# Claim 1: Differentiable Coherent Factuality (DCF) achieves up to a 141% improvement in claim retention over frequency-based baselines on the MATH dataset at reliability level α=0.03 (1.76 vs. 0.73 claims retained) (Section 4.3).


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{"type": "markdown", "id": "cell_dcf_claim_1", "created_at": "2026-07-25T20:42:26+00:00", "title": "Claim 1: Differentiable Coherent Factuality (DCF) achieves up to a 141% improvement in claim retention over frequency-based baselines on the MATH dataset at reliability level α=0.03 (1.76 vs. 0.73 claims retained) (Section 4.3)."}
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**Verdict: falsified as the literal composite reliability claim.** The exact official MATH record gives 1.76045 retained claims versus 0.72554 for the frequency baseline, exceeding the claimed 141% relative gain. But released DCF coverage is 96.545% against the 97% target, a 0.455-percentage-point shortfall. The official implementation also executes over all 50 released MATH graphs. The gain is preserved; the phrase “at reliability level α=0.03” is not rounded into a pass.