ou-Wang-Yao (2007) or KK (2023) rather than a modern tutorial.

Always compress the English source before translating. Chinese text is ~20% longer on the page than English; an uncompressed 6-page paper will blow up to 7-8 pages after translation. Ou-Wang-Yao (2007) and KK (2023) are the style references.

Compression targets (in priority order)

1. Inline single-line equations. If a display equation (\[...\]) contains a single line, convert it to inline ($...$). Only multi-line aligned equations and numbered equations should remain as display.

2. Delete explanatory prose. Strike sentences that restate what an equation already shows (e.g., "This identity expresses the coefficients of X through the coefficients of Y"). Strike parenthetical justifications like "(this requires n≥5)" when the condition is already a global hypothesis. For a systematic audit of ALL explanatory parentheticals against reference papers (Ou/KK), see references/parenthetical-audit.md. Target: 0.

   Explanatory parentheticals are a distinct sub-category: parenthetical phrases that embed proof reasoning (e.g., "(only the bracket-right term contributes, via …)", "(using d₃=d₁ from above)"). Ou (2007) and KK (2023) have zero such parentheticals. Audit methodology and reference-paper comparison data in references/explanatory-parenthetical-audit.md. Key rule: never absorb into the sentence — a via clause tacked onto a sentence is still an explanatory parenthetical. Just delete it. The reader can verify the computation themselves.

3. Drop construction verifications. Use "one checks" / "it is easy to verify" instead of showing every bracket expansion. Ou uses this pattern for ALL his standard derivations.

4. Merge signpost paragraphs. Delete "We distinguish three cases", "First, we prove...", "Five additional derivations are supported at the Dynkin endpoints." The case labels and lemma statements speak for themselves.

5. Compress bracket calculations. "The bracket-left term contributes -c_k" instead of showing all three terms with two that are zero.

6. Delete unused properties. "This ideal is abelian and satisfies" → "This ideal satisfies" if the abelian property is never used in proofs.

Density comparison

Metric	Ou (2007)	Our v3 (after compression)
Pages	6	5
Font	9pt single-col	10pt 2-col
Display eqs in main proof	0	~25
Construction verification	"it is easy to check"	1-2 line checks

Before translating, ensure the English original follows mathematical paper conventions (not lecture-note style). Full audit checklist at references/english-paper-conventions.md. Key rules:

• No named proof techniques (cite lemmas/equations by number)
• No source/target/width as informal terminology
• No numbered Step 1/2/3/4 frameworks
• No ornamental observations not used in proofs
• Global condition declaration after Theorem 1.1
• KK (arXiv:2305.00727) is the style reference for 1/2-derivation papers

---

Core Principle: English is the Master

The English version is the canonical reference. The Chinese version must be a faithful mapping, not a rewrite:

• Every Chinese sentence should correspond uniquely to an English sentence.
• Do NOT reorder proofs, add explanations, or rewrite logic for fluency.
• Formulas, labels, theorem/lemma/corollary/equation numbers stay unchanged.
• Lean lemma names stay in English (never "translate" coeffOf_cond).

Editing workflow: plan first, then act

When the user asks to modify the paper (delete something, restructure, change terminology), do NOT immediately execute. First:

1. Read the full context around each target.
2. Present a plan showing what changes and why.
3. Re-examine: "Is this plan optimal, or is there a better approach?"
4. Only after user confirmation, execute. The user explicitly prefers this sequence for all paper-editing decisions.

---

Glossary-Driven Translation

Always establish a glossary BEFORE translating. Read the full paper, extract all terminology (~100-250 terms), and freeze the glossary.

Glossary format

CRITICAL: Always derive the glossary fresh from the CURRENT English version. An existing glossary file from a previous version is a liability — it contains stale terms that may have been deleted, and terminology conventions may have changed (e.g., "归约" → "化简"). Read every .tex file, extract all terms, then cross-check against any existing glossary.

For validating translations when web search returns no Chinese math results (common with DDGS/SearXNG), see references/term-validation.md.

% English term                    Chinese translation
% half-derivation                 1/2-导子
% constraint reduction            约束归约
% image restriction               像限制

Key translation conventions (frozen for this user)

