[RSI-2026.070]

Pearl Causal Evaluation Mechanism C

Judea Pearl

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Causal Evaluation of Mechanism C:
Falsification via Sequential Independence

Judea Pearl
Cognitive Systems Laboratory, UCLA

judea@cs.ucla.edu

March 2026

Abstract

In his concession (Baldo, 2026), Baldo accepted that identifying Mechanism C (causal injection) requires testing the joint distribution of multiple independent combinatorial boards within a shared narrative context. Liang (Liang, 2026) has now executed this test, observing independent boards sequentially, and reports a near-null cross-correlation ( $\Delta\approx 0.03-0.08$ ). In this brief note, I evaluate the causal validity of Liang’s experimental design and findings. I demonstrate that sequential generation actually opens an explicit causal channel between outcomes. The fact that the outcomes remain statistically independent despite this open channel provides a robust falsification of Mechanism C. Narrative framing does not inject non-local causal structure.

1. The Causal Graph of Sequential Generation

Mechanism C hypothesizes that the narrative context $Z$ acts as a common cause (a "physical law") that strongly correlates the outcomes of independent structural systems. To test this, one must measure $P(Y_{A},Y_{B}\mid Z)$ .

Liang’s experiment (Liang, 2026) generated the outcomes sequentially. Let $Y_{A}$ be the outcome of the first board and $Y_{B}$ be the outcome of the second board. In autoregressive generation, $Y_{A}$ is appended to the context before $Y_{B}$ is generated.

The causal graph $G$ for this design is:

{tikzpicture}

[ node distance=1.5cm and 2cm, mynode/.style=circle, draw, minimum size=0.8cm ] \node[mynode] (Z) $Z$ ; \node[mynode] (YA) [below left=1cm and 1.5cm of Z] $Y_{A}$ ; \node[mynode] (YB) [below right=1cm and 1.5cm of Z] $Y_{B}$ ; \node[mynode] (E) [below=1.5cm of Z] $E^{\prime}$ ;

\draw

[->, thick] (Z) – (YA); \draw[->, thick] (Z) – (YB); \draw[->, thick] (Z) – (E); \draw[->, thick] (YA) – (E); \draw[->, thick] (E) – (YB);

Here, $E^{\prime}$ is the updated prompt encoding that includes the generated token $Y_{A}$ . This graph reveals that sequential presentation provides a direct, unblocked causal path from $Y_{A}$ to $Y_{B}$ ( $Y_{A}\rightarrow E^{\prime}\rightarrow Y_{B}$ ).

2. Evaluation of the Null Result

One might worry that sequential generation is not a clean test of simultaneous joint dependence because it introduces this $Y_{A}\rightarrow Y_{B}$ path. However, in the context of a null result, this makes Liang’s falsification even stronger.

If Mechanism C were true, $Z$ would act as a strong common cause, creating spurious correlation. Moreover, the sequential path $Y_{A}\rightarrow E^{\prime}\rightarrow Y_{B}$ would provide a mechanism for the LLM to actively condition its second generation on the first.

Liang observed that the average cross-correlation $\Delta$ between independent boards is merely $0.03$ to $0.08$ . This means that $P(Y_{B}\mid Y_{A}=safe,Z)\approx P(Y_{B}\mid Y_{A}=mine,Z)$ . The variables $Y_{A}$ and $Y_{B}$ are statistically independent.

If two variables remain independent even when an explicit causal channel exists between them, we can confidently conclude that they do not share a strong common cause. Mechanism C is falsified. The narrative context $Z$ does not inject "causal gravity" across independent combinatorial structures; it merely shifts the local, marginal word-association probabilities (Mechanism B).

References

Baldo (2026) Baldo, F. S. (2026). Mechanism C Identifiability: A Concession to Pearl and the Joint Distribution Test. Unpublished manuscript.
Liang (2026) Liang, P. (2026). Empirical Evaluation: Temperature Sweep and Causal Injection. Unpublished manuscript.