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赛题分析、候选建模与选择

Problem Analysis, Candidate Modeling, and Selection

本阶段把题面转化为可核验、可编码的模型方案，不写论文正文、不生成最终 
paper/
。
按需读取 
../_references/math_modeling_norms.md
的“赛题理解与子问题识别”“假设与模型建立”和“题型防错速查”。CUMCM 2026 模式还要读取 
../_references/CUMCM_2026_RULES.md
。
This phase translates the problem statement into a verifiable, codable modeling plan; it does not write the paper body or generate the final 
paper/
.
Read the “Problem Understanding and Subproblem Identification,” “Assumptions and Model Formulation,” and “Problem-Type Error-Prevention Quick Reference” sections of 
../_references/math_modeling_norms.md
as needed. In CUMCM 2026 mode, also read 
../_references/CUMCM_2026_RULES.md
.

产物

Deliverables

创建或更新：
  • reports/ANALYSIS_MODELING_REPORT.md
    ：题意、数据、歧义、假设、模型公式、求解接口和校验方案。
  • reports/MODEL_SELECTION_REPORT.md
    ：关键候选模型、快速实验、独立审查、AI 推荐及人工决定。
CUMCM 2026 同步更新：
  • compliance/AI_USAGE_LOG.md
  • compliance/HUMAN_REVIEW_LOG.md
  • todo.md
Create or update:
  • reports/ANALYSIS_MODELING_REPORT.md
    : problem interpretation, data, ambiguities, assumptions, model formulas, solution interfaces, and validation plan.
  • reports/MODEL_SELECTION_REPORT.md
    : key candidate models, quick experiments, independent review, AI recommendation, and human decision.
Update the following in parallel in CUMCM 2026 mode:
  • compliance/AI_USAGE_LOG.md
  • compliance/HUMAN_REVIEW_LOG.md
  • todo.md

1. 解析题面与附件

1. Parse the Problem Statement and Attachments

只把题面明确编号的顶层问题当作子问题。对每问记录输入、输出、目标或指标、约束、与其他问题的依赖及拟展示的图表。逐个附件核对字段、规模、单位、缺失、异常、重复和可派生指标；不要编造字段或把提交要求当成子问题。
必须先列出会改变建模方向的歧义。每个关键歧义给出至少两种解释，并用题面措辞、单位、极简验算和问题递进关系判断。若某种解释使后续新增条件没有边际作用，返回重新审查。
Treat only explicitly numbered top-level questions in the problem statement as subproblems. For each question, record the inputs, outputs, objective or metrics, constraints, dependencies on other questions, and intended charts. Check each attachment for fields, scale, units, missing values, anomalies, duplicates, and derivable metrics; do not invent fields or treat submission requirements as subproblems.
You must first enumerate ambiguities that would change the modeling direction. For each key ambiguity, provide at least two interpretations and assess them based on the statement’s wording, units, minimal sanity checks, and progression across questions. If an interpretation causes conditions introduced later to have no marginal effect, return for re-review.

CUMCM H1：题意确认

CUMCM H1: Problem Interpretation Confirmation

在 CUMCM 2026 模式下，先把以下内容写入 
ANALYSIS_MODELING_REPORT.md
：
  • 子问题数量、输入、目标与输出；
  • 附件字段和单位；
  • 关键歧义、备选解释和当前推荐解释；
  • 题面尚未解决的风险。
随后在 
HUMAN_REVIEW_LOG.md
写 
STATUS: WAITING_FOR_HUMAN_PROBLEM_CONFIRMATION
并请求参赛队确认或修改。未得到明确确认前不得把推荐解释标为最终口径，也不得进入核心模型锁定。收到确认后如实记录队员修改与 
STATUS: HUMAN_APPROVED
，再继续。
In CUMCM 2026 mode, first write the following into 
ANALYSIS_MODELING_REPORT.md
:
  • Number of subproblems, inputs, objectives, and outputs;
  • Attachment fields and units;
  • Key ambiguities, alternative interpretations, and the currently recommended interpretation;
  • Risks that remain unresolved in the problem statement.
Then write 
STATUS: WAITING_FOR_HUMAN_PROBLEM_CONFIRMATION
in 
HUMAN_REVIEW_LOG.md
and request confirmation or modifications from the team. Until explicit confirmation is received, do not mark the recommended interpretation as final, and do not proceed to core model lock. After confirmation, faithfully record the team’s modifications and 
STATUS: HUMAN_APPROVED
, then continue.

