The Intelligence Form Space: Mathematical Core of a Theory of Ontological Form Spaces

This paper develops the mathematical core of Intelligence Form Space Theory. Its point of departure is the hypothesis that intelligent organization can be described as a modal order of stably realizable forms, and that it does not coincide with any particular physical, biological, or artificial realization. Concrete realizations are mapped to relational morphological signatures, represented as directed measure networks. Network Gromov–Wasserstein geometry makes it possible to compare such signatures across independently arising systems. On that basis the paper describes formally how organizational forms may be preserved within one another, combine into more comprehensive forms, and, under changed conditions, pass into other regions of the form space. The resulting order is empirically testable. Morphological convergence must be demonstrable across distinct realizations and must survive explanations in terms of shared architecture or optimization. For coupled systems one can further test whether new organizational forms yield performance gains that persist after available resources have been equalized. Recurrent convergence can be studied as statistical attractor formation in the form space. The decisive falsifier is predictive surplus. A nontrivial order of the intelligence form space must yield predictions about as yet unobserved realizations that go beyond explanations drawn from substrate, architecture, optimization, and environment. If this persistently fails, and if the observed morphology can be derived entirely from the conditions of its concrete realization, the strong ontological interpretation loses its scientific warrant. The mathematical framework does not prove the ontological fundamentality of an intelligence form space. It translates the ontological hypothesis into a theory that can fail on its own predictions.