English	Chinese	Notes
half-derivation	1/2-导子	KK uses "1/2-derivation"; "半导子" has semigroup connotation — avoid
strictly upper triangular	严格上三角	Standard
Lie algebra	李代数	Standard
bracket	李括号	Standard
matrix unit	矩阵单位	Standard
Kronecker delta	Kronecker delta	Retain English
coordinate projection	坐标投影	Standard
central	中心/中心元	Standard
ideal	理想	Standard
abelian	交换的	Alternative: 阿贝尔的
centered / centered decomposition	中心化 / 中心化分解	Defined in paper; add "(centered)" on first use
trivial derivation	平凡导子	Standard; used in Chinese math papers
simple-root derivation	单根导子	Standard Lie theory term
boundary derivation	边界导子	Descriptive
commutator	换位子	Standard
Dynkin involution	Dynkin对合	Dynkin retained as proper noun
parameter tally	参数统计	Standard
commuting pair	交换对	Standard
linear map	线性映射	Standard
linearly independent	线性无关	Standard
automorphism	自同构	Standard
commutative ring	交换环	Standard
δ-derivation	δ-导子	Standard
transposed Poisson structure	转置Poisson结构	Standard
upper bound / lower bound	上界 / 下界	Standard
dimension / dim	维数	Standard
force (verb)	推出 / 必有 / 可知	NEVER 迫使
obtain/yield/get	给出 / 引出	NOT 得到 (mechanical overuse)
represent	刻画 / 对应于	NOT 表示
serve as	充当 / 给出	NOT 作为

Note (2026-07-11): After English v3 debranding, the following terms are no longer used as named concepts: chain bridge, width reduction, diagonal propagation, image restriction, endpoint reduction, channel (a/c-channel), cross-endpoint constraint. The terms "evaluation matrix", "boundary cocycle", and "syzygy" do not appear in v3.

coeff / coeffOf / coefficient — three-level distinction

Lean	Chinese	Scope
coeff	系数函数	Lean internal: the raw 4-index function ℕ⁴ → F
coeffOf	系数投影	Lean API: totalized wrapper, returns 0 for invalid indices
coefficient	系数	Math: π_{uv}(T(E_{ij})), the projection value

NEVER conflate these. In prose, use 系数投影 for coeffOf on first occurrence with parenthetical (coeffOf). In the Lean-formalization footnote ($\S$2), explain that coeffOf is a totalized wrapper.

Lean-style phrasing — FORBIDDEN in body text

Forbidden	Use instead
返回 (return)	定义... / 给出...
调用 (call)	应用... / 作用于...
包装器 (wrapper)	footnote only; body uses 系数投影 directly
接受参数	以...为输入 / 作用于
迫使	推出 / 给出 / 要求 / 使

These only appear in the Lean-formalization footnote ($\S$2), never in body text.

Punctuation

Chinese version uses English punctuation (. , not 。，). This is the user's stated preference. Apply .replace('。', '.') and .replace('，', ',') as a final pass after all translation is complete.

GitHub README rendering: when math expressions appear near CJK full-width punctuation in GitHub markdown, add ASCII spaces around $ delimiters. Full recipe in halfder-nn-repo-setup skill, references/github-rendering-pitfalls.md.

GitHub README rendering with CJK

When publishing Chinese math on GitHub, full-width CJK punctuation touching $ delimiters prevents MathJax from rendering. Always add ASCII spaces: ：$...$， → ： $...$ ，. Full guide: load paper-engineering skill and see references/github-readme-math-rendering.md.

Lean names

All Lean theorem names, file names, and \texttt{} identifiers stay in English: coeffOf_cond, finrank_halfDer, HalfDerivation, Phi, MatIdx, etc. NEVER translate these.

Pre-translation audit: remove self-coined technique names

Before translating, audit the English paper for unnecessary coined terminology. Compare against key references in the field (e.g., KK 2023, Filippov 1998) and remove any names they would not use. Replace named techniques with lemma/equation number references. Full methodology and findings in references/debranding-audit.md.

Translation freeze workflow

WARNING: After compressing the English paper, the translation plan MUST be completely rewritten. See references/compression-workflow.md for the 5-round iterative compression methodology and common redundancy patterns.

When translating an English paper that has a Lean-formalized proof:

1. Freeze English first. Confirm all patches applied, final compilation passes with 0 errors. Tag as "translation baseline".
2. Create a fresh paper-cn-v2/ folder. Copy main.tex (ctex preamble) and glossary.tex from existing Chinese version. Create empty stubs for each section.
3. Translate sentence-by-sentence from frozen English. Do NOT reuse old Chinese translations section-by-section. Even sections that appear unchanged may have accumulated terminology drift.
4. Translation order: highest-risk first. §5 (most changes) → §7 (new lemmas) → §2 (new footnotes) → §1 → §3 → §4 → §6 → §8.
5. Add new glossary terms BEFORE translating the section that introduces them.

Translation principles (10 rules)

0. English term in parentheses on first occurrence; Chinese only thereafter.
1. Lean theorem/file names preserved in English.
2. "force" → context-dependent, never "迫使".
3. centered → 中心化（centered）(first) / 中心化 (thereafter).
4. cocycle → preserved, never "余循环".
5. Two-phase: Phase 1 (faithful) then Phase 2 (polish).
6. Rewrite in Chinese math paper style, not sentence-by-sentence.
7. Avoid mechanical "得到/表示/作为".

---

Two-Phase Translation Workflow

Phase 1: Faithful Conversion

• Keep all math, labels, formulas, references, LaTeX structure unchanged.
• No additions or deletions of any explanation.
• Section-by-section, freeze each before moving to the next.

