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

This paper fixes the observation/protocol rules that determine which summaries arelicensable under IIP and how they are read out from the same fixed backbone. Because interiordegrees of freedom are inaccessible to pointwise readout, only boundary/stable summariescan appear as outputs: the same inaccessibility is read as curvature (holonomy-densitycoupling) in geometric channels, as probability/entropy (pushforward and fiber weight) inmeasure channels, and as particle-like modes (localized effective poles/gaps) in dynamicalreadouts. A representation protocol declares an observational channel Πδobs : X → Yδ(typically irreversible); it induces an observational equivalence ∼Π and an operationalphysical space Xδphys := X/∼Π. Irreversibility is quantified by fiber-weight entropy Sobs(y) =kB log µ (Πδobs)−1(y), stated in renormalized form when needed. The principal-part locking(structural rigidity) claim (“almost one” as a series nickname) refers only to principal-partrigidity under the ABC contract: up to declared equivalences, the derivative-quadraticbackbone is fixed, and with a fixed reading protocol the equation template is fixed as well.Time is treated at the Representation Layer: the primary time instance and signal-conesynchronization are closed in Part VIII; the two-time tracking used here serves only toparameterize projection efficiency and does not fix the conservative time variable. IAScompares representation protocols by induced distinguishability; operational gauge is thefiber-preserving symmetry of the declared readout channel.