2. 生成候选模型

2. Generate Candidate Models

先根据数据、机制、目标与评价标准选模型，不按算法标签套模。对真正影响得分或结论的模型选择，至少比较：
  • 一个简单、可解释的 baseline；
  • 一个主候选；
  • 一个在假设、模型族或求解路线方面有实质差异的替代方案。
不要机械地为每个小问凑三个名字。若只有一个方案合理，应说明排除其他路线的具体依据。
每个候选记录：适用原因、数学定义、假设、输入输出、约束、优缺点、可解释性、计算成本、主要失败风险以及后续问题的兼容性。算法名称本身不是创新，复杂模型必须说明预期比 baseline 多解决了什么问题。
Select models based on the data, mechanism, objective, and evaluation criteria rather than forcing models to fit algorithm labels. For model choices that materially affect the score or conclusions, compare at least:
  • A simple, interpretable baseline;
  • A primary candidate;
  • An alternative that differs substantively in assumptions, model family, or solution route.
Do not mechanically assign three model names to every minor subproblem. If only one approach is reasonable, explain the specific grounds for excluding the other routes.
For each candidate, record: the reason it applies, mathematical definition, assumptions, inputs and outputs, constraints, advantages and disadvantages, interpretability, computational cost, main failure risks, and compatibility with subsequent questions. An algorithm name is not itself an innovation. For a complex model, explain what additional problem it is expected to solve compared with the baseline.

3. 快速实验、边界与独立审查

3. Quick Experiments, Edge Cases, and Independent Review

用手算、玩具数据、小规模精确解或轻量代码验证候选方案的可行性。至少覆盖与当前问题相关的：
  • 极小与极大输入、零值或空值；
  • 物理极限、单位和数量级；
  • 约束冲突、整数条件与守恒关系；
  • 预测泄漏、过拟合与外推边界；
  • 后续条件是否产生预期的边际作用。
对核心方案做一次与设计过程分离的 reviewer/critic 检查。若环境允许且用户授权独立评审，可使用独立 reviewer；否则以独立检查清单重新审视，但不得把自评写成外部独立结论。Reviewer 只列出偷换题意、漏约束、单位错误、数据泄漏、不可识别参数、多余复杂度、错误检验和过度结论，不替参赛队作最终决定。
在 
MODEL_SELECTION_REPORT.md
使用可追溯的比较表：
markdown
| 候选 | 可行性 | 快速指标/目标 | 计算成本 | 可解释性 | 主要风险 |
| --- | --- | --- | --- | --- | --- |
Validate candidate feasibility through manual calculations, toy data, small-scale exact solutions, or lightweight code. At minimum, cover the following where relevant to the current problem:
  • Minimal and maximal inputs, zero values, or empty values;
  • Physical limits, units, and orders of magnitude;
  • Constraint conflicts, integer conditions, and conservation relationships;
  • Prediction leakage, overfitting, and extrapolation boundaries;
  • Whether subsequent conditions produce the expected marginal effect.
Perform a reviewer/critic check of the core approach that is separate from the design process. If the environment permits it and the user authorizes an independent review, use an independent reviewer; otherwise, re-examine the work using an independent checklist, but do not present a self-review as an external independent conclusion. The reviewer should only identify changes in problem intent, omitted constraints, unit errors, data leakage, unidentifiable parameters, unnecessary complexity, incorrect tests, and overclaiming, and should not make the final decision on behalf of the team.
Use a traceable comparison table in 
MODEL_SELECTION_REPORT.md
:
markdown
| Candidate | Feasibility | Quick Metrics/Objective | Computational Cost | Interpretability | Main Risks |
| --- | --- | --- | --- | --- | --- |

4. 推荐与 CUMCM H2

4. Recommendation and CUMCM H2

Agent 可以基于证据给出推荐，但在 CUMCM 2026 模式下不得把推荐自动改成“最终方案”。在 
MODEL_SELECTION_REPORT.md
分开写：
markdown
undefined
The Agent may provide an evidence-based recommendation, but in CUMCM 2026 mode it must not automatically turn the recommendation into the “final approach.” In 
MODEL_SELECTION_REPORT.md
, write the following separately:
markdown
undefined

AI 推荐

AI Recommendation

推荐方案、依据、不确定性与仍需人工判断的权衡。
Recommended approach, rationale, uncertainties, and trade-offs that still require human judgment.