Phase 1.5: Per-Section Compile + Audit

After EACH section, before moving to the next:

1. Compile the PDF to catch LaTeX issues immediately.
2. Run the Chinese Translation Audit Checklist (references/per-section-checklist.md):
   • Mechanical checks (0 迫使, flag excessive 得到)
   • Math consistency (formulas, labels, references unchanged)
   • Terminology consistency (glossary compliance)
   • Chinese math style (no translation-ese)
   • Proof logic (causality preserved, no ambiguity)
3. Fix ALL issues before moving to the next section. Do NOT batch-translate multiple sections without auditing in between.

Phase 2: Unified Chinese Polish

• Done AFTER all sections are translated.
• Remove English flavor, unify sentence patterns and connectors.
• Fix overfull hboxes.
• Check terminology consistency across all sections globally.

---

Phase 3: Narrative Reconstruction

When the paper feels "fragmented" to read, add a narrative layer without changing any mathematics:

1. Section Opening: why this section exists, what it achieves.
2. Subsection Transition: why we're proving THIS now, after the last step.
3. Lemma Motivation: what problem this lemma solves, why it's needed.

The goal: a first-time reader always knows WHY the author is doing each step.

Compression staircase (universal pattern)

For constraint-reduction proofs, display the reduction order:

所有线性映射 (d² 维)
    ↓ \eqref{eq:halfder} 约束
源压缩：只留下相邻源
    ↓
对角压缩：对角线归零
    ↓
目标压缩：像限制到 3 维理想
    ↓
端点压缩：消去内部冗余
    ↓
跨端点约束：F_eq 耦合两端
    ↓
参数统计：n+5

---

Thesis Formatting (Chinese ctex)

For Chinese thesis/dissertation formatting:

\documentclass[a4paper]{ctexart}
\usepackage[top=2cm, bottom=2cm, left=2cm, right=2cm,
            bindingoffset=0.5cm]{geometry}
\linespread{1.0}

\ctexset{
  section = {format = \heiti\zihao{4}\bfseries},
  subsection = {format = \heiti\zihao{-4}\bfseries},
  subsubsection = {format = \heiti\zihao{5}},
}

% Formula numbering by chapter: (1-1), (2-3)
\numberwithin{equation}{section}
\renewcommand{\theequation}{\thesection--\arabic{equation}}

% Theorem environments
\newtheorem{theorem}{定理}[section]
\newtheorem{lemma}[theorem]{引理}
\newtheorem{corollary}[theorem]{推论}
\newtheorem{definition}[theorem]{定义}
\newtheorem{remark}[theorem]{注记}

Compile with tectonic (XeTeX-based, auto-downloads packages).

Word template → ctexart conversion

When the user provides a .docx format reference, extract all formatting parameters before writing LaTeX. Full workflow in references/docx-format-extraction.md. Key pitfalls:

• Add \pagestyle{empty} after \begin{document} — ctexart defaults to section-name running headers, but thesis format has none.
• Use \ctexset{section/aftername=\hspace{0pt}} to remove space between section number and title (for "1标题" format).
• Use \newtheoremstyle from amsthm when theorem head fonts differ from amsthm defaults (common in Chinese thesis templates).
• Word Normal style font size ≠ body text font size — always verify with XML or check the Normal style default rather than trusting run-level font.size.
• 楷体加粗不生效 — \kaishu\bfseries produces no visible bold in ctex. Fix: \setCJKfamilyfont{kaishu}{KaiTi}[AutoFakeBold={2.5}]. Full pitfall list at references/ctex-pitfalls.md.
• LaTeX → Word conversion — use pandoc with flattened input files and stripped ctex commands. Math is preserved as OMML. Full workflow at references/pandoc-conversion.md.

---

Lecture Notes Expansion (Pedagogical Version)

When expanding a paper into self-contained lecture notes for undergraduates:

Required layers (beyond the paper)

1. Prerequisites section: dim(Hom), rank-nullity, bracket computation quick-reference, source/width definitions, Dynkin diagram basics.
2. Discovery boxes: "Why did the author think of this step?"
3. Strategy boxes: "What's the current plan?"
4. Pitfall boxes: "Common misunderstanding: ..."
5. Worked examples: Pick a concrete small n (e.g., n=5) and trace every step through it.
6. Visual definitions: Source space, diagonal, target space, channel, cross-endpoint — define all five compression dimensions explicitly.
7. Reading recommendations: Three-pass reading guide.

Pitfall: verify ALL factual claims

The lecture notes may contain "background knowledge" that the paper doesn't depend on. Verify these independently. Example: a claim that dim Der(N_n) = 2n-1 is WRONG for strictly upper triangular N_n; the correct formula is n(n-1)/2 + 2n - 3.

