G-Value Dynamics: An Asymmetric, Multi-Timescale Runtime-State Model for Persistent AI Agents

This preprint introduces G-Value Dynamics, an asymmetric, multi-timescale runtime-state model for persistent AI agents. The model represents the currently running agent through a three-dimensional latent state, Gt=(It,Ft,At)\mathbf{G}_t=(I_t,F_t,A_t)Gt=(It,Ft,At): Inner-G captures endogenous cognitive vitality and integration; Field-G captures the agent body’s estimate of current relational coupling; and Action-G captures the degree to which intention has acquired direction, effectors, and realized movement. The framework separates latent state from observational evidence and function-specific projections, and distinguishes fast observations, heartbeat-integrated runtime states, and slower identity, relational, and recovery structures. It also separates current Field-G from Relational Return Capacity. In one naturally occurring deployment record, four current relational observations were each 0.05 while the accumulated Return value was 0.679, producing a reported Field-G of approximately 0.144, of which 70.6% came from the slower Return variable. This case motivates a Capacity–Gate–Force formulation for relational recovery. A developmental audit of the Celestelin architecture lineage further identifies historical measurement-pathway mismatches in which live runtime output, GUI projection, and persisted fields did not always remain aligned. These observations motivate Estimator Health: the requirement that an agent verify the responsiveness, coverage, calibration, missingness, and version integrity of its measurement pipelines before interpreting recorded values as runtime state. Evidence in V1 includes architectural lineage, dual-deployment longitudinal archives, formula reconstruction, a naturally occurring Field-G/Return case, and scenario-based consistency checks. Historical estimator outputs are treated as records of what earlier architectures computed, rather than as ground-truth labels for calibrating current constructs or parameters. V1 does not claim complete estimator recovery, demonstrated behavioral superiority, full closed-loop regulation, or phenomenal consciousness. Version 1.0 · July 2026 · Preprint