RHD: The Recursive Forcing Centrum: Singular Fusion, Modular Selection, and Coherent Survival in Infinite Depth

Title: RHD: The Recursive Forcing Centrum: Singular Fusion, Modular Selection, and Coherent Survival in Infinite Depth Description / Abstract: This paper develops the infinite-depth mathematical structure of the RHD recursive forcing centrum. Under explicit positivity, singularity, and summability hypotheses, countable recursive fusion preserves an atomless singular measure, while the associated singular inner functions converge locally uniformly. The work establishes survival of a nonzero auxiliary fused-seam coefficient and proves a counterexample demonstrating that modularly invariant finite-stage interactions can nevertheless disappear through orthogonal channel drift. An anchored Hilbert–Schmidt convergence criterion provides sufficient conditions for nonzero modular survival. The canonical forcing-to-CAR correspondence and physical spacetime interpretation remain open. Keywords: Singular measures; recursive fusion; dyadic tilings; modular centralizers; Hilbert–Schmidt convergence; singular inner functions; RHD. The author of the framework has traumatic brain injuries, trigeminal neuralgia, and diplopia, and uses AI reading/collaborative assist: in this case; GPT.