PET-X: Hypothesis of Exogenous Echo Access and Stochastic Inference of Hidden State Variables

PET-X (Exogenous Echo Access) is a labeled, falsifiable extension of Phase–Echo Theory (PET) that explores the possibility that observer access to physical information may be incomplete under standard coarse-graining assumptions. While PET-Core demonstrates that irreversibility arises from the operational collapse of distinguishability under restricted access, PET-X investigates whether additional, weakly coupled degrees of freedom could provide an exogenous observation channel without violating reversibility, thermodynamics, or causal structure. In PET-X, this possibility is formalized as a stochastic observation channel that is not a function of the observer’s standard access map alone. The theory does not assert the existence of such a channel; instead, it specifies the exact mathematical conditions under which it would be detectable and the experimental criteria required to falsify or support the hypothesis. All claims are framed in terms of mutual information, distinguishability, and adaptive inference, preserving the core constraints of Phase–Echo Theory. PET-X reformulates speculative ideas about “hidden memory” or “persistent echoes” into a rigorous inference problem: whether measurable correlations exist beyond known observer access after operational erasure has occurred. The framework is compatible with PET-A (Adaptive Observers) and PET-E (Echo Engineering), treating potential exogenous access as a hypothesis to be tested through controlled noise-driven measurements and stochastic inference rather than as a guaranteed capability. This work does not claim retrocausality, cryptographic reversal, prediction of future states, or recovery of arbitrary past events. Instead, it provides a mathematically grounded structure for experimentally probing the limits of observer access and determining whether additional physical channels exist beyond those currently modeled. PET-X is intended as a hypothesis paper and methodological foundation for future experimental and theoretical investigation into information accessibility, observer limits, and the completeness of coarse-grained physical descriptions.