The D10Z Resolution of the Novikov Conjecture: Homotopy Invariance as Resonant Eigenmode Stability in the Spiderweb Fabric
Year: 2025
Type: article
Abstract: This paper presents a novel physical resolution of the Novikov Conjecture using the D10Z Mechanics of Infinity, recasting homotopy invariance of higher signatures as a property of resonant eigenmode stability within a structured quantum mesh known as the Spiderweb Fabric (TTAϵ) at scale GM = 10⁻⁵¹ m. Key Reinterpretations: Smooth manifolds are embedded as TTA nodal lattices Tε(M)\mathcal{T}_{\varepsilon}(M)Tε(M). The higher signature σf(M)\sigma_f(M)σf(M) is defined via D10Z Nodal Spectral Forms Φσ(Z)\Phi_{\sigma}(Z)Φσ(Z), reflecting resonance topologies. The Novikov Invariance Theorem (D10Z version) states: f≃g⇒Φσ(f∗Z)=Φσ(g∗Z)f \simeq g \Rightarrow \Phi_{\sigma}(f^*Z) = \Phi_{\sigma}(g^*Z)f≃g⇒Φσ(f∗Z)=Φσ(g∗Z) whenever f,g:M→Bπf, g: M \to B\pif,g:M→Bπ are homotopic maps into a classifying space. The conjecture becomes a resonant invariance law: homotopy deformations do not disrupt the global nodal eigenstate structure of the manifold. Keywords:Novikov Conjecture, D10Z Mechanics, Homotopy Invariance, Higher Signatures, Resonant Topology, Spiderweb Fabric, Nodal Geometry, TTA Mesh, Zn Parameter, Law of Sahana, Spectral Stability.
Authors: Al Thani, Jamil, Cisneros, Grace
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893225965
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