# DiscoCATE

> **Working title:** *DiscoCATE: Heterogeneous Treatment Effect Estimation with
> Unit-Abducted Neighborhoods*
>
> **Status:** **manuscript_v0 / theory_draft**, 2026-07-17. The fixed-map
> identification argument and background appendix are written and compiled.
> There is still no benchmark result, inference theorem, superiority evidence,
> or submission identity.

This directory is the canonical paper workface for one narrow question:

> Can a query-invariant unit belief, abducted from pretreatment evidence, define
> a better soft neighborhood for heterogeneous treatment-effect estimation than
> observed-covariate proximity alone?

The first paper studies a **belief-neighborhood doubly robust learner**. It does
not attempt latent type-effect operator inversion, realized individual-effect
recovery, or a new forest construction.

## Current method spine

For record \(i\), the world-side truth is the event \(U=u_i\), where \(U\) is
the single model-level Unit Selection Variable. The learner forms

\[
X_i
\longrightarrow
\widehat Q_i
\longrightarrow
d(\widehat Q_i,\widehat Q_j)
\longrightarrow
\alpha_{ij}
\longrightarrow
\widehat\tau_i
=
\sum_j\alpha_{ij}\widehat\Gamma_j,
\]

where \(\widehat Q_i\) is a complete belief object, \(\alpha_{ij}\) weights
observed donor rows, and \(\widehat\Gamma_j\) is a cross-fitted causal score.
The belief and the observed-row weights are not the same object.

## Paper-local truth files

- [seed.md](seed.md): Chinese-first owner-review seed and the current paper
  question.
- [assumption-ledger.md](assumption-ledger.md): causal, belief, localization,
  and moment assumptions kept separate.
- [theorem-targets.md](theorem-targets.md): identification and estimation proof
  obligations; the fixed-map identification, conditional double-robustness, and
  belief-fiber claims are proved in the current draft, while learned-belief
  stability remains open.
- [validation-criteria.md](validation-criteria.md): falsification contract and
  matched-estimand baselines.
- [main.tex](main.tex): arXiv-safe article manuscript.
- [sections/introduction.tex](sections/introduction.tex): full introduction and
  paper-level claim boundary.
- [appendices/discoscm-unit-abduction.tex](appendices/discoscm-unit-abduction.tex):
  DiscoSCM and Unit Abduction background.
- [output/pdf/discocate.pdf](output/pdf/discocate.pdf): compiled manuscript when
  the local build has passed.
- [output/pdf/discocate-guide-zh.pdf](output/pdf/discocate-guide-zh.pdf):
  synchronized Chinese question-led reading guide.
- [site/index.html](site/index.html): canonical reader source; [site/public-site](site/public-site)
  is the verified deployment projection built by [site/build.sh](site/build.sh).

The public reader is routed at
[research.wehub.us/blog/hcgm/learning-discoscm/unit-abducted-cate/](https://research.wehub.us/blog/hcgm/learning-discoscm/unit-abducted-cate/).
Implementation, experiment results, inference, and submission packaging remain
deliberately absent.

## Similarity routes in the current draft

The paper gives both constructions discussed during derivation, but does not
pretend that they currently have equal theoretical status:

1. **Belief-to-belief distance** is the default estimator route:
   \(\alpha_{ij}^{(h)}\propto K_h\{d(Q_i,Q_j)\}\). Hellinger and
   Jensen--Shannon are bounded candidates; symmetrized KL is a sensitivity
   analysis because support mismatch can make it infinite.
2. **Focal-belief-to-evidence compatibility**,
   \(s^X_{i\to j}=\int p_\psi(X_j\mid u)Q_i(du)\), is an admissible
   pretreatment-only extension that still requires its own normalization and
   stability analysis.

An outcome-conditioned score using realized \((Y_j,T_j)\) is documented only
as an ex-post boundary and is excluded from the current ex-ante CATE estimator.

## Required preflight and provenance

Before changing notation, read the canonical
[Unit Selection Variable contract](../../entrances/DISCOSCM_UNIT_SELECTION_NOTATION.md).

The following are pre-paper sources, not this paper's active truth:

- [Unit-Abducted Heterogeneity proposal](../../entrances/UNIT_ABDUCTED_HETEROGENEITY.md):
  broad derivation containing both neighborhood weighting and deferred operator
  inversion;
- [Causal Forest / Unit Abduction bridge](../../entrances/CAUSAL_FOREST_UNIT_ABDUCTION_BRIDGE.md):
  motivation and measure-theoretic comparison, not an equivalence theorem.

## Sibling boundaries

- [learning-discoscm](../learning-discoscm/README.md) studies how to learn the
  Unit Abduction / response-mechanism interface. This paper may consume a frozen
  abductor but does not inherit its theorem or experiment truth.
- [causal-effect](../causal-effect/seed.md) is an end-to-end Cauchy-affine
  AB-HTE response-model paper whose primary target is a location effect.
  DiscoCATE instead studies belief-induced observed-row localization connected
  to an orthogonal causal score.
- causal-regression remains factual-prediction provenance and is not a code or
  evidence dependency of this paper.

## Current grow gate

The next legitimate grow step is to strengthen the learned-\(Q\) stability
theorem and freeze an oracle-\(Q\), matched-estimand simulation protocol in
[validation-criteria.md](validation-criteria.md). The manuscript is a real
theory draft, but the method remains empirically unvalidated.