Mathematical Modeling LaTeX Projects

Use this skill to create reproducible LaTeX paper projects for MCM/ICM, CUMCM and MathorCup. Use the matching bundled template for MCM/ICM or CUMCM; build the MathorCup project from the verified competition profile and approved paper blueprint. Keep dependencies explicit and avoid embedding real identity information.

Contest-Orchestrator Adapter

在 contest-orchestrator 中，本技能只负责中文竞赛论文的模板、排版、编译和结构预检。输入是项目工作区中的论文入口、已冻结模型/结果/引用、appendix_plan.yaml、AI 工具说明要求和交付约束；不得生成不存在的数字、公式、符号、引用、图表或结论。

• 保护公式、符号、单位、数字、引用键、图表编号、模型逻辑和附录证据；新符号定义缺失时回流，不在排版层猜测。
• 输出节点包包含 status、active_mode、task_card、artifacts、evidence、checks、blockers、next_node，所有生成文件只写项目工作区。
• Formal figure insertion format is SVG（图表正式插入格式为 SVG）；正文使用 \\includesvg{figures/<figure_id>}。PNG 仅作预览和兼容性副本，不使用图片 PDF；论文最终交付 PDF 仍按竞赛要求生成。
• 默认只做文本层、结构、引用、编译和交付约束检查；不截图、不渲染复核，视觉检查由用户肉眼完成，除非用户明确要求。
• 论文、附录和报告不得出现元话语、内部交流、评审记录、调试、失败、旧版本或其他负回响；AI 工具说明按竞赛规则单独生成，不把内部过程写入正文。
• active_mode: full-contest-mathorcup 时，只采用当前项目 competition_profile.yaml 中有官方依据的版式、页数、文件大小、附录、匿名和 AI 说明要求。根据已批准 paper_argument_blueprint.yaml 建立中文 ctexart 工程；不得复制国赛专用扉页、声明、页数口径、附录清单或身份字段。M4 在批准的写作蓝图范围内排版当前批次初稿与接图稿，不要求逐章批准。writer_first_batches 初稿可用内部文字图位占位，不能引用不存在的 SVG；用户确认需求、选定图件后才接入正式图，完整批次须清除占位并核对选定资产。M5 在最终源文件上检查文本层、引用、编译、匿名及官方交付约束。若官方格式未核实，保持待确认，不以国赛默认值代替。

Competition Recognition

• Treat prompts mentioning MCM, ICM, COMAP, Meritorious/Winner papers, team control number, problem A-F, or "Report on Use of AI" as MCM/ICM.
• Treat prompts mentioning CUMCM, National Undergraduate Mathematical Contest in Modeling, 国赛, 全国大学生数学建模竞赛, 承诺书, 编号专用页, 支撑材料, or 中文摘要 as CUMCM.
• Treat active_mode: full-contest-mathorcup or an explicit MathorCup 大数据竞赛 profile as MathorCup, even when the paper is in Chinese.
• If the contest is unclear, infer from language and required fields: English + team control number usually means MCM/ICM; do not infer CUMCM from Chinese language alone.
• If official rules for the current year are provided, follow them over these defaults.

Reference Mode

• Decide use_ref_bib before generating or editing a project.
• Default to use_ref_bib = true for newly generated projects because this skill ships ref.bib and competition papers benefit from citation-key based reference management. The bundled templates use ref.bib directly and do not include an active inline thebibliography fallback. Use inline thebibliography only when the user explicitly asks not to use BibTeX or the local environment lacks BibTeX, and generate that as a separate edit rather than mixing both modes.
• Set use_ref_bib = true when the user asks for ref.bib, BibTeX, citation-key based references, Zotero/JabRef/BibDesk exports, or a reusable bibliography database.
• When use_ref_bib = true, keep ref.bib beside main.tex, cite entries with \cite{...}, and let latexmk run BibTeX automatically. For CUMCM, prefer gbt7714 with gbt7714-numerical and \citestyle{numbers} so references render as numeric entries instead of author-year labels. Replace the sample placeholder-ref entry before final submission. Do not use \nocite{...} unless the user explicitly wants uncited sources listed.
• Do not mix active thebibliography and active \bibliography{ref} in the same generated paper.
• Separate literature citations from cross references: use \cite{bib-key} only for literature/software/data sources in ref.bib; use \label{...} plus \ref{...} or \eqref{...} only for figures, tables, equations, algorithms, appendices, or sections.
• Avoid gratuitous placeholder cross references. Add \ref only when the referenced \label exists and the sentence genuinely needs a numbered table/figure/equation. Keep hypertexnames=false in CUMCM templates to avoid duplicate PDF anchors when counters reset in appendices.
• Before delivering a project, run python scripts/check_latex_refs.py main.tex --bib ref.bib when ref.bib mode is active, and fix all missing labels or missing citation keys.

