The Minimal Morphological Basis for Admissible Persistence

This paper formalizes BB6 as the minimal morphological sufficiency condition required for any system to support non-arbitrary existence, internal differentiation, and persistence under perturbation. BB6 is not a physical constant, computational bound, or dynamical model. It is a pre-dynamical structural criterion: a necessary and sufficient condition that must be satisfied before equations of motion, measurements, algorithms, or observers can be meaningfully defined. The framework shows that any empirically resolvable system must admit: Three independent axes of distinguishability, Two directional orientations per axis enabling orderability, and A closure constraint bounding admissible continuation. Together these yield six admissible degrees of freedom under closure, the minimal configuration space in which exclusion, collapse detection, and persistent identity are possible. The paper demonstrates that BB6 operates implicitly across physics (phase space and identity), computation (halting and resolvability), biology (morphogenesis and cellular closure), cognition (object permanence and perceptual stability), and geometry (projection and construction constraints). It explains why these domains function at all, without modifying their internal dynamics. Formal definitions, minimality theorems, and a projection-operator formulation are provided, alongside concrete empirical anchors (e.g., phase space, droplet stability, control systems, and projective geometry). Explicit falsification criteria are stated. BB6 does not compete with existing theories; it precedes them logically. It explains the structural conditions under which laws, measurements, and identities become admissible in the first place. 3. Keywords by Domain Foundational / Cross-Domain admissibility morphological sufficiency structural persistence closure conditions empirical resolvability minimal configuration space pre-dynamical constraints Physics phase space identity under constraint photon spheres horizons collapse detection bounded dynamics Mathematics dimensional sufficiency rank conditions projection operators topology orderability constraint spaces Computation halting conditions bounded recursion decidability state differentiation minimal grammar Biology morphogenesis cellular closure polarity boundary formation stability under perturbation Cognition object permanence perceptual stability differentiation closure failure hallucination vs persistence Systems & Control boundedness stability criteria input-to-state stability regulation exclusion detection