# Unit Mechanism Learning Paper Program

> Legacy path / artifact label: `HCGM` / `hcgm`。当前 conceptual core 见
> [`../UNIT_MECHANISM_LEARNING.md`](../UNIT_MECHANISM_LEARNING.md)。这里的多个项目共享
> Unit Mechanism Learning 的底层问题，但分别承担不同 scientific question，并保持各自的
> claim、assumption、identification boundary 与 evidence ledger。

修改任一 active paper 的 unit semantics 前，先读 canonical notation contract：
[`../entrances/DISCOSCM_UNIT_SELECTION_NOTATION.md`](../entrances/DISCOSCM_UNIT_SELECTION_NOTATION.md)。

## Top-level Architecture

### Shared Unit Mechanism Learning grammar

所有放在这里的论文都从同一条 outcome-generation logic 出发；causal / counterfactual
semantics 只由各 paper 在需要时激活：

```text
world: U=u* and X=x, E=e -> y=f_theta(x,e;u*)
learner: factual predictors x^F
        -> A_phi(x^F): point / Gaussian / Cauchy unit abduction
        -> candidate u and event noise E enter f_theta(x^Q,E;u)
        -> predictive outcome p_{phi,theta}(y|x^F,x^Q)
```

- `U` 是模型级 unit-selection variable；一次 realization `U=u` 代表一个 token/unit 及其
  embedding。共享模型写成 `Y(x)=f_\theta(x,E;U)`；固定 realization 后才得到
  `Y_u(x)=f_\theta(x,E;u)`；
- observation index 只是 dataset bookkeeping；不要把每条数据行写成 ontology 中的 `U_i`，
  也不要把它误读成一族彼此独立的 response functions；
- 最简单 ML 场景令 predictors `X=x` 同时承担两种角色：先作 factual evidence，再作
  factual mechanism query；为澄清写作 `x^F=x^Q=x`；
- `A_\phi(x^F)` 可以直接输出 `u_hat`，也可以输出 Gaussian 或 Cauchy distribution；
  这些都是 learner 对同一个 actual token 的认识结果，不是 physical identity redraw；
- Cauchy 参数是 location / scale，没有 finite mean / variance；heavy tails 不代表任何 unit
  可以产生任何 outcome；
- candidate `u` 进入 shared generator `f_\theta(x^Q,E;u)`；不同 units 可以
  response-equivalent；
- `selection` 只表示 `U` 选择 token identity/code；treatment `A/T`、sample inclusion
  `S^obs` 与 propensity 属于 assignment / observation process，不是 Unit Selection Variable；
- `P_U` 是 declared target-population token composition；`Q_i` 是 focal-token belief，
  不是 population composition 或 propensity score；
- latent-code `q` / Cauchy full support 不等于 causal positivity；unit abduction 不会自动
  修复 sample-selection bias 或 treatment confounding；
- `E` 表示 event-level noise；
- counterfactual prediction 固定 factual `x^F` 得到的 abduction result，只改变 `x^Q=x'`，
  不得用 `x'` 重新 abduct；
- 当前 mainline 固定 `C=c0`；Context Mechanism Learning 是 future extension；
- cross-world coupling、identification、support 与 reduction rule 必须由每篇论文显式声明。

这套 `actual U=u* -> predictors as evidence -> unit abduction -> f_theta outcome generation`
语法是当前共同架构。Point 与 Gaussian 是 comparison routes；当前多篇论文采用的
**Cauchy abduction + affine mechanism** 是第一个可解析、可验证的 tractable family，
不是 Unit Mechanism Learning 的定义。读者面优先使用 `f_theta`、`p_theta` 与 sampling
computation；Markov-kernel notation 仅在理论附录确实需要时定义。

### Scientific migration gate

一些 regression manuscript、theorem ledgers 与 finite-type worked example
早于 2026-07-16 ontology clarification。它们可能显式定义 population prior、Bayesian
posterior 或 reader-unfriendly response-kernel notation。它们不能仅因数学上兼容就被
当作当前 point / Gaussian / Cauchy abduction ontology 的 canonical expression。

Until each item is audited, it must be classified as one of:

1. active point / Gaussian / Cauchy abduction method；
2. valid Bayesian special case / contrast artifact；
3. theory-only kernel notation kept in an appendix；
4. pre-clarification claim that must be revised or demoted。

Do not mechanically replace symbols inside theorem statements, code, generated CSV schemas, or
paper equations. Every active paper must instead answer: what is actual `u*`, what does `X=x`
evidence reveal, which abduction family is used, what query enters `f_theta`, and what stays fixed
for a same-token counterfactual?

