Most approaches to AI governance focus on outputs: accuracy, bias, explainability, and auditability. These approaches implicitly assume that the informational basis of decisions can be reconstructed after the fact. This paper examines a different limitation. Once AI-mediated reasoning influences belief or action, no durable record of the reasoning state that produced that influence typically exists. We show that conventional logging and audit mechanisms are insufficient because influence arises through multi-turn interaction, narrative compression, and uncertainty collapse rather than isolated responses. We define the concept of a reasoning ledger as a necessary evidentiary object and specify the properties such a ledger must possess to restore reconstructability. This paper does not propose a standard, recommend adoption, or evaluate implementations. Its purpose is to define the class of artifact required, in principle, if AI-mediated reasoning is to remain explainable under later review.