Block-Universe Bilocal Gravity and Its Operational Equivalent: A Unified Framework for Future-Mass Projection Theory

We present a comprehensive and pedagogical formulation of Future-Mass Projection (FMP) gravity within two mathematically equivalent but conceptually distinct perspectives: (i) the block-universe perspective, where spacetime exists as a complete four-dimensional geometric entity and gravity responds to a covariant bilocal functional of baryonic stress-energy across a finite future domain, and (ii) the operational (in-time) perspective, where an observer computes identical effects using only present-time fields, their derivatives, and appropriate boundary conditions via the Schwinger-Keldysh closed-time-path formalism. We demonstrate that the apparent "future dependence'' in the block-universe formulation does not violate causality but instead reflects specific boundary conditions analogous to Wheeler-Feynman absorber theory in electrodynamics. The bilocal kernel is rigorously constructed through worldline projection using matter flow, yielding a mathematically tractable one-dimensional convolution along material worldlines. Central to the framework are the zero-DC condition (ensuring background neutrality), finite horizon ∇T ∼ 3-4 Gyr (providing a natural cutoff), and diffeomorphism invariance (guaranteeing covariant conservation \( \nabla_\mu T^{\mu\nu}_{\mathrm{eff}} = 0 \). We derive the explicit kernel form, compute its moments, and establish the equivalence theorem connecting both perspectives under well-defined validity domains. The framework offers several theoretical advantages over the particle dark matter paradigm: it eliminates the need for undetected exotic particles, provides a unified explanation across galactic and cosmological scales with minimal free parameters (4 fundamental parameters versus 6+ for ΛCDM with dark matter), and makes falsifiable predictions testable with current surveys. We discuss observational constraints including gravitational wave speed \( (|c^2_{\mathrm{GW}} - 1| \lesssim 10^{-76}) \), PPN parameters \( (|\gamma - 1| \lesssim 10^{-25}) \), and gravitational slip \( (\Phi = \Psi \) for the trace-adjusted projector). This work synthesizes developments across multiple FMP formulations, presenting a reader-friendly exposition suitable for researchers entering the field.