Scarlet–VanAcker Cosmological Framework (Scarlet 2.0)

This release marks a major structural and manuscript milestone for the Scarlet Cosmological Framework (Scarlet 2.0), integrating the revised Appendix AJ text and the accompanying Python validation pipeline for aperiodic quasicrystal spectra. What's New & Updated Rigorous Operator Foundations & Manuscript Revision (Appendix AJ) Formalized Self-Adjointness: Finalized Theorem 1 regarding the global Covariant Laplacian \Delta_K = B^* B over \mathcal{H}_{\text{phys}}, backed by the Hellinger-Toeplitz theorem to guarantee a strictly real-valued energy spectrum (\lambda \in \mathbb{R}). Epistemic Delineation: Explicitly separated proven linear algebra from heuristic number-theoretic conjectures, detailing the precise obstructions in spectral prime mappings. High-Performance Vectorized Engine Prefix-Subspace Scaling: Optimized vectorization supporting M=3 (and higher boundary scales), enhancing vertex generation and perpendicular window filtering (\Vert{}P_\perp n\Vert{}\infty \le 0.5). Algebraic Loop Extraction: Automated extraction of discrete action bands S{\text{ren}}(\gamma) = c_1 + c_2 \phi within the quadratic field extension \mathbb{Q}(\sqrt{5}). Advanced Spectral Analysis Pipelines Level Spacing & Quantum Chaos Toolkit: Integrated the Python spectral unfolding and nearest-neighbor spacing (P(s)) calculation scripts directly into the codebase to investigate GUE/GOE level repulsion. Installation & Usage Clone the repository and run the updated verification pipeline: git clone https://github.com/Slowvan7/Scarlet-Cosmological-Framework.git cd Scarlet-Cosmological-Framework python3 -m pip install -r requirements.txt