### Four independent active lenses and application lines

```text
HCGM paper program
|
|-- learning-discoscm/       active flagship: How to learn DiscoSCM?
|
|-- unit-mechanism-learning/ independent general ML framework paper
|
|-- token-causation/           independent causal ontology / attribution paper
|
|-- unit-abducted-cate/        independent HTE localization theory draft
|
|-- unit-level-response-function-learning-review/  narrative literature review
|
|-- causal-regression/          corrected factual precursor + historical provenance
|
`-- Treatment-indexed response line
    |-- causal-effect/           binary-treatment clean-room paper
    `-- continuous-treatment/   continuous-treatment sibling paper
```

1. **Learning DiscoSCM** 是当前 flagship end-to-end ML paper：从 DiscoSCM ontology、
   Unit Selection Variable 与 latent token code 推导 unit abduction、uncertainty geometry、
   learnable architecture 与 falsifiable tests。第一篇只处理 fixed-context、one-factual-row、
   single outcome mechanism，不冒充完整多节点 DiscoSCM。
2. **Unit Mechanism Learning** 与 **Token Causation** 保留独立论文身份。前者抽象一般
   shared unit-modulated generator 与 predictive-law learning；后者承担 token ontology、
   same-token linkage 与 response prediction / singular attribution 边界。它们不是 flagship
   的章节，也不互相继承 theorem 或 evidence。
3. **DiscoCATE** 是独立 HTE localization paper。它把 pretreatment evidence-indexed
   unit beliefs 转换为 observed donor-row weights，并与 cross-fitted orthogonal causal
   scores 组合。当前只支持 fixed-map localized-effect identification；不继承 Learning
   DiscoSCM 的实验，也不声称 learned belief、focal CATE 或 latent type truth 已被恢复。
4. **Causal Regression** 保留 corrected factual-prediction precursor、历史 provenance 与
   复现证据。当前实现没有独立 target-query channel，因此不是 Learning DiscoSCM 的
   Layer 3 实现，也不向 flagship 自动输送性能证据。
5. **Treatment-indexed response line** 研究同一个 actual token 在不同 intervention
   index 下的 predictive outcomes 与 causal contrasts。`causal-effect/` 是从自身
   assumptions 和 evidence 重新建立的 binary-treatment clean-room paper；
   `continuous-treatment/` 是它的 continuous-dose sibling，新增 support、smoothness、
   finite-dose contrast、local derivative 与 cross-dose process 等独立问题，不是
   binary paper 的附录。

这些论文共享 primitives，但不是一篇大稿的章节拆分。放在同一个 `hcgm/paper/` 下表达
共同 research program，不表示 claim 或 evidence 可以互相继承。

### Project roles

- [`learning-discoscm/`](learning-discoscm/)：当前 program flagship。总问题是
  **How to learn DiscoSCM?**；第一篇学习一个 token-modulated outcome mechanism，明确
  factual diagonal 可学习性、latent observational equivalence、off-diagonal 与 causal
  identification 边界。其英文稿、中文导读、implementation 与 ledgers 独立维护。

- [`token-causation/`](token-causation/)：独立 causal ontology / theory paper。把共享的
  outcome-generation grammar 读作**单数 / token 因果**的计算理论，并显式声明
  「预测 token 响应律」与「归属 singular causal attribution」的边界。其 claim 与证据
  独立维护，不继承 siblings 的实验数字。

