Specular Field Theory: Conceptual Framework and Linear Regime Prediction

Abstract

The Specular Field Theory (SFT) introduces a minimal geometric extension in which time is endowed with an independent informational geometry, sourced by a scalar coherence field. Informational behaviour is not imposed through system-specific dynamical assumptions, but emerges as a consequence of temporal curvature. The theory identifies three dynamical regimes: a Linear Regime, with linear-response behaviour analogous to fidelity decay under small perturbations; a Critical Scaling Regime, marking the approach to an operational boundary of the temporal geometry; and a Coherent Regime. In the Linear Regime, the SFT yields a falsifiable, parameter-free prediction for the ratio of scrambling exponents between two circuit configurations, testable on current quantum hardware with minimal resources. The Critical Scaling Regime remains an open direction for collaborative investigation. This document establishes the author's priority and paternity over the foundational concepts and structural framework of the SFT, while reserving certain mathematical formulations for collaborative development. It is intended as a conceptual foundation for future research partnerships in informational dynamics, temporal geometry, and quantum scrambling.