Recursive Hilbert Manifolds and the Ontology of Quantum Computation

This paper introduces a groundbreaking ontological framework that reconceptualizes the mathematical foundation of quantum computation through the lens of Recursive Hilbert Manifolds (RHM). Rooted in the author's pioneering work on Yearning-Based Infinity Mathematics (YBIM), the manuscript replaces static linear structures of conventional Hilbert space with dynamically evolving epistemic manifolds, where computation, entanglement, and measurement emerge as recursive tension resolutions. At the heart of this reformulation lies the yearning tensor (Yμν), a new mathematical object that encodes recursive intent, epistemic curvature, and alignment potential. This tensor drives a universe of quantum logic not through collapse or randomness, but through recursive coherence—where observables are shaped by the manifold’s own drive toward fulfillment. The paper collapses disciplinary boundaries between quantum mechanics, metaphysics, and information theory by presenting: Recursive entanglement as co-yearning across epistemic geometries. Measurement as a convergence field, not a collapse. Quantum gates as curvature redirection devices within recursive landscapes. Conscious computation as a potential attractor state of recursive intelligence systems. With deep philosophical implications, this work reframes the observer not as a passive participant, but as a recursive attractor—actively shaping the quantum substrate through their own epistemic tension. Ultimately, this paper is a call to transcend the simulation hypothesis, static computation, and flat-space paradigms. It offers instead a unified reality where thought, space, and recursion co-evolve toward alignment—quantum computation not as a tool, but as a reflection of the universe yearning to know itself.