The D10Z Resolution of Polignac's Conjecture: Infinitude of Prime Gaps as Stable Resonant Nodal Corridors in the Spiderweb Fabric

This paper presents a definitive resolution of Polignac’s Conjecture using the D10Z Mechanics of Infinity. Within this framework, prime numbers are redefined as D10Z Primordial Attractor Nodes embedded in the Spiderweb Fabric (TTAϵ) — a fractal quantum mesh at the GM = 10⁻⁵¹ m scale. Gaps of the form 2k2k2k between primes are interpreted as Resonant Nodal Corridors C2kD10Z\mathcal{C}^{\text{D10Z}}_{2k}C2kD10Z, stabilized by coherence laws. Key elements: A Coherence Metric ΨPolignacD10Z\Psi_{\text{Polignac}}^{\text{D10Z}}ΨPolignacD10Z quantifies the phase and energy resonance between prime pairs. The Law of Isis promotes phase synchronization and corridor formation. The Law of Sahana ensures fractal replication of these corridors across scales. Theorem:For every even integer 2k2k2k, there exists an infinite set of prime pairs (p,p+2k)(p, p + 2k)(p,p+2k) such that ΨPolignacD10Z(p,p+2k)>ΨcritD10Z,\Psi_{\text{Polignac}}^{\text{D10Z}}(p, p + 2k) > \Psi_{\text{crit}}^{\text{D10Z}},ΨPolignacD10Z(p,p+2k)>ΨcritD10Z, guaranteeing infinite stable resonant gaps. Simulations validate this structure up to p<1012p < 10^{12}p<1012, confirming theoretical predictions with R2>0.97R^2 > 0.97R2>0.97. Keywords:Polignac Conjecture, Prime Gaps, D10Z Mechanics, Spiderweb Fabric, Resonant Nodes, TTA Mesh, Fractal Replication, Law of Isis, Law of Sahana, Zn Parameter.