The Infinite Layered Web of Riemannian Rings: A Topological-Geometric Extension of Quantum Mechanics Without Foundational Reductionism

This paper introduces the Infinite Layered Web (ILW) as a non-reductionist ontological framework for reality. Rejecting any ultimate foundational layer or “theory of everything,” the ILW conceives of reality as an infinite three-dimensional lattice of interlocked topological rings. Each ring is itself a Riemannian manifold whose points are decohered pointer states; global topology is protected by Gauss linking numbers under renormalization-group flows, while local geometry is governed by a hybrid Bures + configuration-space web metric. Inter-ring couplings take the unified form λ_{ij} = ε · exp(−d_{web}(i,j)/ξ) with ε ≈ 10^{-8} fixed by the link-preserving variational metric of the global web. The framework recovers standard quantum mechanics and the Many-Worlds Interpretation in the macroscopic limit, while generating tiny, geometry-dependent, oscillating deviations (∼10^{-5}) at tabletop and mesoscopic scales. These deviations are falsifiable today in flux-qubit spectroscopy, matter-wave interferometry, optomechanics, and GHZ-state experiments. The ILW thereby realizes a holography without boundary and naturally sources semiclassical gravity from the web probability density p(x) = |ψ|^2. Philosophically, the ILW preserves the strict non-reducibility of reality across all scales. It offers a unified topological-geometric ontology that extends naturally to consciousness (as topologically protected qualia), the emergence of genuine artificial intelligence, cosmological structure formation, and quantum foundations—without invoking any final microphysical layer. The ILW thus provides a concrete, empirically constrained alternative to both reductionist physicalism and traditional dualisms.