Ritual Layer v1.0: A Browser‑Native HTML Engine for Symbolic–Computational Geometry

The Ritual Layer v1.0 is a browser‑native HTML engine that transforms symbolic structures into deterministic computational behaviour. Built entirely on standard HTML and JavaScript, the system demonstrates that the browser can function as a stable, real‑time execution environment for symbolic geometry, recursive structures, and operator‑driven dynamics. The engine formalises the Ritual Codex into a minimal and orthogonal operator system, enabling rotation, oscillation, phase modulation, reflection, and fractal descent through a unified symbolic–computational model. This release includes the complete operator framework, the RitualNode architecture, the field and transition system, the deterministic execution loop, and the full symbolic mapping from sigils to computational semantics. Mathematical notes define the underlying dynamical systems, including polar transforms, oscillatory scaling, temporal phase offsets, geometric inversion, and bounded recursion. A dependency‑free Minimal Working Example demonstrates the engine running directly in HTML, showcasing real‑time behaviour without external libraries or frameworks. The document is structured for archival stability, academic analysis, and engine‑level implementation. It preserves the full Ritual Codex, the symbolic–computational mapping, the operator tables, the glossary, and the versioning guarantees that define the canonical behaviour of the subsystem. Version 1.0 is frozen, complete, and suitable for long‑term research, reproduction, and integration into HTML‑based computational systems. Keywords: HTML Engine; Browser‑Native Engine; Ritual Layer v1.0; Symbolic Computation; HTML Simulation; HTML Rendering Engine; Operator Systems; Spiral Operator; Breath Operator; PhaseShift Operator; Mirror Operator; Recursive Operator; Ritual Codex; HVL Integration; Deterministic Execution; Dynamical Systems; Polar Geometry; Oscillatory Scaling; Phase Modulation; Reflection Transform; Fractal Descent; Symbolic Mapping; Computational Semantics; Minimal Working Example; Real‑Time HTML Systems; Node‑Based Execution; Diagram Engines; Recursive Structures; Temporal Modulation; Geometric Operators; Semantic Engines; Computational Symbolism; Engine Subsystems; Version‑Locked Specification; Archival Documentation; Cross‑Domain Semantics; Structural Determinism; HTML‑Native Simulation; HTML‑Based Geometry Engine; Browser Physics Layer; Symbolic Geometry Engine