Figure Insertion Contract

MathorCup 图件接入使用现有 figure_registry 中的资产 ID、正文 label/序号、选定版本、画布/插入尺寸、实际论文副本与源文件引用，遵循 contest-orchestrator/references/mathorcup_execution_protocol.md。默认只同步受影响图件并编译；恢复正文后重新核对副本，不能因 PDF 仍可打开就认为新图已接入。保留一份权威正文源，通过入口开关生成含附录／无附录版本，不维护两份独立正文；两种提交版本分别检查本届格式与源码新鲜度。论文接入检查不替代图件 QA，也不重复已批准未变图件的完整 QA。

• Load the svg package in every bundled paper template and use \\includesvg{figures/<figure_id>} for formal figure insertion.
• Treat the SVG as the authoritative figure asset. Keep the matching PNG beside it for preview and visual QA; do not register or deliver an image PDF, EPS, TIFF, or JPEG.
• Before compilation, verify that the SVG exists, is non-empty, has the expected figure identifier, and is paired with the registered PNG. Preserve the editable source and the source-to-figure mapping in the project workspace.
• Compile with shell escape when the local svg package requires conversion support, for example latexmk -xelatex -shell-escape main.tex for CUMCM or latexmk -pdf -shell-escape main.tex for MCM/ICM. Use only local tools; if SVG conversion is unavailable, block compilation instead of silently replacing the figure with a PDF image.
• This contract applies to figure assets only. The compiled paper PDF remains the formal paper deliverable.

Page-layout contract for figures

For the bundled CUMCM templates, the figure generator decides the visual encoding and canvas shape; this skill decides how the finished SVG occupies the paper page. Record one layout_mode in the orchestrator figure registry and use the matching macro:

Use minipage for stable two-column blocks and adjustbox for width/height bounds in CUMCM. MCM/ICM keeps the same SVG/PNG asset contract but uses its own template primitives. Do not use [H], raw \includegraphics, or an image PDF. Page placement remains a source-level check; visual rendering is off by default unless the user explicitly requests it.

Reader-evidence placement

排版层只执行已批准的视觉论证与 figure_registry.layout_mode，不自行增加图表或改变 SciPilot 的表示语义。每个 figure 必须在源文中有前置引导语和后置解释语；table 与 text 按登记的读者职责落位。优先使用 single、side_by_side、wrap_short、tall_constrained 四种受控入口：短图或短表可与解释文字并排，长图限制最大高度并保持宽高比，信息密度不足的图不通过缩放或留白补足。禁止用连续浮动体、强制 [H]、手工 \vspace 或重复图表制造页数；发生溢出时调整受控布局入口、尺寸或论证落位，并保留 SVG 正式资产与 PNG 预览副本。

MathorCup Generation Rules

For active_mode: full-contest-mathorcup, select ctexart and XeLaTeX as the neutral Chinese implementation, then set title page, abstract, section order, bibliography, appendices and disclosure from the approved paper blueprint and verified competition_profile.yaml. Do not copy a CUMCM template into a MathorCup project. Keep ref.bib only for genuine cited sources and run scripts/check_latex_refs.py when using it. Compile with latexmk -xelatex -shell-escape main.tex when the SVG package needs local conversion; if the renderer is unavailable, report compilation as incomplete. Use scripts/check_pdf.py with official page/size flags only when those limits are recorded in the project profile. Preserve SVG+PNG figure assets, the text-layer paper PDF and editable source; do not create image PDFs.

MCM/ICM Generation Rules

• Start from templates/mcm-icm/main.tex.
• Use the official LaTeX package class when available:

\documentclass{mcmthesis}

• Treat mcmthesis as a formal LaTeX package normally managed by TeX Live or MiKTeX. Do not copy mcmthesis.cls into the project by default.
• Include placeholders for team control number, problem letter, title, summary, keywords, model sections, references, appendices, and Report on Use of AI.
• Support use_ref_bib with templates/mcm-icm/ref.bib; the bundled template uses BibTeX directly.
• Include a table of contents after \maketitle for MCM/ICM by default, matching the mcmthesis demo pattern. Remove it only if the current official rules or user request say not to include it.
• Keep all identity fields generic. Use placeholders such as 0000000, A, and Paper Title Placeholder.
• Do not add school names, author names, adviser names, regions, email addresses, phone numbers, or acknowledgements that reveal the team.

