The Necessity and Uniqueness of an Informational Feasibility Constraint in Realizable State Spaces

Persistent structure is empirically observed across a wide range of physical and biological systems, including cosmology, gravitational lensing, large-scale matter distributions, and biological regulatory networks. In each case, structured informational organization survives transformations—state-space expansion, coarse-graining, dimensional projection, and invertible reparameterization—that, under entropy-only or purely dynamical expectations, should generically erase or destabilize such structure.

This work establishes a necessity and uniqueness result for an informational feasibility constraint governing realizable state spaces. Rather than proposing a new dynamical law or microscopic mechanism, the paper adopts a deliberately structural perspective: given the empirically observed persistence of structure, what class of constraints is required to delimit which states are realizable as persistent configurations?

We identify a set of non-negotiable admissibility requirements imposed directly by observation and formalize them independently of representation, dynamics, or domain. All known alternative explanatory classes—including entropy-only descriptions, dynamical fine-tuning, symmetry-based arguments, algorithmic complexity measures, anthropic selection effects, and hidden-variable microphysical explanations—are shown to violate at least one required condition. In particular, such alternatives fail to simultaneously account for invariance under projection, representation independence, domain generality, and controlled failure in explicitly unregulated systems.

A projection-only empirical test with strict null controls is included to isolate dimensional projection as a decisive admissibility constraint. This demonstration shows that structured systems retain a non-zero informational lower bound under non-invertible projection, while null controls collapse under the same operator, ruling out preprocessing, spectral, or metric-specific artifacts.

We show that the only surviving explanatory class is a non-dynamical feasibility constraint enforcing a lower bound on realizable informational entropy. This constraint is not an empirical fit, not a dynamical law, and not tied to any specific physical substrate. Any admissible alternative formulation is shown to be mathematically equivalent to this constraint, differing only in representation rather than substance.

The result establishes information as an ontologically real constraint on realizability and provides a foundational basis for understanding why entropy-only frameworks are insufficient to characterize persistent structure. The framework is explicitly falsifiable and admits controlled failure in noise-dominated or unregulated systems. Subsequent work will explore domain-specific implementations and implications, but the present contribution is intentionally foundational.