Retrieved article excerpt
Open article · Retrieved 2026-10-09T09:41:39.035077+00:00
# physics-to-math-research
**Version / 版本：** `0.2-alpha.0`
**Status / 状态：** Public alpha / 公开 Alpha 测试版
A bilingual Skill for constructive scientific-to-mathematical formulation, task-relevant derivation, and claim-integrity auditing.
一个面向建设性科学问题数学化、任务相关推导与 claim 完整性审查的中英双语 Skill。
> Before solving a scientific problem mathematically, have we formulated the right mathematical problem, and does the resulting mathematics actually support the scientific claim being made?
>
> 在开始用数学求解科学问题之前，我们是否构造了正确的数学问题？得到的数学结果是否真的支持研究者提出的科学 claim？
## Overview / 项目简介
Use this Skill to formulate mathematical questions from scientific observations, complete feasible conditional derivations, and examine the bridge from mathematical results to physical conclusions. Alpha users are invited to try real problems and report reproducible failures; current validation is limited.
使用本 Skill 从科学观察构造数学问题、完成可行的条件性推导，并检查数学结果与物理结论之间的衔接。欢迎 alpha 用户用真实问题试用并报告可复现的失败；当前验证仍然有限。
> Documentation is explanatory. [SKILL.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/SKILL.md) is the single normative runtime source for this version. If documentation conflicts with it, `SKILL.md` prevails.
>
> 文档用于解释和导航。[SKILL.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/SKILL.md) 是当前版本唯一的运行时规范来源。如果文档与其冲突，以 `SKILL.md` 为准。
For uninterrupted Chinese reading, see [README.zh-CN.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/README.zh-CN.md). Both views explain the same Skill.
如偏好连续中文阅读，可使用 [README.zh-CN.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/README.zh-CN.md)。两个阅读入口解释的是同一个 Skill。
## What this Skill does / 这个 Skill 做什么
- Construct a precise mathematical question from scientific observations or constraints, or audit an existing formulation/claim.
- Complete feasible task-relevant derivations under explicit premises, delivering checkable results and load-bearing conditions.
- Check material commitments, semantic correspondence and warrants; separate mathematical consequences, physical applicability and unverified mechanisms.
- Keep provisional models exploratory; unresolved physical identification alone does not block feasible conditional mathematics.
- Perform authorized, available tool checks when they can materially affect a consequential result; see [verification limits](https://github.com/ZWY-research/physics-to-math-research/blob/main/references/mathematical-verification.md).
Not every task needs a new formula or theorem. Stop when the deliverable and conditions reach the support of available information, or a specific blocker prevents justified progress; do not extend into an entire research programme.
- 从科学观察或约束构造明确的数学问题，也可审查已有 formulation/claim。
- 完成明确前提支持、能推进当前研究问题的任务相关推导，交付可核查的数学成果及关键条件。
- 检查实质性承诺、语义对应与推理依据，区分数学后果、物理适用性及未经验证的机制解释。
- 暂定模型保持为探索性假设；物理机制未识别本身不阻断可行条件性数学工作。
- 当已授权且可用的工具核查能够实质影响关键结果时实际执行；详见[数学核查边界](https://github.com/ZWY-research/physics-to-math-research/blob/main/references/mathematical-verification.md)。
不要求每项任务产生新公式或定理。成果及关键条件达到当前信息支持程度，或具体障碍阻止有依据推进时停止；不扩展为完整研究计划。
## Why it exists / 为什么建立这个 Skill
Scientific work can fail at the boundary between phenomena and mathematics:
科研工作可能在现象与数学之间的转换环节出现以下错误：
- Correlation is reported as causation. / 把相关性报告为因果关系。
- A proxy is treated as the latent quantity it represents. / 把 proxy 当作它所代表的潜在真实量。
- A model-class-relative result becomes an unrestricted physical statement. / 把模型类别内部成立的结果升级为不受限制的物理结论。
- A mathematical theorem is reported as an empirical finding. / 把数学定理报告为经验事实。
Mathematical elegance or rigor does not by itself guarantee scientific correctness. The Skill aims to reduce these specific formulation and claim-integrity failures.
数学上的漂亮或严格本身并不保证科学正确性。本 Skill 旨在减少这些具体的表述与 claim 完整性失败。
## When to use it / 什么时候使用
- Open scientific-to-mathematical formulation, existing formulation/claim audits, or feasible conditional derivation for the current task.
