OTF I: Physical Admissibility, Gluing Defects, and Reflexive Stability

This paper is the mathematical core of a three-paper programme around the Ontological Totality Functional (OTF). Its claim is not that physics needs one more totalizing action, but that it lacks a rigorous language for physical admissibility: the conditions under which a configuration can count as physically stable rather than merely mathematically specifiable. The paper recasts the OTF accordingly. The backbone is a local-to-global construction on a finite 2-complex of contexts. Local states, pointer subalgebras, and quantum channels are assigned to vertices and edges. Two defect terms measure admissibility: the gluing defect, defined from failures of triangular composition of channels in the diamond norm, and the noetic defect, defined from distance to a pointer subalgebra via conditional expectations. Together with a sector-dependent effective action, they define an admissibility functional whose minimizers form the admissible set at cutoff Lambda. Four controlled results are proved in finite-dimensional truncations: existence of minimizers, a zero-defect criterion for the noetic sector, an observable bound implying approximate classicality when the noetic defect is small, and a global path-consistency theorem showing that local triangle defects bound route dependence across any filled disk in the context complex. A continuum scalar surrogate for coarse-grained coherence defects is also introduced, and its effective stress tensor is shown to be conserved on shell. Finally, the paper defines the central target of the programme: mixed category-algebra-scale fixed points, namely compatible families of admissible minimizers across cutoffs. This record is part of the Ontological Totality Functional (OTF) series. Companion works include OTF II, OTF III, OTF IV, and the OTF Master Edition. Companion records in the OTF series:OTF II — DOI: 10.5281/zenodo.19075284OTF IV — DOI: 10.5281/zenodo.19076867OTF Master Edition — DOI: 10.5281/zenodo.19077303