Self Deriving Algebra Through Rendered Frame Theory

Self-Derivation Algebra (SDA) is a novel mathematical framework establishing a rigorous foundation for self-evolving, observer-dependent symbolic equations. At its core are Self-Deriving Equations (SDEs), which recursively generate their next state based on prior states, intrinsic logic, and observer input. SDA unifies concepts from AI, consciousness modeling, and cosmology into a single algebraic system. This release (v2) includes: Formal LaTeX document with foundational axioms, Λ-operator theorems, existence and uniqueness proofs, spectral stability analysis, and canonical SDE examples. Simulation testbed (Python/Colab) for iterative SDE evaluation, stability analysis, and observer-parameter sweeps. Falsifiable predictions enabling experimental validation in EEG-perception loops, cosmological redshift observations, and autonomous agent entropy reduction. SHA-512 hashes for all files, ensuring reproducibility and cryptographic provenance. SDA is designed to serve as a new branch of mathematics, fully integrable with Rendered Frame Theory (RFT) and capable of generating infinite recursive structures with observer-context influence.