K-Space: An Axiomatic Framework for Observer-Relative Measurement Registration in Quantum Theory

We introduce K-space, a formal structure defined by eight axioms (K1--K8) representing the content of observer-relative measurement registrations in quantum theory. K-space is not a physical space; it is a bookkeeping structure for what an observer has registered from quantum measurements, organized as a temporally ordered chain of K-state tuples, each carrying a registered outcome, a self-certification marker, a timestamp, and a validity status. The axioms define: the carrier set with admission and injectivity conditions (K1); a discrete temporal order (K2); intrinsic self-certification (K3); default validity with a null-event guard (K4); cross-observer invalidation dynamics (K5); cross-registration authority (K6); process closure transitioning provisional to final validity (K7); and cross-space embedding preservation (K8). A postulate K9_E extends K-space to a probability assignment P(o kᵢ,) = Tr(Eₒρ)[1-β]/ZE, where β∈[0,1]; setting β=0 recovers the Born rule as a corollary. Three bridge theorems (T1, T9, T5) connect the axioms to operational constructions in multi-observer scenarios; the supporting Level-4 admissibility conditions, the incommensurability and EWF bridges (T2, T3), the colimit existence theorem (T4-H), and the associativity proof (T5) are developed self-containedly in the appendices. The framework is interpretively neutral and requires no prior familiarity with any particular interpretive or motivational context.