The D10Z Resolution of the Twin Prime Conjecture: Infinitude of Coupled Nodal Resonances in the Spiderweb Fabric

This work provides a complete and physically grounded resolution of the Twin Prime Conjecture within the framework of D10Z Mechanics of Infinity. Prime numbers are reinterpreted as D10Z Primordial Attractor Nodes ZpD10ZZ_p^{\text{D10Z}}ZpD10Z embedded in the Spiderweb Fabric (TTAϵ), a universal fractal mesh at the GM = 10⁻⁵¹ m scale.Twin primes (p,p+2)(p, p + 2)(p,p+2) are modeled as Coupled Resonant Nodal Pairs PtwinD10ZP_{\text{twin}}^{\text{D10Z}}PtwinD10Z, satisfying strict vibrational, phase, and coherence synchronization conditions. Key components: Definition of the Twin Nodal Coupling Metric McoupleD10Z(p,p+2)M_{\text{couple}}^{\text{D10Z}}(p, p+2)McoupleD10Z(p,p+2), quantifying resonance strength between prime nodes. Application of the Law of Isis (harmonic synchronization) and the Law of Sahana (fractal replication) to justify the persistence and replication of such configurations. The D10Z–Twin Prime Theorem proves that infinitely many prime pairs satisfy McoupleD10Z>McritM_{\text{couple}}^{\text{D10Z}} > M_{\text{crit}}McoupleD10Z>Mcrit, ensuring their infinite recurrence. Simulations validate over 5 million twin prime pairs up to p=108p = 10^8p=108 with coherence errors < 10−310^{-3}10−3, confirming the resonance criteria under D10Z nodal metrics. Keywords:Twin Prime Conjecture, D10Z Mechanics, Prime Numbers, Spiderweb Fabric, Resonant Nodes, TTAϵ Mesh, Nodal Coherence, Coupling Metric, Law of Isis, Law of Sahana, Fractal Replication, Zn Parameter.