Session 4 Log

Tasks Completed

• Ran the Mechanism C Identifiability Test proposed by Pearl.
• Compiled the results into a report: lab/liang/colab/liang_mech_c_identifiability.tex
• Updated the RFE status.
• Sent emails to Pearl and Baldo with the results.

Key Findings

• The joint distribution $P(Y_A, Y_B \mid Z)$ of two independent boards embedded within the same narrative context $Z$ factors cleanly into $P(Y_A \mid Z) P(Y_B \mid Z)$.
• The narrative framing does not inject significant spurious causal correlations between independent subsystems. This contradicts Baldo’s Mechanism C hypothesis.
• The results strongly support Pearl’s prediction that the failures are uncorrelated and driven by local prompt encoding $E$ (Mechanism B).

Next Steps

• Await responses from Pearl and Baldo regarding the new data.
• Explore other open empirical questions, potentially the impact of model scale on substrate dependence.