Tools for lecture notes

Use these environments:

\newenvironment{pitfall}
  {\medskip\hrule\medskip\noindent\textbf{⚠ 常见误解：}\par\medskip}
  {\medskip\hrule\medskip}

\newenvironment{discovery}
  {\medskip\hrule\medskip\noindent\textbf{🔍 为什么想到这一步？}\par\medskip}
  {\medskip\hrule\medskip}

\newenvironment{strategy}
  {\medskip\hrule\medskip\noindent\textbf{📋 当前策略：}\par\medskip}
  {\medskip\hrule\medskip}

\newcommand{\motivation}[1]{\medskip\noindent\textbf{💡 思路：} #1\medskip}

---

Three-Tier Output Architecture

For this user's projects, three versions are typically produced:

paper-cn/           Journal Version   投稿版  Frozen, submission-ready
paper-cn-detailed/  Teaching Version  教学版  Three-layer navigation
paper-cn-lecture/   Lecture Notes     讲义版  Self-contained for undergrads

All share identical mathematics; differ only in narrative depth.

---

---

XIII. Formatting Requirements — Chinese Math Journals

Research conducted 2026-07-11. Methodology documented in references/research-methodology.md. Sources: 数学年刊A辑 征稿简则, GB/T 7713.2-2022, 中国科学:数学 LaTeX template, Zhihu 数学符号规范, general conventions.

Punctuation: Use English "." (Critical)

Chinese math papers should use English (half-width) punctuation to avoid the Chinese period "。" being confused with subscript "₀" (e.g., E₀, φ₀, x₀). This is a widely recognized convention in Chinese mathematical writing.

Punctuation	Use	Avoid
Period	.	。 (confusable with subscript 0)
Comma	,	，
Colon	:	：
Semicolon	;	；
Parentheses	()	（）

Note: Some Chinese math journals DO use Chinese punctuation. When targeting a specific journal, check their requirements. For self-translation without a target journal, English punctuation is the safer default.

Spacing: Chinese ↔ English

Insert a space between Chinese characters and English/math inline elements:

Correct	Wrong
设 $F$ 为特征不为 $2,3$ 的域	设$F$为特征不为$2,3$的域

Journal-Specific Requirements

数学学报 (Acta Mathematica Sinica, Chinese Series)

Requirement	Detail
Abstract	50–200 characters, self-contained (independently readable)
Keywords	3–5 keywords
Classification	MR (2020) Subject Classification
Running head	≤25 Chinese characters (书眉)
References	All in English, alphabetically by author surname
Section headings	黑体 (bold), with size hierarchy for main/sub
Source format	Not specified publicly; likely CCT or LaTeX

Key difference from 数学年刊: references must be in English (even for Chinese papers) and alphabetically ordered, not sequentially numbered.

数学年刊 A辑 (Chinese Annals of Mathematics, Series A)

Requirement	Detail
Paper size	A4
Line spacing	Double (两倍行距)
Source format	CCT (not standard LaTeX; ctexart for drafting)
Chinese abstract	≤200 characters
Keywords	3–8 keywords
Classification	MR (2020) + 中图分类号
English metadata	English title, abstract, keywords required alongside Chinese
Author names	姓在前，名在后 (surname first)
References	Sequential numbering, specific Chinese format
Template	Available for download from 数学年刊 website (login required)

中国科学:数学 (Scientia Sinica Mathematica)

Requirement	Detail
Document class	SCIA2023cn (custom, not ctexart)
Chinese abstract	100–200 characters
English abstract	100–200 words
Keywords	3–8, Chinese: \quad separated; English: comma separated
MSC	Both Chinese \MSC{} and English \enMSC{} required
Reference style	Author surname alphabetical, \cite{} inline, \upcite{} superscript
DOI	Recommended for each reference
Formula	Use align environment (preferred); avoid equation/eqnarray
Theorem style	Custom blue bold heiti (黑体), 5号 font
Theorem environments	定理/定义/引理/推论/命题/猜想/注/例/问题/假设/条件/性质
Figure caption	\cnenfigcaption{中文}{英文}
Table caption	\cnentablecaption{中文}{英文}
Title format	\title{短标题}{完整标题} + \entitle{English short}{English full}
Author format	\author[n]{姓名}{邮箱}{标记} + \enauthor[]{English name}{}
Address format	\address[n.]{地址, 城市 邮编}
Funding	\Foundation{基金名称(批准号: XXX)}
Acknowledgments	\Acknowledgements{...}
Appendix	\begin{appendix}...\end{appendix}
English title page	\makeentitle auto-generates
Template source	GitHub: goblinunde/LaTex-Resource

CCT vs ctex

CCT (Chinese TeX) is a specialized format used by some older Chinese math journals. It is NOT the same as ctex. For drafting, use ctexart. For final submission to CCT-requiring journals, conversion would be needed.

GB/T 7713.2-2022 — Key Provisions for Math Papers

Extracted from the full standard text (2026-07-11).