- [`unit-level-response-function-learning-review/`](unit-level-response-function-learning-review/)：
  中文叙述性综述与未来英文投稿版的共同 workspace。它查验 VCM、mixed effects、HTE / dose-response
  与 conditional function generation 的方法谱系、数据证据和失败边界，但不把相邻 HCGM 论文的
  内部实验当成外部文献证据。当前中文版是 narrative review v0.3；英文 full manuscript 尚未完成。
- [`unit-mechanism-learning/`](unit-mechanism-learning/)：当前 foundational framework
  working paper，固定 `C=c0`，把 actual token、point/Gaussian/Cauchy abduction result 与
  candidate-conditioned outcome generation 分开，并将
  `p_{phi,theta}(y|x^F,x^Q)` 设为 one-shot population 的预测对象；同时把 Causal Regression、Cauchy-affine 与 binary treatment
  模型放回 specializations。其 manuscript、clean-room code、outputs 与 claim ledger 独立。
- [`unit-abducted-cate/`](unit-abducted-cate/)：独立的 HTE algorithm/theory draft
  **DiscoCATE: Heterogeneous Treatment Effect Estimation with Unit-Abducted
  Neighborhoods**。它研究完整 unit-belief geometry 如何诱导 observed-row localization，
  以 AIPW score 估计 fixed-bandwidth soft-population effect；当前没有 benchmark result、
  learned-belief inference theorem 或 superiority evidence。
- [`causal-regression/`](causal-regression/)：HCGM 下的原 Causal Regression corrected
  submission、历史投稿/代码/实验的 provenance 入口，以及研究线重启空间；项目本体在
  `/Users/cms/.openclaw-causaclaw/workspace/projects/causal-regression/`。修复版五种子
  结果只支持该论文明确列出的性能结论，历史结果也不能自动成为其他 HCGM 新稿证据。
- `arxiv-hcgm-regression/`：retired historical entity，已由 `learning-discoscm/` 取代。
  旧 tracked manuscript、推导与 PDF 只通过 Git / archive provenance 恢复；它不再是
  active directory、reader route 或独立第四篇论文。
- [`causal-effect/`](causal-effect/)：独立的 binary-treatment clean-room working
  paper，研究从 factual predictors `x^F -> q_phi(du|x^F)` 到 treatment-indexed
  `f_theta(t,E;u)` 的异质 causal
  location effect；其 estimand、assumptions、identification 与实验从本目录重新建立。
- [`continuous-treatment/`](continuous-treatment/)：独立的 continuous-treatment
  sibling working paper **Counterfactual Prediction with Continuous Treatments**；将
  binary arm 扩展为 continuous dose-indexed mechanism，并单独处理 supported marginal
  predictive dose-response distributions、finite-dose contrasts、local derivatives 与未识别的 cross-dose
  joint process。

### Claim and evidence isolation

共享 architecture 不等于共享完成度。每个 manuscript 必须在自己的目录内维护并验证：

- scientific question 与 estimand；
- modeling、identification、support 和 cross-world assumptions；
- theorem scope、code、experiment、benchmark 与 evidence status；
- 可以公开写出的 claims 与明确 non-claims。

一个项目中的 theorem、toy、实验数字、benchmark 结果或 submission history，默认都
**不能**作为另一个项目的证据。确需复用时，必须在目标 manuscript 中显式重述适用
assumptions、记录来源并重新验证；否则只算 provenance。这个隔离原则也适用于
`causal-regression/` 的历史资产、binary 与 continuous treatment 两稿之间，以及
Cauchy-affine family 上的任何局部结果。

### 10 Paper Portfolio packaging bridge

Portfolio 只消费 paper-family 的成熟度与 exact evidence references，不接管 scientific
truth。当前 typed mapping：

| HCGM source | Portfolio role | Current status | Boundary |
|---|---|---|---|
| `learning-discoscm/` | `RQ16/P16` active flagship science source | Portfolio seed, not an active submission package | factual-law learnability 不偷渡 latent/off-diagonal/Layer 3 identification；primary benchmark 尚待执行 |
| `token-causation/` | independent causal ontology paper | active seed | 不把 `p_{phi,theta}(y|x^F,x^Q)` 的预测写成 singular causal attribution；不继承 siblings 实验数字 |
| `causal-effect/` | `RQ23/P23` delivery lane | package preflight | 不把 robust fit 写成 universal dominance，不把 factual fit 写成 ITE truth |
| `unit-mechanism-learning/` | independent general method paper | active working paper | 不因 flagship 使用其 implementation 就转移 theorem / experiment truth |
| `unit-abducted-cate/` | independent HTE localization paper | manuscript v0 / theory draft | fixed-map target identified；learned-Q stability、inference 与 empirical advantage 尚未建立 |
| `continuous-treatment/` | independent second-wave incoming candidate | incoming | 不作为 binary paper appendix；等待独立 RQ/P allocation |
| `causal-regression/` | `RQ25` historical provenance + corrected-submission workspace | not yet a new Portfolio promotion | 历史 submission/code 不自动成为 current claim；修复版证据也不自动升级为 Portfolio 录用线 |

Machine-readable bridge:

```text
/Users/cms/.openclaw/workspace/projects/two-month-ten-conference-papers/state/hcgm-paper-bridge-v0.yaml
```

