Regime, Point of Departure, and Structural Coherence

Persistent divergences in the interpretation of complex mathematical structures rarely arise from local failures. They generally derive from the implicit adoption of distinct regimes of observation. This text records a structural framework in which the choice of the point of departure determines whether coherence is treated as an asymptotic outcome or as a condition of existence. The discussion is formulated in operational terms, with reference to the finite interval [1, 2] and to the role of 1/2 as a regime threshold. The document makes explicit presuppositions usually left implicit and delineates the functional consequences of different observational regimes.