# Token Causation via Unit Mechanism Learning

> Working title: **Token Causation from a Single Row: Unit Mechanism Learning
> as a Theory of Singular Causal Response**
>
> Status: independent active causal-ontology paper; not submitted.

This directory is the causal-ontology and singular-attribution lens of the Unit
Mechanism Learning / HCGM program. It reframes the shared outcome-generation grammar as a computational
account of **token (singular) causation** under the one-factual-row-per-unit
regime, and states the honesty boundary that separates *predicting* a token's
response law from *attributing* singular causation.

## Conceptual contract

This paper owns the singular-causation motivation and the token↔UML
mapping. The shared grammar is:

```text
world: U=u* selects the actual token
  -> Y_u*(x) = f_theta(x,E;u*)

learner: factual predictors x^F
  -> point / Gaussian / Cauchy abduction about the same u*
  -> candidate u + query x^Q enter f_theta(x^Q,E;u)
  -> p_{phi,theta}(y | x^F,x^Q)
```

At model level, `U` selects a token/unit and a realization `U=u*` is its actual
embedding. The shared object is `Y(x)=f_theta(x,E;U)`; fixing the realization
yields `Y_u*(x)=f_theta(x,E;u*)`. A dataset or sequence index is
bookkeeping only, so the active paper notation does not turn each row into a
separate row-level `U_i` or function.

In ordinary supervised prediction, `X=x` has two roles: it is factual evidence
`x^F` for recognizing the token and the factual mechanism query `x^Q=x`.
Abduction can return `uhat=a_phi(x)`, a Gaussian candidate distribution, or a
Cauchy candidate distribution. Distributional prediction is
`p_{phi,theta}(y|x^F,x^Q)=integral p_theta(y|x^Q,u)q_phi(u|x^F)du`.
For sample \(i\), the complete learner-side belief object is

\[
Q_i(B):=q_\phi(U\in B\mid X=x_i)\approx P(U\in B\mid X=x_i),
\]

under the declared model and evidence convention. The index belongs to the
belief \(Q_i\), evidence \(x_i\), and actual realization \(u_i\); it does not
create a row-specific random variable \(U_i\). The approximation sign states
the intended amortized-inference target. Predictive training alone does not
guarantee posterior equality, calibration, or identification of the latent
coordinate system.
For a same-token counterfactual, keep the abduction result from factual `x`
fixed and change only the query to `x'`; never re-abduct from `x'`.

Cauchy has location and scale but no finite mean or variance. Here it represents
globally open heavy-tailed uncertainty over candidate individual mechanisms,
not a guarantee that every outcome can be generated by every token.

The flagship's positive claim is that UML *predicts* a token's response law from
one row; its negative claim is that one-shot data do not identify the actual
token mechanism, so UML does *not* deliver strict singular causal attribution in
the Lewis / Halpern sense.

## Scientific lineage and program role

- `token-causation/` is an independent **conceptual anchor**.
  `../unit-mechanism-learning/` is an independent general-method paper, not a
  subordinate formalization of this paper.
- `../learning-discoscm/` is the current program flagship and asks how the first
  token-modulated DiscoSCM outcome mechanism can be learned. It may use this
  paper as an ontology lens, but its theorems and experiments are not evidence here.
- `../causal-effect/` and `../continuous-treatment/` are empirical causal
  specializations. Their claims and outputs are not evidence for this paper.
- `../causal-regression/` is historical provenance; not promoted here.
- `../unit-level-response-function-learning-review/` is the narrative literature
  surface; it may cite this flagship but does not supply its evidence.

No historical submission, result table, or frozen implementation is modified or
silently promoted here. The flagship's claims are its own and must be validated
inside this directory.

## Owner workface

Before extending the manuscript, read `seed.md` (the token↔UML mapping
spark) and `assumption-ledger.md` (framework + token-causation assumptions). The
checkpoint-style ledgers (`claim-register.md`, `validation-criteria.md`) preserve
the current evidence status.

## Build and checks

```bash
./build.sh
```

The English PDF is copied to:

```text
output/pdf/token-causation-flagship.pdf
```

## Truth boundary

- UML predicts a token's response distribution
  `p_{phi,theta}(y|x^F,x^Q)` from factual evidence;
  it does not
  identify the actual token mechanism, latent coordinate system, or unit/event
  scale split.
- Predicting `p_{phi,theta}(y|x^F,x^Q)` is **not** singular causal attribution. Strict token causation
  (Lewis counterfactual dependence, Halpern actual causality) requires the actual
  mechanism, which one-shot data do not reveal.
- Context Mechanism Learning, repeated-unit identification, non-Cauchy general
  theory, and nonlinear mechanism recovery are deferred.
- Distributional `q_phi(u|O)` is a directly learned, amortized belief intended
  to approximate the conditional law of the single model-level `U` given the
  admissible evidence. It is not automatically equal to or identified as the
  true posterior, is not a posterior over response functions, and must not be
  replaced mechanically by an unconditional population prior.

See `assumption-ledger.md`, `claim-register.md`, and `validation-criteria.md`
before strengthening any manuscript statement.