Lossless Functional Compression: Cross-Domain Convergence of Four Functional Roles

This paper develops a compression procedure for identifying the minimal functional roles on which stable organization depends across heterogeneous domains. Beginning from a recurrent candidate set, the procedure subjects each candidate to sustained explanatory pressure along three audit dimensions: functional, typing, and perspective. Candidates whose full functional role can be reconstructed from existing structure are relocated to the derived layer; those that cannot are retained. Compression proceeds until no further absorption paths remain. The procedure initially converges on three roles—State, Relation, and Constraint. A self-audit of this triadic kernel reveals that differentiability has been silently absorbed into State, constituting a hidden compression. Kernel competition is thereby reopened, and Attribute emerges as an independently irreducible role. Final closure is reached on four functionally non-interchangeable roles: State, Attribute, Relation, and Constraint (S.A.R.C.). Quantum stress-testing tightens the definitions of these roles without expanding them, and cross-domain verification across six heterogeneous domains yields no case sustaining a further primitive role. The result is a cross-domain convergence on four functional roles, established as the point at which compression ceases to proceed.