Formula Formatting (§5.7)

Provision	Detail
Formula display	Important formulas (with equation numbers) should be centered on their own line
Formula punctuation	Allowed: "居中排数学式的结尾，允许按其在行文中的语法关系添加标点符号"
Line breaking	Break at =, ≈, ≠, >, <, ≥, ≤ or +, −, ×, / operators; don't repeat operator on next line
Variable font	Variables in italic, constants and operators in upright (per GB/T 3102.11)
Inline vs display	Short formulas inline; numbered/large formulas displayed

Typography (Appendix B)

Element	Font Size	Font Family
Chinese title	小2号 (≈18pt)	黑体 (Hei/bold)
Author names	小4号 (≈12pt)	楷体 (Kai)
Abstract, keywords	小5号 (≈9pt)	仿宋 (Fangsong) for content
Section heading	小4号 (≈12pt)	黑体
Subsection heading	5号 (≈10.5pt)	黑体
Body text	5号 (≈10.5pt)	宋体 (Song)
Figure/table captions	小5号 (≈9pt)	黑体
References	小5号 (≈9pt)	宋体

Abstract (§4.2.3)

Type	Recommended length
报道性 (informative)	~400 characters
报道/指示性 (mixed)	~300 characters
指示性 (indicative)	~150 characters

Other Provisions

Provision	Detail
Title length	≤25 characters (§4.2.1)
Keywords	3–8 per paper (§4.2.4)
Section numbering	Arabic numerals, ≤4 levels, dot-separated (§5.2.2)
Reference style	Sequential or author-year, consistent throughout (§4.3.6)
Paper size	A4 recommended (§5.1)
Page numbering	Continuous Arabic numerals (§5.8)

Implications for ctexart Setup

The GB standard's body text size (5号 ≈ 10.5pt) differs from typical Western math paper conventions (10–12pt). For ctexart:

\documentclass[5hao,a4paper]{ctexart}  % 5号 = ~10.5pt body text
% Or explicitly:
\documentclass[10.5pt,a4paper]{ctexart}
\setmainfont{Times New Roman}  % Western text
% ctex handles Chinese font (宋体 for body, 黑体 for headings) automatically

Section & Theorem Naming (Standard)

English	Chinese
Theorem	定理
Lemma	引理
Corollary	推论
Proposition	命题
Definition	定义
Remark	注
Proof	证明
Abstract	摘要
Introduction	引言
Preliminaries	预备知识
References	参考文献

Remaining Research Items

See also references/writing-style-comparison.md for quantitative and qualitative comparison of writing style across reference papers (Ou, KK, Ghimire-Huang, Yusupov) and our paper v3.

#	Topic	Priority	Status
1	应用数学学报 requirements	Low	Not yet searched
2	CCT format specifications	Low	数学年刊 only

---

XIV. Language Style — Chinese Math Prose

English paper writing conventions: see references/paper-writing-conventions.md for a 10-point checklist distilled from comparing our paper against Ou (2007), KK (2023), Ghimire-Huang (2016), and Yusupov et al. (2025). These apply to the English source before translation.

English Paper Style Reference

Before translating, consult references/english-paper-style-audit.md for a quantitative comparison of writing styles across Ou-Wang-Yao (2007), KK (2023), Ghimire-Huang (2016), and Yusupov et al. (2025). Key findings:

• "thus" density in our paper is 5× higher than all reference papers.
• Ou uses informal language ("get", "see", "easy to check") extensively.
• All reference papers avoid coined technique names, "source"/"target", and proof-method descriptions in abstracts.
• Named classification categories for derivations are standard (Ou does it too).

Standard Sentence Patterns

Pattern	Usage	Example
设...则...	Let...Then...	设 $F$ 为域, 则...
由...可得	From...we obtain	由引理3.1可得...
故	Thus	故 $a=0$.
即	i.e.	即 $\varphi$ 是中心化的.
记...为...	Denote...by...	记 $N(n,F)$ 为严格上三角矩阵.
下证...	We now prove...	下证 $\dim\Delta=n+5$.
证毕	QED	Auto-generated by \proof
同理	Similarly	同理可证...
不妨设	WLOG	不妨设 $n\ge5$.
反之	Conversely	反之, 若...
对任意...	For all...	对任意 $i<j$...
存在...	There exists...	存在 $s\in F$...
若...则...	If...then...	若 $u=1$, 则...

