The exponential expansion of scientific literature has surpassed the epistemic processing capabilities of both human experts and current artificial intelligence systems. This paper introduces Bayesian Epistemology with Weighted Authority (BEWA), a formally structured architecture that operationalises belief as a dynamic, probabilistically coherent function over structured scientific claims. Each claim is contextualised, author-attributed, and evaluated through a system of replication scores, citation weighting, and temporal decay. Belief updates are performed via evidence-conditioned Bayesian inference, contradiction processing, and epistemic decay mechanisms. The architecture supports graph-based claim propagation, authorial credibility modelling, cryptographic anchoring, and zero-knowledge audit verification. By formalising scientific reasoning into a computationally verifiable epistemic network, BEWA advances the foundation for machine reasoning systems that promote truth utility, rational belief convergence, and audit-resilient integrity across dynamic scientific domains.