The Time-Symmetric Parity Constraint IV : Discriminator observables in cosmology – What would falsify a spacetime structure?

Summary – Contemporary observational cosmology has achieved remarkable precision by refining parameters within a shared spacetime framework. However, many quantities treated as observational tests function primarily as internal consistency checks, rather than as probes capable of distinguishing between fundamentally different spacetime structures. As a result, certain foundational assumptions, including the operational universality of cosmic time, the manner in which isotropy is tested, and the attribution of geometric effects to matter, are rarely interrogated empirically. This paper introduces the concept of discriminator observables: empirically meaningful questions whose answers would bear directly on global spacetime structure, rather than on parameter values within a fixed cosmological ansatz. The emphasis is methodological rather than model-specific. No new data are presented, and no attempt is made to fit existing observations. Instead, the paper asks which observables, if posed cleanly and analysed without enforcing equivalence assumptions a priori, could genuinely falsify an assumed spacetime structure rather than be absorbed into parameter freedom or extended phenomenology. Using the Time-Symmetric Parity Constraint as a motivating example, a hierarchy of six discriminator observables is identified. The primary stress test concerns the tracer-independence of cosmic time inferred from physically distinct clocks. Secondary and tertiary discriminators probe independent consequences of global structure through the redshift evolution of anisotropy, gravitational lensing interpreted as geometry rather than mass, environmental time sampling in cosmic voids, entropy patterning, and statistical time-reversal asymmetries at the population level. The paper clarifies what falsification would look like in practice and emphasises that clean null results are as informative as positive detections. By distinguishing structural discrimination from parameter sensitivity, the work aims to broaden the empirical scope of observational cosmology and to make explicit which of its most basic assumptions are empirical claims rather than operational necessities. The entire compendium of TSPC research papers is now to be found at https://spacetimeparity.eu/ Revisions v.2 Identifier added