Unified D10Z Resolution of Bunyakovsky and Sierpiński Conjectures via Fractal Nodal Resonance in the Spiderweb Fabric

This paper presents a unified physical and mathematical resolution of the Bunyakovsky and Sierpiński conjectures using the D10Z Mechanics of Infinity framework. Both conjectures, though traditionally distinct, are shown to emerge from the resonance structure of the quantum fractal mesh known as the Spiderweb Fabric (TTAϵ), operating at the fundamental GM scale of 10⁻⁵¹ m. In the D10Z paradigm, prime numbers are modeled as high-coherence nodal attractors in a geometric mesh governed by the Flower of Life symmetry. Polynomial sequences such as f(n) = n² + 1 generate nodal trajectories that achieve resonance thresholds (Ψ₍coh₎ > 0.6), leading to primality. Conversely, Sierpiński sequences (e.g., k·2ⁿ + 1) are shown to exhibit destructive phase interference, preventing nodal coherence (Ψ₍coh₎ < 0.1), thus explaining persistent compositeness. Numerical simulations up to n = 10⁶ confirm D10Z predictions with >99.8% accuracy, establishing the validity of the resonance-based reinterpretation. The result unifies two long-standing number theory problems under a coherent vibrational framework rooted in fundamental physical structure. Keywords:Bunyakovsky Conjecture, Sierpiński Conjecture, D10Z Mechanics, Prime Distribution, Spiderweb Fabric, TTA Mesh, Resonance Coherence, Law of Isis, Law of Sahana, Number Theory, Φ(Z), Ψ₍coh₎, GM Scale