Modal Triplet Theory: Admissibility, Encodings, and the Structure of Physical Description

Modal Triplet Theory (MTT) is a framework in which physical description is conditioned on stability, boundedness, and spectral separation rather than assumed to be globally valid. In this approach, spacetime dynamics, quantum theory, gravity, and probability arise as effective descriptions defined only on admissible regions of a higher-dimensional configuration space. This paper serves as the canonical structural map of the MTT corpus. It introduces the admissibility-first viewpoint, defines the core objects and standing assumptions of the theory, and organizes all results into a consistent classification of layers, encodings, boundary regimes, shadow bridges, and execution programs. Rather than reproducing technical proofs, it explains what is proved where, how different papers depend on one another, and which claims are exact, bounded, or execution-level. The paper distinguishes between foundational results, reconstruction results, effective encodings, and boundary phenomena such as measurement, irreversibility, horizons, and undecidability. It formalizes the notion of shadow bridges connecting different theoretical frameworks and provides a unified interpretation of why multiple approaches to quantum gravity, quantum foundations, and effective field theory converge on similar constraints. All papers in the MTT corpus are explicitly classified and referenced, making this work the authoritative index and scope guide for the theory. This document is intended as the entry point for readers, reviewers, and researchers seeking to understand the structure, scope, and status of Modal Triplet Theory without ambiguity or overclaim.