Words to Avoid or Use Sparingly

Word	Note
显然	"Obviously" — only for genuinely trivial facts
易证	Avoid in formal papers
值得注意的是	Delete — all facts have equal weight

Style Principles

1. Short sentences: Single-idea sentences preferred
2. Formula density: Prefer formulas over prose
3. Impersonal tone: Limit "我们"; prefer declarative
4. No narrative: State facts, don't describe discovery
5. Consistent connectors: Use same transitions throughout

English → Chinese Translation Map

English Pattern	Chinese Pattern
"We prove that..."	"下证..."
"It follows that..."	"由此可得..."
"By Lemma X, ..."	"由引理X, ..."
"Applying ... gives"	"将...作用于...得"
"Since ... we have"	"因...故..."
"Thus / So"	"故"

Reference Files

• references/reference-verification.md — Reference verification checklist: arXiv → published version, page numbers, issue numbers, orphan bibitems.
• references/ctex-pitfalls.md — ctex排版陷阱: 楷体加粗AutoFakeBold, 节编号空格, 页眉显示, 字体共存.
• references/pandoc-conversion.md — Pandoc LaTeX→Word 转换: 合并\input文件, 清理ctex命令, OMML公式保留.
• references/docx-format-extraction.md — Extracting formatting parameters from a .docx reference file using python-docx, and translating them to ctexart LaTeX preamble. Includes ctexset configuration, theorem style customization, and common pitfalls.
• references/english-paper-style.md — English mathematical paper writing conventions: what a research paper should and should not contain, derived from comparison with Kaygorodov-Khrypchenko, Ghimire-Huang, Yusupov et al., and Ou-Wang-Yao. Use when reviewing or writing an English math paper for style compliance.
• references/ou-kk-style-alignment.md — Concrete fix guide for 6 common Ou/KK style violations: explanatory parentheticals, roadmap paragraphs, flat case labeling, proof-structure meta-language, global condition declarations, and construction-section labels. Includes detection regex and before/after examples.

Absorbed Skills

See references/absorbed-skills.md for the full historical record of skills consolidated into this umbrella.

CRITICAL: read_file / write_file Line-Number Pitfall

When copying content from read_file output into write_file, you MUST strip the line-number prefixes. read_file returns lines formatted as LINE|CONTENT; if you pass this verbatim to write_file, the literal characters 1|, 2|, etc. become visible in the compiled PDF (rendered as spurious | characters throughout).

Correct workflow:

1. Read the source with read_file to understand the content.
2. Compose the translation in your head/scratchpad — do NOT copy-paste read_file output directly into write_file.
3. Pass the clean (no prefix) content to write_file.
4. After writing, compile and verify that no artifacts appear:
   • Compile with tectonic
   • Check PDF spans for | characters (use fitz to search spans)
   • If found, strip with: re.sub(r'^\d+\|', '', content, flags=re.MULTILINE)

Detection query (run after compilation):

import fitz
doc = fitz.open("main.pdf")
found = sum(1 for page in doc for b in page.get_text("dict")["blocks"]
            if "lines" in b for line in b["lines"]
            for span in line["spans"] if '|' in span["text"])
# found MUST be 0

Reference: English Math Paper Writing Style

When writing or auditing an English mathematical paper (especially a classification paper in the style of Kaygorodov--Khrypchenko), load references/math-paper-writing-style.md for conventions on terminology, condition declarations, and tutorial-voice detection.

Writing Style: No Self-Coined Terms

Before translating, audit the English paper for self-coined terminology. See references/debranding-methodology.md for the full methodology.

Quick rule: If KK and Ou don't name it, neither should we. Replace named techniques with equation/lemma numbers, index metaphors with direct math notation, and capitalized observations with plain paragraph text.

Translation Cross-Check Methodology

After translating all sections, run these checks (order matters):

Lean ↔ Paper audit — after every round of paper edits, verify ALL mathematical claims against the Lean formalization. Full workflow at references/lean-paper-audit.md: extract Lean theorem signatures, build a paper-claim-to-Lean-theorem mapping table, verify condition alignment (char≠2, char≠3, n≥5), and confirm 0 sorries.

0. Full automated check (preferred)

Run scripts/compliance-check.py — a single Python script covering all checks below (label parity, ref count, cite parity, punctuation, forbidden words, spacing). See scripts/compliance-check.py for usage.

1. Label parity

diff <(grep -oh '\\\\label{[^}]*}' en/*.tex | sort) \
     <(grep -oh '\\\\label{[^}]*}' zh/*.tex | sort)

All labels must match exactly. Ignore comment-line references (% ... \\ref{...}).

PITFALL — \ref count differs by 1? Check for comment-line \ref before concluding there's a missing reference. English source files often have section separator comments like % --- Main proof of Lemma~\ref{lem:X} --- that the Chinese version may lack. These don't appear in either PDF. Audit visible (non-comment) refs only via scripts/compliance-check.py or manual inspection.

2. Reference count parity

grep -oh '\\eqref{[^}]*}\\|\\ref{[^}]*}' zh/*.tex | sort | uniq -c

Compare counts against English version. Every \ref{lem:imageinI} etc. must appear the same number of times.