CUMCM Generation Rules

• Prefer templates/cumcm/main-cumcmthesis.tex when cumcmthesis.cls is available:

\documentclass[withoutpreface,bwprint]{cumcmthesis}

• This skill includes a lightweight templates/cumcm/cumcmthesis.cls compatibility class so the default CUMCM entry can compile offline. Treat it as a portable compatibility layer, not as a guarantee of official current-year formatting. Do not assume third-party cumcmthesis variants can be installed with tlmgr.
• Also provide templates/cumcm/main.tex for the default cumcmthesis-compatible entry point and templates/cumcm/main-ctexart-fallback.tex as a no-class fallback.
• Use XeLaTeX for all Chinese templates.
• Default to electronic version options withoutpreface,bwprint.
• Include a dedicated abstract page, keywords, body sections, references, appendices, and a supporting-material file list. For CUMCM 2026, place the AI declaration before the references and put AI工具使用详情.pdf in the supporting-material package.
• For CUMCM 2026 electronic submission, use a text-layer PDF, omit the table of contents. Body page count starts from the main body (abstract NOT included), covering main body, AI-use declaration before references, and references, at most 30 pages; appendix is outside the 30-page body limit. Total submission PDF (abstract + body + references + appendix) hard cap is 51 pages, recommended range 35–51 pages. Keep the PDF at or below 20 MB.
• The declaration and detail must be truthful and concise about actual use, and explicit about human verification and team ownership of core modeling and analysis.
• Support use_ref_bib with templates/cumcm/ref.bib; the bundled template uses BibTeX directly.
• Do not generate a table of contents in CUMCM electronic submissions by default. Keep only commented optional \tableofcontents lines for years or local rules that explicitly require it.
• For the user's Hunan regional workflow, submit PDF rather than Word; total submission PDF hard cap is 51 pages (recommended 35–51 pages), not a local 50-page recommendation.
• Do not generate school, team member, adviser, instructor, campus, province, or regional identity information. Leave identity-related class commands absent or blank unless the user explicitly supplies non-sensitive placeholders required by official rules.

CUMCM Extras Macros (cumcm-extras.sty)

国赛模板默认加载 templates/cumcm/cumcm-extras.sty，提供建模论文常用快捷命令。不用可在 main.tex 中注释掉 \usepackage{cumcm-extras}。

• 数学符号：\mat{A}（矩阵粗体正体）、\vb{x}（向量粗体斜体）、\trans（转置上标）、\R（实数集）、\argmin/\argmax（自动下标）、\Var/\Cov、\upcite{key}（上标引用）
• 定理环境：definition、theorem、lemma、corollary、assumption、remark、property、example 等 13 种，中文，按 section 编号
• 算法伪代码：algorithm + algorithmic 环境，中文关键字自动汉化（输入、输出、当、则、遍历、返回等）
• 智能引用：\cref{fig:1} 输出"图1"，\cref{tab:1,eq:2} 输出"表1和式(2)"，支持 \crefrange
• 表格增强：\topline/\midline/\bottomline 三线表快捷命令，Y（居中 X 列）/J（左对齐 X 列）列类型，longtable 跨页表格
• 插图宏：\PaperFigure、\PaperTwoColumn、\PaperWrapFigure、\PaperTallFigure；正式图片使用 SVG，均保持 [!htbp] 或受控环绕布局（禁止 [H]）
• 脱敏占位：\email{...}/\phone{...} 编译输出 [已脱敏]
• 写作标记：\todo{...}（橙色）、\draftnote{...}（红色），终稿前必须清除
• 浮动参数：与 contest-orchestrator figure_policy.md 一致（topfraction=0.85, textfraction=0.1, topnumber=3），支持 \FloatBarrier 章末防跨章

