Three Exercises on the Intensity Clause of Theorem 1 with a Realised-Accuracy Proxy: Research Note, Pre-specifications, Data and Scripts

This record deposits, with every input, script, log and output, three exercises that took a measure of a language model's realised accuracy as a proxy for the informativeness the marginal entrant attributes to a derivative aggregate and asked whether primary entry on Stack Overflow fell more where that proxy was higher (Theorem 1(i) of The Causal Partition of Information, SSRN 7174958). Design 1 (pre-specified 16 September 2026; internal, not externally time-stamped): nineteen language tags; dose = code-davinci-002 pass@1 on MultiPL-E (August 2022); slope on dose −0.11 (HC3 s.e. 0.58; 95 per cent interval −1.33 to 1.10), Spearman −0.23, terciles −0.54/−0.48/−0.49, event-study post average −0.002 (s.e. 0.72), fragile to composition (−0.94, s.e. 0.43, on twelve languages). Design 2 (pre-specified 17 September 2026; internal): within-language knowledge-cutoff triple difference over fifty-two tag-cohorts; DDD −0.23 (HC3 s.e. 0.41; interval −1.02 to 0.57; permutation p 0.64). Design 3: Stack Exchange cross-site with an MMLU per-subject dose, stopped at its pre-specified power gate on pre-shock data (literal-rule minimum detectable slope 0.70 against a 0.6 gate); no post-shock data were pulled and the collector's guard is deposited.

Verdict, in the manuscript's words: the two executed exercises did not detect the predicted gradient and lacked the power to reject it; a test of the clause as stated needs a measure of the informativeness entrants attribute to the aggregate, which neither had. They are evidence neither for nor against the clause. Two earlier files with the wording "not supported" are kept unchanged as the historical record and superseded by the research note. The manuscript cites this record in one sentence of its measurement section and in register rows 19 and 20 of Part EV.1; nothing in its results depends on these exercises.