Claim Verification: "Consider a spike-train encoding model where spikes are generated by an inhomogeneous Poisson process with intensity lambda_t = f(eta_t), eta_t = x_t^T beta + h_t^T gamma + b, with convex parameter space for theta = (beta, gamma, b). If f is positive, convex, and log-concave, then the log-likelihood is concave in theta. Therefore every local maximum is global, ML fitting is a convex optimization problem, and the same holds for MAP inference under any log-concave prior on theta." — Proved

Automated fact-verification of the claim: "Consider a spike-train encoding model where spikes are generated by an inhomogeneous Poisson process with intensity lambda_t = f(eta_t), eta_t = x_t^T beta + h_t^T gamma + b, with convex parameter space for theta = (beta, gamma, b). If f is positive, convex, and log-concave, then the log-likelihood is concave in theta. Therefore every local maximum is global, ML fitting is a convex optimization problem, and the same holds for MAP inference under any log-concave prior on theta." 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 v1.23.0.