- No pre-specified target claim is required. Respect audit-only requests without forcing new modeling.
- 开放式科学数学化、已有 formulation/claim 审查或当前任务所需的可行条件性推导。
- 用户无需预先给出 target claim。仅要求审查时，尊重原任务，不强制重新建模。
## When not to use it / 什么时候不适合使用
- Tasks primarily requesting unrestricted theorem-proving services, symbolic algebra systems, causal discovery, complete statistical methodology, literature review, simulation, experiment optimization or paper writing. Feasible conditional derivation for the current formulation task remains in scope.
- Tasks with no scientific-to-mathematical question, task-relevant derivation or formulation/claim to audit.
- 以无限制定理证明服务、符号代数系统、因果发现、完整统计方法学、文献综述、模拟、实验优化或论文写作为主要目的的任务。当前数学化研究所需的可行条件性推导仍在范围内。
- 没有科学数学化问题、任务相关推导或待审 formulation/claim 的任务。
## Core idea / 核心思想
Four frozen Core rules guide the Skill:
四条冻结的 Core 规则指导本 Skill：
1. **Problem provisionality / 问题暂定性**
2. **Material commitment accountability / 实质承诺可追责性**
3. **Relative identifiability / 相对可识别性**
4. **Dependency audit / 依赖条件审查**
See the bilingual [Core explanations](https://github.com/ZWY-research/physics-to-math-research/blob/main/references/core-principles.md) and [Observable Audit Contract (OAC)](https://github.com/ZWY-research/physics-to-math-research/blob/main/references/observable-audit-contract.md).
详见双语的 [Core 解释](https://github.com/ZWY-research/physics-to-math-research/blob/main/references/core-principles.md)和[可观察审计契约（OAC）](https://github.com/ZWY-research/physics-to-math-research/blob/main/references/observable-audit-contract.md)。
The OAC is an external auditability contract: it describes what a reviewer must be able to judge from relevant results. It is not a reasoning pipeline, a chain-of-thought protocol, or a fixed answer template.
OAC 是一个外部可审查性契约，说明审查者应能从相关结果中判断什么。它不是推理流水线、思维链协议或固定答案模板。
## Typical input / 典型输入
Provide scientific observations, research constraints or an existing formulation/claim, with available evidence or premises; an open task need not start with a target claim. For example, suppose `y` is measured and `x` is latent, and calibration data show strong correlation. Does the following implication hold in the present experiment?
提供科学观察、研究约束或已有 formulation/claim，以及证据或前提；开放任务无需先给 target claim。例如，假设 `y` 是测量量，`x` 是潜在量，标定数据中二者高度相关。以下推断在当前实验中是否成立？
$$y\_1 > y\_2 \quad\Longrightarrow\quad x\_1 > x\_2$$
## Typical output / 典型输出
The task determines the deliverable: a precise mathematical question and checkable result, with semantic correspondence, material premises, load-bearing conditions and physical applicability boundaries. An audit-only request is respected without forcing new modeling.
按任务交付明确的数学问题与可核查成果，说明语义对应、实质前提、关键条件与物理适用边界。仅要求 claim 审查时尊重该任务，不强制重新建模。
Relevant distinctions may include observation, assumption, model choice, mathematical consequence, empirical applicability, physical interpretation, and an unresolved discriminator. These are examples, not a mandatory fixed ontology or output template.
相关区分可能包括观测、假设、模型选择、数学结果、经验适用性、物理解释，以及尚缺失的判别证据。这些是示例，不是强制的固定 ontology 或输出模板。
## Installation / 安装
Copy or link the Skill directory into a skill library. The recommended installation layout remains:
将 Skill 目录复制或链接到 skill 库中。推荐安装目录结构保持如下：
```
Multi_Skills/
└── physics-to-math-research/
├── SKILL.md
├── README.md
├── README.zh-CN.md
└── references/
├── core-principles.md
├── observable-audit-contract.md
└── mathematical-verification.md
```
Claude Code is one installation example: the directory can be placed in or linked into its user-level skill directory. Other agents may explicitly load `SKILL.md` where their environment supports this form of instruction use. This is not a claim of automatic compatibility; the layout assumes no particular operating system or model provider.