详细用法见 templates/cumcm/STYLE_GUIDE.md 第 9 节。

CUMCM Excellent-Paper Style Rules

• For CUMCM, follow templates/cumcm/STYLE_GUIDE.md when generating paper structure or examples.
• Use the default section order: 摘要, 问题重述, 问题分析, 模型假设, 符号说明, 数据预处理, 模型建立与求解, 模型检验, 模型评价与推广, 参考文献, 附录.
• Render level-one CUMCM sections as Chinese numerals with a dunhao, such as 一、问题重述; render subsections as 1.1 问题背景.
• Do not create a standalone subsection named 总体思路, 总体模型思路, 整体思路, or similar in CUMCM final-style papers. In excellent-paper style, 问题分析 should normally be organized by subproblem, such as 2.1 问题一的分析, 2.2 问题二的分析, and 2.3 问题三的分析. If a route explanation is needed, write it as a short paragraph inside the relevant analysis section or use a 模型流程图; do not add 2.4 总体思路.
• CUMCM keywords must be mathematical-modeling terms, preferably terms found in mathematical modeling textbooks or common contest papers. Use model/method/algorithm/evaluation terms such as 优化模型, 线性规划, 混合整数规划, 目标规划, 动态规划, 蒙特卡洛模拟, 回归分析, 聚类分析, 主成分分析, 层次分析法, 综合评价, 风险决策, 敏感性分析, 鲁棒性分析, 时间序列, and 灰色预测. Avoid using research objects, industry scenarios, or题目背景词 as keywords, such as 农作物种植策略, 乡村农业, 蔬菜销售, or 交通问题, unless they are paired with a recognized modeling method and the user explicitly requires a domain keyword.
• Before delivering a CUMCM project, run python scripts/check_latex_keywords.py main.tex and revise keywords that fail the modeling-term check.
• Standardize the data section title as 数据预处理. Do not use 数据读取与预处理, 数据剔写, 数据说明与读取, or other ad-hoc titles in final-style CUMCM papers.
• Write model assumptions as a numbered list. Each item must follow the pattern 假设 n：...。解释：... so the assumption and its modeling justification are both visible.
• Do not add non-paper chapters such as 编译测试结果, LaTeX 测试说明, or standalone 算法实现说明 to CUMCM example PDFs. Put run commands, compile notes, and code explanations in README or appendices.
• In the abstract and result sections, never invent numerical results. Use explicit placeholders when no solver output exists.

Reference and Cross-Reference Hygiene

• Use ref.bib for references by default. Keep all bibliographic metadata in ref.bib; do not leave a live thebibliography block in final-style examples.
• Cite data sources, papers, and software with \cite{...} when they are genuine sources used by the paper. For CUMCM 2026, disclose AI tools in the paper declaration and AI工具使用详情.pdf in supporting materials; do not add an AI tool bibliography entry solely to record AI use. If an AI tool is independently used as a software or research source, cite only the specific technical claim it supports.
• Reference figures, tables, formulas, and appendices with \label{...} and \ref{...} / \eqref{...}. The label must exist in the same project.
• Do not cite tables with \cite and do not cite papers with \ref.
• Do not use \nocite{placeholder-ref} in final examples, because it creates references that are not grounded in the text.
• Run scripts/check_latex_refs.py before compiling final deliverables; then compile and ensure the log has no undefined references or Citation ... undefined warnings.

Layout Reference（精细排版速查）

遇到图文混排、复杂表格、彩色框、页面布局、公式间距、子图、算法伪代码等精细排版需求时，读取 references/latex_layout_cheatsheet.md（数学建模论文 LaTeX 精细排版速查表），覆盖15个大类：图文混排（wrapfig/floatrow）、左右并排（minipage/tabular）、复杂表格（booktabs/multirow/tabularx/longtable）、彩色框（tcolorbox/mdframed）、页面布局（geometry/fancyhdr/titlesec）、公式精细调整（amsmath/mathtools/间距/编号）、子图（subcaption）、算法伪代码（algorithm+algpseudocode）、代码高亮（listings/minted）、字体、颜色、图形绘制（tikz/pgfplots）、其他实用包（hyperref/caption/enumitem/siunitx）、常见问题速查、国赛模板已加载的包。每个包给出用途、核心命令、最小示例和注意事项。

Compilation Rules

• Use latexmkrc; it defaults to XeLaTeX.
• Compile according to contest/template:

# MCM/ICM, mcmthesis workflow
latexmk -pdf -shell-escape main.tex

# CUMCM Chinese workflow
latexmk -xelatex -shell-escape main.tex
# or, when this skill's latexmkrc is present in the project directory
latexmk -shell-escape main.tex

