From Proper Time to Update Index: A Pre-Metric Construction of Time in Finite-Trace Systems

This paper clarifies the relationship between Special and General Relativity and the Bottleneck-Normalized Computational Theory (BNCT). While relativity treats time as a continuous metric coordinate embedded in a spacetime manifold, BNCT identifies time as a monotone index generated by irreversible updates under finite trace capacity. We demonstrate that BNCT does not contradict the relativistic framework. Instead, it formalizes the generative layer of time upon which the relativistic representation layer remains silent. By introducing a register-determined reconstruction assumption, we prove the necessity of structural dissipation (slip) in any finite system. BNCT does not derive spacetime metrics; it specifies pre-metric generative constraints under finite trace capacity. This layered interpretation resolves the apparent tension between the block-universe symmetry of relativity and the experienced unidirectionality of time, without modifying relativistic field equations or introducing observer-dependent assumptions.