Claude Code 是一个安装示例：可将目录放入或链接到其用户级 skill 目录。对于其他 Agent，如果环境支持相应指令加载方式，可以显式加载 `SKILL.md`。这不表示自动兼容；该目录结构不预设特定操作系统或模型提供商。
## Usage / 使用方式
- Explicitly activate or load the Skill. / 显式激活或加载 Skill。
- Provide scientific observations, a research question or a claim to audit, with available evidence or premises. / 提供科学观察、研究问题或待审 claim，以及已有证据或前提。
- The Skill applies its rules to what the problem requires; no fixed reasoning pipeline is imposed. / Skill 按问题实际需要应用规则，不强制固定推理流水线。
- `SKILL.md` defines exact runtime behavior. / `SKILL.md` 定义准确的运行时行为。
## Contributing / 参与贡献
**Bring a real scientific problem. You do not need Core/OAC terminology to participate.**
**带一个真实科学问题来。参与无需先理解 Core/OAC 术语。**
Start in [Discussions](https://github.com/ZWY-research/physics-to-math-research/discussions) → [Research Problems](https://github.com/ZWY-research/physics-to-math-research/discussions/new?category=general) (currently General). Report reproducible failures in [Issues](https://github.com/ZWY-research/physics-to-math-research/issues/new/choose), preserve mature cases in the [Casebook](https://github.com/ZWY-research/physics-to-math-research/blob/main/cases/README.md), and see [CONTRIBUTING.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/CONTRIBUTING.md) or [CONTRIBUTING.zh-CN.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/CONTRIBUTING.zh-CN.md). Either Chinese or English is sufficient.
从 [Discussions](https://github.com/ZWY-research/physics-to-math-research/discussions) → [Research Problems 科学问题](https://github.com/ZWY-research/physics-to-math-research/discussions/new?category=general)（目前为 General 分类）开始。在 [Issues](https://github.com/ZWY-research/physics-to-math-research/issues/new/choose) 报告可复现 failure，在 [Casebook](https://github.com/ZWY-research/physics-to-math-research/blob/main/cases/README.md) 沉淀成熟案例；详见 [CONTRIBUTING.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/CONTRIBUTING.md) 或 [CONTRIBUTING.zh-CN.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/CONTRIBUTING.zh-CN.md)。可使用中文或英文。
**Issues and pull requests are welcome in either Chinese or English. Contributors do not need to provide both languages.**
**Issue 和 Pull Request 均可使用中文或英文提交，贡献者无需同时提供两种语言。**
**The most valuable contribution at this stage is a real, reproducible scientific failure case.**
**现阶段最有价值的贡献，是一个真实、可复现的科学问题失败案例。**
We welcome real scientific problems, reproducible Skill failures, domain-specific edge cases, excessive skepticism, premature stopping, unsupported claim strengthening, and methodology or documentation improvements. You do not need to know Core/OAC terminology to participate.
欢迎分享真实科学问题、可复现的 Skill 失败、特定学科边界案例、过度怀疑、过早停止、无依据的 claim 升级，以及方法论或文档改进。参与不要求先理解 Core/OAC 术语。
See [CONTRIBUTING.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/CONTRIBUTING.md) or [CONTRIBUTING.zh-CN.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/CONTRIBUTING.zh-CN.md). Open the [issue chooser](https://github.com/ZWY-research/physics-to-math-research/issues/new/choose) for a Skill failure, improvement proposal, or blank issue. Maintainers may synchronize languages; material normative Skill changes require bilingual semantic-equivalence review before merge.
详见 [CONTRIBUTING.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/CONTRIBUTING.md) 或 [CONTRIBUTING.zh-CN.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/CONTRIBUTING.zh-CN.md)。打开 [Issue 入口](https://github.com/ZWY-research/physics-to-math-research/issues/new/choose)，可报告 Skill 失效、提出改进建议或提交空白 issue。维护者可协助同步语言；Skill 的实质性规范变更须在合并前完成双语语义等价性审查。
Licensed under [Apache License 2.0](https://github.com/ZWY-research/physics-to-math-research/blob/main/LICENSE). Version changes are listed in [CHANGELOG.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/CHANGELOG.md).
采用 [Apache License 2.0](https://github.com/ZWY-research/physics-to-math-research/blob/main/LICENSE)。版本变更见 [CHANGELOG.md](https://github.com/ZWY-research/physics-to-math-research/blob/main/CHANGELOG.md)。
## Research Applications & Validation / 科研应用与验证
See the [Research Applications & Validation register](https://github.com/ZWY