Claim Verification: "For a correctly specified discrete-time spike train model with conditional spike probabilities p_k, define A_m = sum_{k=tau_{m-1}+1}^{tau_m-1} -log(1-p_k) and R_m = A_m - log(1 - U_m * p_{tau_m}), where U_m ~ Uniform(0,1) independently. Then R_m are i.i.d. Exp(1), equivalently Z_m = 1 - exp(-R_m) are i.i.d. Uniform(0,1)." — Proved

Automated fact-verification of the claim: "For a correctly specified discrete-time spike train model with conditional spike probabilities p_k, define A_m = sum_{k=tau_{m-1}+1}^{tau_m-1} -log(1-p_k) and R_m = A_m - log(1 - U_m * p_{tau_m}), where U_m ~ Uniform(0,1) independently. Then R_m are i.i.d. Exp(1), equivalently Z_m = 1 - exp(-R_m) are i.i.d. Uniform(0,1)." Verdict: PROVED Files proof.py — Re-runnable Python verification script proof.md — Structured proof report proof_audit.md — Full verification audit trail proof_narrative.md — Plain-language summary proof.json — Machine-readable structured data Generated by Proof Engine v1.24.0.