RHD: A Centrifugally Recursive Forcing Centrum: A Finite-Stage Modular Selector, Recoverable Residual, and a Density-Cone Obstruction

Title: RHD: A Centrifugally Recursive Forcing Centrum: A Finite-Stage Modular Selector, Recoverable Residual, and a Density-Cone Obstruction Description / Abstract: This mathematical paper introduces a finite-stage recursive forcing centrum within Relational Horizon Dynamics (RHD). Alternating dyadic tiling, singular-measure fusion, and density-constrained selection, it constructs a completely positive, idempotent modular selector at an exact four-index resonance. Nonselected components are preserved through an explicitly recoverable residual. The analysis establishes a nonzero finite-dimensional resonant exchange and identifies limitations of modular averaging and singular-measure convergence. It distinguishes an exact finite-stage operator construction from the unresolved forcing-to-CAR and infinite-depth physical representation problems. Keywords: Relational Horizon Dynamics; Cohen forcing; modular theory; CAR algebra; density constraints; recoverable residual; operator algebras. Thue author of the framework has traumatic brain injuries, tirgeminal, neuraligia, and double vision, and usues AI reading/collaborative assist: in this case GPT.