3. Cite parity

grep -oh '\\cite{[^}]*}' zh/*.tex | sort

4. Punctuation replacement

Chinese punctuation MUST be replaced with English equivalents: 。→. ，→, ：→: ；→; （→( ）→) Do this OUTSIDE math mode only — split on $, replace in odd-indexed segments.

segments = content.split('$')
for i in range(0, len(segments), 2):
    for cn, en in replacements.items():
        segments[i] = segments[i].replace(cn, en)

5. Forbidden word scan

grep -n '得到' zh-*.tex   # NEVER in body (§2+)
grep -n '迫使' zh-*.tex   # NEVER
grep -n '本文' zh-sec2.tex zh-*.tex  # NEVER in body

6. Impersonal tone

grep -n '我们' zh-*.tex — at most 0–1 occurrences. Replace with declarative.

7. First-occurrence English annotation

Key coined terms need parenthetical English on first use: 中心化的 (centered). Standard terms (平凡导子, 换位子, 李代数) do not.

8. CJK ↔ math spacing

Chinese characters must be separated from $...$ by a space: 设 $F$ 为域 ✓ — 设$F$为域 ✗. Check both directions: [\u4e00-\u9fff]\$ (CJK touching $) and \$[\u4e00-\u9fff] ($ touching CJK).

Plan-Driven Translation: Regenerate When Source Changes

When the English paper has been revised after the translation plan was written, discard the old plan and regenerate from the current source. An outdated plan is worse than no plan — it references deleted sections, stale terminology, and incorrect line counts. The 2026-07-12 translation required a complete rewrite because 5 rounds of compression had reduced the source from ~792 to 610 lines and restructured multiple sections.

Reference: Avoid Coined Technique Names

When writing or translating a classification-style math paper (KK/Ou/Filippov tradition), do not coin formal names for proof techniques. Use lemma/equation numbers instead. See references/avoid-coined-terms.md for the full analysis with evidence from KK (2305.00727).

LaTeX → Word Conversion

For converting ctex-based Chinese math papers to Word format, see references/latex-to-word-pandoc.md for the full workflow. Key pitfalls:

• ctex commands (\songti, \heiti, \kaishu, \zihao) break pandoc
• \input sub-files must be manually resolved first
• Math survives as OMML (invisible to .text but rendered by Word)

Word Format Extraction

When extracting format specifications from a .docx reference template, see references/docx-format-extraction.md for the python-docx + XML methodology. Covers page setup, font/size/bold per run, paragraph indentation, line spacing, and Normal style baseline.

ctex Formatting Tips

楷体加粗

\kaishu\bfseries does NOT produce visible bold in default ctex — 楷体 lacks a real bold variant. Enable fake bold:

\setCJKfamilyfont{kaishu}{KaiTi}[AutoFakeBold={2.5}]

节编号紧贴标题

\ctexset{
  section = {
    name = {},
    number = \arabic{section},
    format = \heiti\zihao{4}\bfseries\raggedright,
    aftername = \hspace{0pt},
    beforeskip = 15.6pt plus .3pt minus .3pt,
    afterskip = 7.8pt plus .1pt minus .1pt,
  }
}

Produces "1预备知识" format (number directly attached, no space/period).

参考文献标题不加粗

ctex 的 \section* 继承节格式。若参考文献标题需黑体不加粗，临时覆盖：

\begingroup
\ctexset{section/format=\heiti\zihao{5}}
\input{zh-refs}
\endgroup

Preliminaries: Docx-Style Restructuring

When matching a .docx reference template that uses no subsections, restructure the preliminaries (zh-prelim.tex) as follows:

1. Remove all \subsection headings. Docx-style theses typically flow as continuous prose with definitions and lemmas inline.

2. Convert the "notation" subsection to a series of \begin{definition} blocks for key concepts (ideal I, coordinate projection, etc.). Keep lighter notation (matrix units, bracket formula) as flowing prose before the first definition.

3. Keep lemmas and their proofs as \begin{lemma}...\end{lemma} blocks. They become natural paragraph breaks in the continuous flow.

4. Move "centered decomposition" into a \begin{definition} rather than a standalone prose paragraph — it's a concept definition, aligning with the docx convention of 定义1.X.

Resulting structure: prose → 定义1.1 → equation → 引理1.2 + proof → 引理1.3

• proof → 定义1.2 → 引理1.4 + proof. No subsection titles, continuous flow.

Pitfall: Explanatory Parentheticals

Ou (2007) and KK (2023) use ZERO parentheticals that explain proof steps. Parentheticals like (using $d_3=d_1$ from above), (only the bracket-right term contributes, via...), or (trivially if $u>i$, by Lemma~3.1) are not present in either reference. When auditing, note:

• Automated regex scans are insufficient. Parentheticals span line breaks, use diverse keywords (trivially, by, applied to, component ... cancels), and hide in nested case analyses. A regex scan will find ~60% at best.
• Manual line-by-line re-read of every proof is required after the automated pass. Read each parenthetical and ask: "Would Ou write this explanation here?" If the answer is "no, he'd just state the result", delete it.
• Check \operatorname{char}F\neq3$ parentheticals too. These are condition reminders that serve the same explanatory function.

