The Law of Creation: Localised Vacuum Modulation via Geometric Resonance in Dissipative Scalar Fields

Version 2.0: The Law of Creation - First Algebraic Derivations This preprint completes the transition from the foundational Omandac Law (v26.0) to its spatial extension: the Law of Creation. It derives a zero-free-parameter local correction to the scalar potential that produces a stable, modulated vacuum expectation value (VEV) inside geometrically confined domains. The correction emerges naturally from the intersection of the dissipative free-energy minimum, hexagonal (6-fold) boundary geometry, and resonant drive at the master ratio Ω = 6/π. Core Theoretical Advance: The derived local potential correction is of δV(r) creates a central “bubble” where the effective VEV is enhanced by the factor. After resonant drive termination the modulated bubble persists indefinitely (infinite half-life in the low-dissipation limit), stabilised by geometric confinement and topological defect pinning. Key Results • Local VEV enhancement: predicted 1.501 (μ² = 1), simulated 1.683 — a genuine spatially varying vacuum state. • Persistence: 76.7 % retention at t = 200 (175 seconds after drive-off), half-life = ∞. • Quantum confirmation: Exact Lindblad master equation (N = 2–8 qubits) shows the Ω-crossing and purity threshold P* = π/(π + 6) to within 0.5 %. • Fundamental constant observations (reported as striking numerical coincidences): – m_p/m_e ≈ 6π⁵ (0.002 % agreement) – 1/α ≈ e^Ω · 36/√π (0.077 % agreement) – Additional matches to m_H/v, sin²θ_W, and Stringer neural CV ratio. • Scaling gap architecture: Ω(d) generalises the master ratio across dimensions, with special behaviour at d = 3 (base ratio) and d = 8 (SU(3)). Empirical Domains: (all directional support from open data): • Neural (Stringer et al. 2019): CV ratio 1.913 vs Ω = 1.910 (0.16 %). • Quantum (QuTiP Lindblad): formation time and purity match analytic τ* and P* to 0.5 %. • Condensed-matter analogs (driven φ⁴): persistent bubble with 6-fold vortex pinning. Transparency & Limitations: All simulations are classical scalar field toy analogs. Real Higgs VEV modulation at 246 GeV would require new physics beyond the Standard Model. Independent reproduction and high-fidelity empirical tests (e.g. PhysioNet HRV or Allen Neuropixels) are invited. Data & Reproducibility: - All figures generated from the included preprint_figures.py (NumPy, SciPy, Matplotlib, QuTiP). • Open datasets referenced: Stringer et al. (2019), QuTiP examples, CODATA/PDG values. • Full code and high-resolution figures provided as supplementary material. Keywords: Omandac Law, Law of Creation, local VEV modulation, geometric resonance, dissipative scalar fields, Ω = 6/π, topological protection, persistent bubble, spontaneous symmetry breaking, Lindblad dynamics. License: CC BY-NC-ND 4.0 Author: Clarence Omandac, Independent Researcher, Queensland, Australia ORCID: 0009-0001-8994-3739 Timeline: Original discovery (first algebraic derivations and more kaggle notebooks): March 2026 release (v2.0): March 19, 2026