Metaformalism and Meta-Existence: Fractal Structure, Bidirectional Dynamics, and Geometric Operators of Phase Selection

We introduce metaformalism as an operational theoretical framework in which mathematical constructions are treated as experiments performed within a formal reality. We show that a stable, time-directed reality cannot emerge either from complete symmetry or from unrestricted chimeric variability; instead, it necessarily requires generation, selection, and palindromic stabilization. Within this framework, we define palindromic and chimeric operators, introduce phase-selection operators with geometric realization, and formalize integral operators as aggregations over families of admissible projections. In particular, Platonic solids are interpreted as eidetic geometric phase-selection operators enforcing minimal palindromically stable symmetry constraints on a meta-structure and selecting admissible regimes of realization. The metaformal apparatus is tested through a series of mathematical “experiments,” including Euclidean geometry, the fundamental theorem of arithmetic, diffraction and interference as phase-boundary effects, integral and path-integral formalisms, and discrete dynamics exemplified by the Collatz process. We demonstrate that the unresolved components of the Riemann hypothesis and the Goldbach conjecture are extra-metaformal, as they pertain to realized quantitative structures and thus remain within the domain of classical mathematics. The role of metaformalism is to expose their structural necessity, not to enforce technical closure. We further argue that the visible world and human cognition are themselves metaformal processes, which explains the principled intelligibility of reality. Metaformalism substantially expands the role of “paper experiments,” enhancing the quality and scope of theoretical investigation. A program of subsequent works is outlined, wherein symmetric tensor and spin operators arise as derived representations of phase-selection operators at the level of physical realization.