The Carrier Grammar Unification

We present a carrier-free separator grammar for complex systems: a divider set that partitions regimes in a chosen analysis space, an optional Z2-type involution that induces an even/odd diagnostic split, and a stability criterion expressed as local hyperbolicity or an appropriate proxy. Cross-domain comparisons are treated strictly as carrier languages rather than claims of identical microphysics. A carrier is admitted only if it preserves divider topology under modest analysis-lens perturbations, supports a no-peeking construction of the pairing involution, and fails under at least one declared null transformation; these veto conditions are non-negotiable and define the operational meaning of “invariance” in this work. Within this framework we formalize the universal local normal form of saddle-driven separation on two-dimensional reductions: a hyperbolic critical structure generates a four-sector partition with a separatrix skeleton that extends to a global divider graph separating pocket/basin components. When a Z2 pocket-exchange action is present, we define a window pairing involution and construct a parity certificate consisting of an iota-even diagnostic magnitude and an iota-odd marker that inverts under the pairing. The certificate is evaluated via residuals and acceptance thresholds determined from replicate uncertainty, and it is rejected if it is lens-fragile, null-insensitive, or pairing-tuned. We then show how the same separator grammar can be instantiated in distinct representation spaces without changing its falsifiable content: gradient/landscape reductions (drift-null ridges in effective potentials), fluid-slice carriers (streamfunction separatrices and transport barriers), parameter-space carriers (admissibility boundaries in spectral portraits), and iterated-map carriers (invariant basin boundaries with dendritic recursion). These instantiations are presented as optional exemplars whose role is to demonstrate translation constraints, not to assert shared microphysics. The result is a disciplined unification tool: a reusable, veto-admitted diagnostic grammar for separators, parity hinges, and stability across heterogeneous systems. This manuscript advances a carrier-free separator grammar: a divider set that partitions regimes in an analysis space, an optional Z2-type involution that induces an even/odd diagnostic split, and a stability criterion expressed as local hyperbolicity or its appropriate proxy. Cross-domain references are treated as carrier languages rather than claims of identical microphysics. A proposed carrier is admitted only if it preserves the divider topology under modest lens perturbations, supports a no-peeking involution test for the parity split when an involution is asserted, and fails under at least one declared null transformation.