Einstein-Karahan Framework v130 — THE TWIN-SCALAR DARK-MATTER CANDIDATE: Exact Two-Pole Gravity, Cosmological Status, and a Complete Pre-Hardware Falsification Architecture

Version 130 consolidates the Einstein-Karahan Framework at the point where its Twin-Scalar sector becomes a sharply defined, experimentally falsifiable candidate for physics associated with dark matter. The framework predicts a constrained two-pole gravitational structure with linked residues, masses, interaction ranges, and a fixed relation between the light and heavy scalar sectors once the branch parameter and one absolute scale are specified. This structure is not introduced by fitting an arbitrary dark-matter profile. Instead, the observable Twin-Scalar signature follows from the internal branch relations of the theory and yields correlated short- and long-range predictions that can be tested without independently refitting each channel. The dark-matter interpretation is treated conservatively. The heavy Twin-Scalar mode remains a mathematically viable coherent dark-matter candidate, but a fully source-native cosmological production and abundance mechanism has not yet been derived. In particular, the previously investigated thermal and high-temperature reset branches do not by themselves provide a parameter-free origin of the required late-time abundance. The cosmological dark-matter identification therefore remains conditional rather than experimentally established. The central advance of v130 is the completion of the corresponding experimental falsification architecture. The PSD-3 / Z1-Z20 program develops a Poisson-null, Yukawa-active source concept, dual-scale short- and long-range channels, deterministic finite-geometry kernels, an independent branch-following range-null bridge, direct Newtonian m=3 fabrication metrology, reaction-rotor gravity control, electrostatic and patch-field witnesses, bearing and motor-transfer gates, runout and current monitoring, and a correlation-robust global error budget. The final pre-hardware design is frozen under explicit fail-closed rules. Newtonian leakage, electrostatic coupling, mechanical transfer, current harmonics, runout, source fabrication error, and other same-irrep backgrounds are not assigned independent ad hoc tolerances; they must satisfy one shared preregistered acceptance structure before any science result can be released. No Twin-Scalar particle, fifth force, or dark-matter signal is claimed to have been detected. Version 130 instead establishes a concrete theoretical target and a finite hardware acceptance protocol designed to force the surviving Twin-Scalar hypothesis to confront experiment with a clear pass-or-fail outcome.