Structure by Exclusion: Constraint, Zero and the Persistence of Physical States

We investigate the emergence of physical structure as the fixed point of iterative constraint rather than as the result of unconstrained dynamics. Central to this work is the idea that zero is not a physical state but a boundary condition that defines exclusion. Physical states are modelled as elements of a state space subjected to repeated filtering by constraints, where violation corresponds to elimination through the zero boundary and removal from the survivor set. Multiple computational tests instantiate this framework across classical and physically motivated systems. Coarse-graining is shown to impose a measurable free-energy cost, demonstrating that compression of microscopic detail is not thermodynamically neutral. Relevance filtering under coarse-graining removes information that does not contribute to macroscopic persistence, yielding a reduced but structured state space. Iterative application of constraint produces survivor sets that converge toward stable residual structures. Entropy measurements before and after constraint reveal a consistent reduction in Shannon entropy associated with survival under exclusion rather than optimisation. Application of the same framework to a simplified vacuum landscape shows that stability and survival constraints select a narrow distribution of long-lived states compatible with observed physical scales. Across all tests, physical structure is revealed through exclusion rather than fine-tuning: states are not driven toward zero as a physical destination, but are eliminated upon crossing the zero boundary, leaving a coherent survivor set that persists under energetic, entropic and temporal constraints. In this view, zero functions as a limiting boundary that defines what cannot exist, while physical reality corresponds to what remains.