PET-VE: Temporal Inference Engineering

PET-VE (Temporal Inference Engineering) extends Phase–Echo Theory (PET) by transforming temporal inference from a descriptive concept into an explicit control and optimization problem. While PET-V established the necessary and sufficient conditions under which information about past events can be inferred from present observations, PET-VE addresses the complementary question: how agents can act in the present to maximize the future recoverability of those actions under irreversible dynamics.

Within the PET framework, global physical evolution is reversible, but observer access collapses over time due to coarse-graining and entropy growth. PET-VE formalizes action placement as a control policy that shapes how correlations with an event variable are distributed across physical subsystems. Inferability is defined as a mutual-information functional between an event variable and future accessible observations, and optimal action policies are derived by maximizing this functional subject to physical and resource constraints.

The theory introduces the concepts of traces, trace persistence time, and echo-collapse rates, providing a rigorous explanation for why durable records, evidence, and memory structures must be redundant, distributed, and physically stable. PET-VE proves that while agents cannot guarantee universal recoverability of all past events, they can systematically engineer which aspects of the present remain inferable in the future.

PET-VE does not invoke retrocausality, time travel, or new physical laws. It remains fully compatible with PET-Core, PET-A (Adaptive Access), PET-E (Echo Engineering), and PET-V (Temporal Inference), and is agnostic to PET-X (Exogenous Echo Access). Instead, it provides the strongest possible framework for “time viewing” within known physics, understood as the deliberate preservation and optimization of accessible historical traces.

This work serves as a foundational reference for research on memory persistence, forensic inference, record stability, long-horizon planning, and the engineering of recoverable pasts in physical, computational, and social systems.