Variational Backbone and Regime Closures IV: Observational Projection and Protocol Theorems Fiber-volume entropy, two-time bookkeeping, and dark-sector interpretation

This paper fixes the Representation Layer protocol template that connects a fixed backbone E and a chosen reading (R1/R2/R3) to observation and data. A representation protocoldeclares an observational channel Πδobs : X → Yδ(typically irreversible); it induces an observational equivalence ∼Π and an operational physical space Xδphys := X/∼Π. Irreversibility isquantified by fiber-weight entropy Sobs(y) = kB log µ(Πδobs)−1(y), stated in renormalizedform when needed. The “almost one” claim refers only to principal-part rigidity under theABC contract: up to declared equivalences, the derivative-quadratic backbone is fixed, andwith a fixed reading protocol the equation template is fixed as well. Time is treated at theRepresentation Layer: the primary time instance and signal-cone synchronization are closedin Part VIII; the two-time bookkeeping used here serves only to parameterize projectionefficiency and does not fix the conservative time variable. IAS compares representationprotocols by induced distinguishability; operational gauge is the fiber-preserving symmetryof the declared readout channel.