Quadratic Scaling of Closure Costs in Bounded Systems: Constraint- Reconciliation with Empirical Support

A paper on neuromorphic hardware efficiency and a study of photosynthetic light-harvesting seem unrelated. So do seismic ruptures, ocean eddies, and magnetism. Yet across these radically independent physical systems, the same scaling relationship emerges: relational complexity curves upward quadratically, not linearly. This paper proposes that the pattern is not coincidence but consequence—that closure (mandatory compression of relational information under bounded capacity) is a universal structural principle through which any finite system must manage the apparently incompatible demands of Shannon’s measurability, Landauer’s thermodynamic cost, Kolmogorov’s irreducibility, Wheeler’s information-physics coupling, and Maxwell’s constraints. Using Intel Loihi 2 neuromorphic architecture calibrated to empirical performance data, the work demonstrates that R ∝ C² emerges under full relational tracking (R² = 0.9999924) and collapses to linearity when interaction tracking is artificially suppressed, isolating pairwise combinatorics as the causal mechanism. The scaling signature appears reproducible, falsifiable, and substrate-independent—suggesting closure as a testable structural operation fundamental to how bounded systems reconcile multiple information-theoretic constraints simultaneously.