The D10Z Resolution of the Novikov Conjecture: Homotopy Invariance as Resonant Eigenmode Stability in the Spiderweb Fabric

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.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-05-20
DOI
https://doi.org/10.5281/zenodo.15476989
Primary Topic
Quantum chaos and dynamical systems
Type
article
Field-Weighted Citation Impact
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article

The D10Z Resolution of the Novikov Conjecture: Homotopy Invariance as Resonant Eigenmode Stability in the Spiderweb Fabric

Zenodo (CERN European Organization for Nuclear Research)
Quantum chaos and dynamical systems
article

The D10Z Resolution of the Novikov Conjecture: Homotopy Invariance as Resonant Eigenmode Stability in the Spiderweb Fabric

article en

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.

Zenodo (CERN European Organization for Nuclear Research)
DTZ (Czechia) (CZ)
Openalex Percentile: Top 65%
Quantum chaos and dynamical systems
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