P29 — Uniqueness of the Probabilistic Measure in Coherent Informational Dynamics

This paper is part of a coherent research program developing an informationally emergent physical framework. P29 addresses the problem of the uniqueness of the probabilistic measure arising in coherent informational dynamics. Building on the emergence of probabilistic structure established in earlier papers, the analysis shows that a unique and consistent probability measure is selected by coherence, stability, and invariance requirements of the informational framework. The paper clarifies why alternative probabilistic prescriptions are excluded and demonstrates how the effective probability measure emerges as a structural necessity rather than an arbitrary choice. This result provides a key consistency condition for the quantum-like probabilistic behavior derived within the framework. While this paper can be read independently, its full significance becomes clear only within the complete sequence of papers (P00–P32). The reference entry for the full framework, including priority timestamp and complete context, is:DOI: 10.5281/zenodo.18369063