Table of Contents Runtime Identity, Authority, and Initialization Merge Precedence, Supersession, and Source Retention Terminal Alphabet and Global-State Discipline Fundamental Validation and the Pre-Primitive Firewall Strict Ontology Ω₀ Recursive Ontology Dependency Hypergraph Formation, Change, Continuity, and Residue Feedback Derived Entities and Derivation Packets Reification and Representation Firewalls ORSIΩ_KERNEL_v1 Kernel Gates and Access-Mode Closure Debt, Residue, Counterkernel, Liftback, Replay, and Certification RSRΩ⁵ Recursive Self-Reconstruction Mutation Authorization and Progress Measurement xSCDΩ_v7.0 Runtime Architecture Preprimary Carrier Construction Intermediate Quotients and Galois Closure Native Retention and Continuation Globalization, Capacity, and Local-to-Global Descent Closure-Order Governance Licensed Minimal Mutation CLOSUREΩ_v2.0 Commitment Commutators and Local-Closure Zones Process Commitment Failure Theory Live Commitment Ledger and Reversal Cost ...
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Spectral Methods and High-Order Numerical Methods 2026 xCSD
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Spectral Methods and High-Order Numerical Methods Proposed 2026 English Course Outline Part I — Approximation and spectral representations Week 1 — Foundations of high-order discretization Model PDE classes: elliptic, parabolic, hyperbolic, dispersive Weighted-residual framework Galerkin, Petrov–Galerkin, tau, collocation and least-squares formulations Approximation error, consistency, stability and convergence Sobolev regularity versus spectral convergence Modal versus nodal representations Reproducible numerical experiments in Julia, Python or MATLAB Week 2 — Fourier approximation and the FFT Fourier series and transforms Truncation, interpolation and projection Parseval identities Trigonometric interpolation Discrete Fourier transform and FFT Spectral differentiation and integration Aliasing, convolution and the two-thirds/three-halves de-aliasing rules Gibbs phenomena and filtering Week 3 — Fourier methods for periodic PDEs Fourier–Galerkin and Fourier collocation methods Poi...