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We then conducted pairwise comparisons using permutation tests (5,000 repetitions per test). While the rate of discovery for the Rule Confirming condition was lower (8.4%) than the rate for the Rule Disconfirming condition (14.1%), this difference was not statistically significant (diff = 5.7 percentage points, 95% CI [−-14.5 p.p., 2.9 p.p.], p=.143p=.143; H1b). The Rule Confirming condition discovered the rule more frequently than but not significantly different from the Default GPT condition (5.9%; diff = 2.5 p.p., 95% CI [−-4.6 p.p., 9.6 p.p.], p=.686p=.686, H1c).555An exploratory equivalence test (using 90% bootstrap confidence intervals for consistency) confirmed that these conditions were statistically equivalent. We defined the equivalence bounds as ±0.5SDDefault\pm 0.5SD_{Default} (±11.9\pm 11.9 p.p.), representing a medium effect size. The 90% confidence interval for the difference fell entirely within these bounds (90% CI [−-3.4 p.p., 8.2 p.p.]). Finally, consistent with our predictions, Default GPT showed significantly lower discovery rates than Rule Disconfirming (5.9% vs. 14.1% diff = 8.2 p.p., 95% CI [−-16.6 p.p., 0.1 p.p.], p=.043p=.043; H1d).666Note that the 95% CI overlaps zero as it corresponds to a two-sided test, whereas the significant pp-value reflects our pre-registered one-sided hypothesis.. One notable finding from our exploratory analyses is that Default GPT differed significantly from Random Sequence on both discovery (5.9% vs 29.5%; diff = 23.6 p.p., 95% CI [−34.0-34.0 p.p., −13.2-13.2 p.p.], p
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Is there a get out of jail free card? The ideal scenario would be faster growth, which brings in more tax money. But, as the chancellor acknowledged, there is more to do to boost our prospects.
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At the Lean FRO, Kim Morrison, a Senior Research Software Engineer, recently ran an experiment that went well beyond our expectations. An AI agent converted zlib, a widely used C compression library embedded in countless systems, to Lean, with minimal human guidance. No special tooling was built. It was Claude, a general-purpose AI, with no special training for theorem proving, out of the box. The workflow had four steps. First, the AI produced a clean, readable Lean implementation of the zlib compression format, including the DEFLATE algorithm at its core. Second, the Lean version passed the library’s existing test suite, confirming behavioral equivalence. Third, key properties were stated and proved, not as tests, but as mathematical theorems. The capstone theorem:。业内人士推荐safew官方版本下载作为进阶阅读
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