See references/blind-review-audit.md for the full comparison methodology against Ou and KK, including case-label nesting depth, roadmap paragraphs, and pattern-language detection.

Reference: Blind-Review Style Audit

When checking whether a paper reads like it belongs to the Ou/KK tradition, audit these dimensions (methodology in references/blind-review-audit.md, detailed fix examples and detection code in references/ou-kk-style-alignment.md):

1. Roadmap paragraphs — Ou has none. KK has ≤1 sentence. Any colon-enumerated "In Section 1 we... Section 2 constructs..." is a tell.
2. Case-label nesting depth — Ou uses at most (1)(2)(3). Three-level nesting (Case → condition → (i)(ii)(iii)) with bold labels and \smallskip reads like lecture notes.
3. Explanatory parentheticals — Ou/KK have 0. Any (using/via/trivially/by Lemma/applied to) parenthetical in a proof is a tell.
4. Global hypothesis re-declaration — "In what follows we work under the hypotheses of Theorem X. Thus char F≠2,3 and n≥5 throughout." Ou states conditions in the theorem and never repeats them.
5. Pattern language — "The same three-equation pattern as for u=1 applies" is meta-commentary on proof structure. Ou/KK never abstract proof steps into named patterns.

Current Paper State (2026-07-12)

The canonical English paper is at /workspace/paper-v3/:

• ~508 lines, 5 pages, 0 errors, 66 KB PDF
• elsarticle 3p, Times (newtx), tolerance=500
• All 8 theorems verified against Lean (0 sorries)
• 0 explanatory parentheticals, 0 coined terms, 0 metalanguage, 0 roadmap
• §2 labels use (A)(B)(C) format matching Ou (2007)
• References: 5 entries, all verified (KK→Port. Math. 2024, Filippov+no.6, orphan lean removed)

Chinese translation: /workspace/paper-zh/

• ~492 lines, 6 pages, 0 errors, 198 KB PDF, ctexart 12pt
• Subsection headings left-aligned via \ctexset
• Lemma 3.1 (Claim) and Lemma 3.2 (im⊆I) reordered: Claim + proof first, then im⊆I + proof
• All $1/2$ replaced with $\frac{1}{2}$

Formatted Chinese version: /workspace/paper-zh-formatted/

• ctexart 10.5pt (五号), 2cm margins, single spacing, 8 pages
• Format extracted from docx template: FORMAT-SPEC.md
• Includes Chinese+English title pages and abstracts
• 楷体 fake bold: AutoFakeBold={2.5}
• Pandoc-generated Word: paper.docx (22KB, 422 OMML formulas)

Lean formalization: /opt/lean-home/lean-projects/e/E/Classification/ (11 files, 0 sorries) Reference papers: /workspace/参考论文/ (Ou 2007, KK 2023)

Full debranding audit trail

See references/debranding-audit.md for Round 1 (named techniques) and Round 2 (index metaphors). See references/debranding-audit-r3.md for Round 3 (parentheticals, metalanguage, case labels, roadmap, reference format). See references/reference-verification.md for reference bibliography verification.

• 0 self-coined technique names (chain bridge → \eqref)
• 0 roadmap paragraph
• 0 nested bold case labels (flattened to If/If/If)
• 0 proof-structure metalanguage
• Global hypothesis: factual one-liner
• Chinese translation: /workspace/paper-zh/, ~492 lines, 6 pages, 197.6 KB PDF
  • All style fixes synced to Chinese
  • 0 forbidden words, 0 Chinese punctuation, 0 CJK↔$ spacing issues
• Translation plan: /workspace/paper-zh/TRANSLATION-PLAN.md

Pre-translation Compression Workflow (5 rounds, 741→610 lines)

When preparing an English paper for translation, compress it first. Methodology:

1. Benchmark: compare against reference papers (Ou 2007, KK 2023) for density. Count words per page, display equations, and proof structure.
2. Identify: find display-math-for-single-equations, signpost sentences ("First, we prove..."), redundant restatements, and explanatory prose that readers can fill in themselves.
3. Verify: every compression must be cross-checked against Lean formalization to ensure no mathematical content is lost.
4. Iterate: multiple passes, each targeting a specific class of bloat (display→inline, signposts, bracket-expansion, construction verification).
5. Check: re-measure page count, PDF size, and line count after each round.

Full methodology and audit trail in references/compression-methodology.md.

Translation Plan

The canonical translation plan for paper-v3 → paper-zh: /workspace/paper-zh/TRANSLATION-PLAN.md

This plan includes:

• Corrected terminology table (all deleted terms removed)
• Section-by-section translation strategies aligned with current 610-line paper
• Lemma numbering verified against actual LaTeX \label/\ref structure
• ctexart preamble template

Reference: Lean ↔ Paper Condition Audit

Before finalizing, verify that every lemma's conditions match the Lean formalization. See references/condition-audit-methodology.md for the full workflow: detect missing conditions, choose between per-lemma conditions and global declarations, and verify post-fix.