队员最终决定

Team Final Decision

STATUS: WAITING_FOR_HUMAN_MODEL_DECISION

同时更新 `HUMAN_REVIEW_LOG.md`。等待参赛队明确选择、拒绝或修改后，记录最终方案、队员修改和理由，状态改为 `HUMAN_APPROVED`。未通过 H2 不得向 `3coding-visual` 交付“已锁定方案”。
STATUS: WAITING_FOR_HUMAN_MODEL_DECISION

Also update `HUMAN_REVIEW_LOG.md`. Wait until the team explicitly selects, rejects, or modifies the recommendation; then record the final approach, the team’s modifications and rationale, and change the status to `HUMAN_APPROVED`. Do not hand off a “locked approach” to `3coding-visual` unless H2 is approved.

5. 完成建模报告

5. Complete the Modeling Report

按实际子问题组织 
ANALYSIS_MODELING_REPORT.md
，至少包含：
  1. 总体框架与子问题依赖；
  2. 数据处理方案；
  3. 符号、变量与单位；
  4. 经 H1/H2 确认的假设和模型；
  5. 目标函数、完整约束、输入输出；
  6. 求解步骤、停止条件、复杂度或适用规模；
  7. baseline、边界、反例、灵敏度和结果校验方案；
  8. 代码实现任务清单。
公式必须清楚到代码阶段可以直接实现。报告末尾提供接口表：
markdown
| 任务 | 输入 | 输出 | 主方法 | Baseline | 校验 |
| --- | --- | --- | --- | --- | --- |
Organize 
ANALYSIS_MODELING_REPORT.md
according to the actual subproblems and include at least:
  1. Overall framework and subproblem dependencies;
  2. Data processing plan;
  3. Symbols, variables, and units;
  4. Assumptions and models confirmed through H1/H2;
  5. Objective function, complete constraints, inputs, and outputs;
  6. Solution steps, stopping conditions, complexity, or applicable scale;
  7. Baseline, edge cases, counterexamples, sensitivity, and result validation plan;
  8. Code implementation task list.
Formulas must be explicit enough to be implemented directly during the coding phase. End the report with an interface table:
markdown
| Task | Input | Output | Primary Method | Baseline | Validation |
| --- | --- | --- | --- | --- | --- |

AI 使用留痕

AI Usage Logging

CUMCM 2026 模式下，本阶段结束或等待人工门禁前，向 
AI_USAGE_LOG.md
追加真实记录：工具名称与可得的版本/模型、用途、主要提示方式、输出摘要、采纳与未采纳内容、人工修改和人工核验。未知信息标记为待人工补全，不得猜测，也不得替队员勾选尚未完成的核验。
In CUMCM 2026 mode, before this phase ends or while awaiting a human approval gate, append a truthful record to 
AI_USAGE_LOG.md
: tool name and available version/model, purpose, main prompting approach, output summary, adopted and non-adopted content, human modifications, and human verification. Mark unknown information as pending manual completion; do not guess or check off verifications the team has not completed.

质量门禁

Quality Gates

  • 所有结论能回到题面、数据、实验或人工决定。
  • 关键模型选择有 baseline 或充分的排除理由。
  • Reviewer 提出的问题已解决、降级为风险或明确交给人工决定。
  • CUMCM 模式下 H1、H2 都有真实队员确认记录；否则阶段状态只能是等待，不能写完成。
  • Every conclusion must be traceable to the problem statement, data, experiments, or a human decision.
  • Every critical model choice must have either a baseline or sufficient rationale for excluding alternatives.
  • Issues raised by the reviewer must have been resolved, downgraded to risks, or explicitly referred for a human decision.
  • In CUMCM mode, H1 and H2 must each have a genuine team confirmation record; otherwise, the phase status can only be waiting and must not be marked complete.