## Boundary

当前只允许 paper 围绕已经足够稳定的问题 grow。不要把旧 HCGM guide 整体搬进 `paper/`。

默认 flagship 是 `learning-discoscm/`，但 flagship 表示当前总问题与推进优先级，不表示它
拥有 `token-causation/`、`unit-mechanism-learning/` 或 `unit-abducted-cate/` 的 claim truth。四篇各自维护 manuscript、
theorem、experiment、failure 与投稿身份。

`causal-regression/` 是原论文的修复版、受限 factual-prediction precursor 与更宽研究线入口；
它不是 `learning-discoscm/` 的旧名字。retired `arxiv-hcgm-regression/` 也不是 active precursor
目录：其历史内容只通过 Git / archive provenance 恢复。

`causal-effect/` 是 owner 于 2026-07-11 启动的独立论文。它继承 Cauchy
abduction + linear mechanism 的窄 learnability seed，但 causal estimand、binary
treatment、identification assumptions、cross-world coupling 和 experiment
evidence 都在自己的目录里重新建立；不要把旧 causal-regression 的历史实验数字直接
promote 到这篇论文。

`continuous-treatment/` 继承 binary paper 的 latent abduction 与 Cauchy-affine
predictive-distribution calculation，但研究对象是 continuous treatment 下的
counterfactual prediction。当前 synthetic evidence、VCNet/DRNet Simu1/IHDP/News
official protocols 与 exact-density support diagnostics 已执行并写入稿件；SCIGAN、
TCGA、formal finite-sample uncertainty 与真正的 real continuous-treatment causal
design 仍是进入更强 submission claim 之前的 evidence gates。

Learning DiscoSCM 当前最小问题：

```text
How can the first token-modulated outcome mechanism in DiscoSCM be learned
from one factual observation per token?
```

Regression prediction 必须完整写出中间的 unit-abduction bridge：

```text
actual world: U=u*, X=x, E=e -> y=f_theta(x,e;u*)
learner: x^F=x -> point / Gaussian / Cauchy unit abduction
factual prediction: x^Q=x^F=x -> f_theta(x^Q,E;u)
counterfactual: freeze the factual abduction result, change only x^Q=x'
```

distributional route 得到
$p_{\phi,\theta}(y\mid x^F,x^Q)=\int p_\theta(y\mid x^Q,u)q_\phi(du\mid x^F)$；
point route 是其退化版本。`q` 是 learner 对同一个 actual token 的 uncertainty，不是
physical identity redraw。

Owner-expression guardrails:

- $U=u^\star$ should first be read as one actual token/unit and its embedding;
  learner-side candidate draws must be marked separately.
- $f(x,E;u)$ is the personalized outcome-generating structural equation.
- Predictors $X=x$ are factual evidence for unit abduction and, in ordinary
  factual regression, the same numerical value is also the mechanism query.
- The paper should foreground primitively heterogeneous prediction.
- An alternative target $x'$ is evaluated using the abduction result from
  factual $x$; causal interpretation additionally requires intervention semantics.
- Cauchy parameters are location / scale and do not supply finite mean / variance.
- Interpretability and robustness over ordinary ML counterparts are validation targets, not already-proven claims.
- End-to-end learnability is currently guarded by the Cauchy-distribution +
  linear-causal-mechanism assumption seed.

Current supporting and provenance artifacts:

- `../toy/hcgm-regression-worked-example/` is a finite-type Bayesian special case. It keeps its posterior filenames as provenance and illustrates one distributional-abduction route, not the full three-way comparison.
- `../toy/cauchy-affine-response-kernel/` is the first toy for the Cauchy +
  linear learnability seed. It verifies that independent Cauchy abduction
  uncertainty plus an affine response mechanism yields a closed-form Cauchy
  predictive outcome distribution, with quartile-level sampling checks. The folder
  and generated filenames retain `response-kernel` only as provenance.
- `learning-discoscm/README.md` 是 flagship 的 current status/workface；其
  `theorem-targets.md`、`assumption-ledger.md`、`claim-register.md`、
  `validation-criteria.md` 与 `experiment-ledger.md` 分别拥有 proof、assumption、claim 与
  evidence truth，不由 program README 代替。
- `entrances/LEARNING_DISCOSCM.md` 与 `/learning-discoscm/` 是 reader-first V2 logic
  contract，先固定 “How to learn DiscoSCM?” 的推导顺序；它们不证明 manuscript、benchmark
  或 PDF 已完成。