A Deterministic Information-Geometric Holographic Boundary Framework: Irreversible Dynamics, Compact Projection, and Emergent Temporal Ordering

Version 1.1 presents the complete formulation of a classical, information-geometric holographic boundary framework. Bulk fields are mapped to a finite-capacity, expanding boundary through diffusion, compact projection, geometric scaling, and saturation. The boundary records coarse, irreversible traces of bulk evolution, and temporal ordering emerges from the non-invertible update process rather than from explicit time labels. The construction is scale-independent and does not rely on quantum or gravitational physics.

Version 1.1 includes three supplements:
S1 – full stepwise development and conceptual structure;
S2 – mathematical foundations, operator framework, expanding geometry, and stability;
S3 – discrete and computational formulations, network interpretation, and reconstruction limits.
Together, they provide a complete, self-contained formulation.

Terminology is defined structurally: ‘coarse information’ denotes components that survive smoothing and projection; ‘capacity’ refers to finite distinguishable states per boundary area; ‘record’ and ‘trace’ describe persistent boundary configurations and their irreversible sequence. The compactness of the bulk-to-boundary map implies intrinsic information loss, and only stable low-frequency modes are reconstructible.

No external datasets were generated or analysed.