The Structural Incompatibility Theorem A Computationally Reducible Proof That Composition of Correct Structures Necessarily Produces Incompatibility

We prove that any system of sufficiently many non-trivially coupled computational struc-
tures, each individually correct, necessarily loses full structural compatibility. The proof is
computationally reducible: every deduction is a finite step from the preceding step and the
stated axioms, and the entire argument has been compiled and verified by machine. Two
axioms are required, each independently established: thermodynamic irreversibility (Lan-
dauer) and undecidability of semantic properties (Rice). Non-trivial coupling is definitional.
The key structural result is an exact counting bound over vertex-disjoint coupling edges
(a matching), where independence holds by construction rather than by assumption. In
any system where matching size and coupling strength exceed a computable threshold, the
compatible subspace collapses to empty. The monotonic suppression of the Entropic Lattice
Ontology’s accessibility field emerges as a corollary, not a premise