Invariant Temporal Ordering Framework V25/F5: A Foundational Theory of Temporal Succession, Realized Physical Change, the Cosmic Moment Axiom, and Relativistic Measurement

The Invariant Temporal Ordering Framework V25/F5 develops a foundational ontology of time from one common cosmic-stage domain and one fixed, irreversible earlier–later ordering: T_ITOF = (S_C, ≺_C). Time does not denote matter, energy, a field, a force, a coordinate, a metric interval, a proper-time functional, a clock output, or a causal participant in change. It denotes the universal ordering and succession of common cosmic stages. The physical content, magnitude, rate, mechanism, and observability of change remain properties of individual physical systems. The Cosmic Moment Axiom provides the governing link between stage unity and the multiplicity of physical change. At every common later stage, every qualified physical system whose identity is then realized undergoes its own bearer-specific physical change: CMA(s) → ∀A ∈ S_phys(s), PhysReal_A⁺(s). Unity of stage does not imply identical physical states, mechanisms, magnitudes, rates, or observational outcomes. Spatial separation affects signal propagation, records, and access; it does not divide the common cosmic stage or postpone the realization of change in distant systems. Each physical system has an identity-bounded physical history: H_A = (I_A, ≺_C|I_A, X_A). The history begins when the system’s identity becomes physically realized and ends when that identity ceases through transformation into one or more successor systems. The constituents may continue in those successors, each of which possesses its own identity domain and physical history within the same cosmic ordering. V25/F5 also clarifies stability and recurrence. A system may remain stable relative to a declared criterion while continuing to change physically. A later phase may resemble or repeat the physical content of an earlier phase without restoring the earlier cosmic stage or reversing succession. Apparent constancy, equilibrium, periodicity, or a null observational result does not by itself establish complete physical stasis. Observation and measurement are treated as physical processes occurring within the same cosmic ordering. A finite record may support a model-bounded inference concerning change, but it does not become identical with the source stage and does not uniquely identify the exact cosmic stage at which the underlying change began or first became detectable. Non-detection establishes only the limits of the selected variables, sensitivity, sampling, model, and observation window. Clocks are treated as changing physical systems that convert selected cycles, transitions, or signals into standardized numerical records. They do not measure time itself or count cosmic stages. Clock readings, coordinate values, proper-time functionals, redshift relations, and metric quantities remain distinct typed objects. The manuscript directly confronts relativistic temporal ontology. It analyzes Lorentz transformations, proper-time functionals, spacetime metrics, curvature, signal propagation, and clock comparisons without identifying any of those quantities with time itself. The work does not propose a replacement dynamical theory for special relativity, general relativity, quantum theory, thermodynamics, or other domain sciences. Its contribution is foundational: it specifies the ontological type of time, the bearer of physical change, the limits of measurement and representation, and the conditions under which cross-category inferences are or are not warranted. V25/F5 supersedes V24/F4 as the active theoretical formulation. The transition is developmental rather than adversarial. Earlier versions supplied substantial analyses of systems, measurement, clocks, light, relativity, recurrence, and empirical testing. V25 preserves those contributions while replacing system-specific stage domains and pairwise simultaneity constructions with one common cosmic-stage domain governed by the Cosmic Moment Axiom. SCIENTIFIC SCOPE V25/F5 presents:• one common cosmic-stage domain;• one fixed and irreversible cosmic ordering;• the Cosmic Moment Axiom;• universal continuing physical change;• bearer-specific, identity-bounded physical histories;• a disciplined account of stability, recurrence, and apparent stasis;• separation of ontic state from operational description;• a record, measurement, and clock architecture;• analysis of distant records and signal propagation;• direct temporal-ontological confrontation with relativistic quantities;• quantum-stationary and difficult-system test cases;• explicit empirical and type-theoretic accountability.