• Do not use latexmk -pdf for CUMCM Chinese templates; it forces pdfLaTeX in many latexmk versions and can fail on ctexart/XeLaTeX font handling.
• For MCM/ICM, run scripts/check_latex_env.py --contest mcm-icm first to verify mcmthesis.cls. If mcmthesis.cls is missing, stop MCM/ICM project generation or compilation and tell the user to install mcmthesis through TeX Live, MiKTeX, or their TeX package manager before retrying.
• For CUMCM, run scripts/check_latex_env.py --contest cumcm first. Prefer the local templates/cumcm/cumcmthesis.cls compatibility class when copied with the project. If no local or TeX-tree cumcmthesis.cls is available, default to templates/cumcm/main-ctexart-fallback.tex; this is a warning, not a failure, as long as the ctexart fallback is available.
• Only when the user explicitly requires a third-party/full cumcmthesis class or strict official-class compatibility beyond the local compatibility class, ask the user to provide that class and verify its license/font requirements/current-year compliance.
• If use_ref_bib = true, add --use-ref-bib to the same contest-specific environment check, for example scripts/check_latex_env.py --contest mcm-icm --use-ref-bib.
• Do not make successful compilation depend on network access. Network downloads are not a valid build step.
• Before the contest, freeze the final compilable template and dependencies together, including allowed class files. Do not bundle font files unless their license clearly permits redistribution and the user intentionally provides them.

Prohibited Behavior

• Do not add third-party .cls files with unclear redistribution rights. The bundled templates/cumcm/cumcmthesis.cls is a lightweight compatibility class; keep third-party class files separate unless the user intentionally provides them and their license permits redistribution.
• Do not invent official year-specific page limits, size limits, AI disclosure rules, or submission rules. Use the current official contest documents when supplied.
• Do not insert real schools, names, student IDs, adviser names, regions, emails, phone numbers, or acknowledgements.
• Do not switch Chinese templates to pdfLaTeX.
• Do not enable ref.bib without also keeping the ref.bib file in the copied project directory.
• Do not depend on online images, online bibliographies, or online package installation during final compilation.
• Do not include a table of contents in the CUMCM fallback electronic template unless the user explicitly requests it.

Checklists

Before writing a project:

• Identify the contest as MCM/ICM, CUMCM or MathorCup from the task's active_mode and verified competition profile.
• Decide whether use_ref_bib is true or false.
• Choose the matching template directory for MCM/ICM or CUMCM; for MathorCup create a neutral ctexart project from the approved blueprint and official profile.
• Run scripts/check_latex_env.py --contest mcm-icm or scripts/check_latex_env.py --contest cumcm for those contests, adding --use-ref-bib when BibTeX is needed. For MathorCup verify local XeLaTeX, ctexart, SVG conversion and bibliography tools directly; do not pass an unsupported contest value to the environment checker.
• Decide whether class dependencies are installed locally or whether a fallback is needed.

Before final submission:

• Compile from a clean directory with the contest-appropriate command: latexmk -pdf -shell-escape main.tex for MCM/ICM, and latexmk -xelatex -shell-escape main.tex for Chinese CUMCM/MathorCup projects when SVG conversion is required.
• Run the structural and text-layer checks for the PDF. Do not perform visual inspection by default; perform visual inspection only when the user requests it. Confirm AI-use and appendix sections in extracted text only when the current contest profile requires them.
• If official page and file-size limits are known, run scripts/check_pdf.py <paper.pdf> --max-pages <official-page-limit> --max-size-mb <official-size-limit-mb>.
• If official limits are not provided, run scripts/check_pdf.py <paper.pdf> without page or size flags, then note that the official current-year limits still need manual confirmation.
• Treat default identity keyword matches from check_pdf.py as warnings that need human review. For the final gate, run scripts/check_pdf.py <paper.pdf> --identity-mode strict, using repeated --ignore-keyword <word> only for reviewed false positives such as institution names in references or data sources.
• Confirm manually that the PDF does not contain real personal, school, adviser, team, email, phone, or regional identity information.
• Confirm all generated figures, tables, code listings, references, and supporting-material filenames match the final paper.

模板复制与编译要点

When copying a bundled template into a new paper project, copy the template-local latexmkrc as well. The CUMCM template-local latexmkrc enforces XeLaTeX and provides a BibTeX fallback; the MCM/ICM template-local latexmkrc only provides the BibTeX fallback so latexmk -pdf -shell-escape main.tex remains the expected workflow.

CUMCM 图表标题与附录格式

• For CUMCM Chinese templates, table and figure captions must omit the colon: use 表 1 主要符号说明 / 图 1 模型流程图, not 表 1: 主要符号说明.
• Appendix section headings must render as 附录A ..., 附录B ..., 附录C .... After \appendix, set \thesection to 附录\mbox{\Alph{section}} and reset the CTeX section style to use number = \thesection so xeCJK does not insert a visual space between 附录 and A.
• Do not simulate appendix or captions manually in text; use LaTeX \section, \caption, \label, and \ref.