A Temporal-Integral Constraint Framework for Systemic Coherence Under Uncertainty

This work introduces the Voigtian Field, a domain-independent temporal constraint framework for analyzing systemic viability under uncertainty. The Voigtian Field formalizes how temporal cost accumulates, how systemic coherence decays, and how response dynamics become asymmetric in complex systems operating under sustained load. Unlike traditional models based on instantaneous states, thresholds, or predictive forecasting, this framework reconstructs system posture exclusively from temporal behavior, without requiring semantic interpretation of signals or domain-specific assumptions. A central contribution of this work is the treatment of time as an active structural variable, rather than a passive index. By integrating temporal cost over persistence, the framework reveals an operational arrow of time that governs irreversibility, hysteresis, and loss of recoverability independently of thermodynamic entropy. From this formulation, a small set of emergent temporal regimes naturally arises — Stable, Gas, Torpor, and Nano — which precede observable failure and constrain the set of viable system trajectories. These regimes do not predict outcomes; instead, they characterize structural exhaustion and recovery feasibility. The Voigtian Field is scale-invariant and applicable across socio-technical, biological, ecological, organizational, and computational systems. It enables early detection of latent structural stress, coherence cliffs, and regime drift long before catastrophic transitions occur. This work is intended as a foundational theoretical contribution. It does not replace domain-specific models, nor does it prescribe control strategies. Instead, it introduces a new class of temporal constraint fields, in which long-term system viability is governed by accumulated time rather than instantaneous performance or energy availability. Mathematical formulations referenced in the text are consolidated in visual appendices to preserve conceptual clarity and accessibility.