Report
From Recursive Ontology to Deterministic Systems: Glitchgod Protocol Framework into the OmegaGENESIS Mathematical Architecture
| Title: | From Recursive Ontology to Deterministic Systems: Glitchgod Protocol Framework into the OmegaGENESIS Mathematical Architecture |
|---|---|
| Authors: | Gary Charles Gonzalez |
| Publisher Information: | Zenodo, 2026. |
| Publication Year: | 2026 |
| Subject Terms: | recursive computation, blockchain systems, non-commutative transformations, dynamical systems, hyperbolic geometry |
| Description: | From Recursive Ontology to Deterministic Systems Formalizing the GlitchGod Conceptual Framework into the OmegaGENESIS Mathematical Architecture Author: Gary Charles GonzalezVersion: v1.0Date: 2026 Abstract Conceptual frameworks often precede formal mathematical systems. Historically, philosophical models of feedback, recursion, and information have evolved into rigorous scientific disciplines. The GlitchGod conceptual framework proposed a recursive ontology centered on identity, system interaction, and self-referential computational processes. While originally expressed through symbolic and philosophical language, elements of this framework can be mapped onto deterministic dynamical architectures. This paper presents the formalization pathway from the GlitchGod conceptual structure to the OmegaGENESIS computational system, demonstrating how recursive ontology, identity anchoring, and layered system evolution can be represented through geometric embeddings, non-commutative rotational dynamics, and deterministic signal pipelines. 1. Introduction The relationship between conceptual frameworks and formal systems has played a recurring role in scientific development. Examples include: cybernetics emerging from philosophical ideas of feedback information theory arising from communication models neural networks inspired by biological cognition Similarly, the GlitchGod framework proposed a conceptual architecture centered on recursion, identity, and system interaction. While originally expressed through symbolic constructs, these ideas can be translated into computational and mathematical structures. OmegaGENESIS represents an attempt to formalize aspects of this conceptual framework into a deterministic transformation pipeline. 2. The GlitchGod Conceptual Framework The original GlitchGod framework describes a recursive ontology in which: systems interact through feedback loops identity acts as an anchor for system evolution recursive interaction generates emergent structures In abstract form, the conceptual model can be described as: Identity → Interaction → Feedback → Recursive Evolution This structure describes a general pattern observed across many dynamical systems. 3. Conceptual Mapping to Computational Architecture The OmegaGENESIS architecture maps the conceptual elements of the framework into computational components. Conceptual Element Computational Representation Identity anchor deterministic seed parameter recursive interaction ordered transformation sequence system evolution dynamical state updates feedback coherence interference metrics system closure cryptographic commitment This mapping converts symbolic constructs into explicit computational processes. 4. Identity-Seeded State Initialization The system begins with an identity-derived seed value. This seed generates parameters controlling subsequent transformations within the system. Identity-derived parameters ensure: reproducibility deterministic outputs unique state evolution per seed. 5. Geometric State Space OmegaGENESIS embeds its initial state within a curved geometric environment using hyperbolic representations. Hyperbolic embeddings allow hierarchical expansion and structured evolution of system states. The geometric layer defines the initial conditions for the transformation pipeline. 6. Non-Commutative Interaction Engine System evolution occurs through a sequence of ordered transformations on the Lie group SO(3). A set of direction vectors on the sphere generates rotation axes. All pairwise combinations produce a dense interaction network. The resulting transformation pipeline contains 231 ordered rotation gates. Because rotations in SO(3) are non-commutative, transformation order produces path-dependent dynamics. This stage acts as the primary mixing engine of the system. 7. Recursive Signal Evolution The evolving state is processed through phase modulation layers that generate interference structures. Two complementary evolution paths are constructed and combined to produce a coherence metric. This process reflects the recursive interaction structure described in the original conceptual framework. 8. System Closure via Cryptographic Commitment The final signal state is sealed through cryptographic hashing. This step produces a reproducible commitment that verifies system output while preserving deterministic behavior. The commitment layer completes the transformation cycle. 9. Conceptual to Mathematical Transition The evolution from the GlitchGod framework to OmegaGENESIS demonstrates a broader methodological pattern: Conceptual model ↓ architectural abstraction ↓ mathematical formalization ↓ computational implementation Many scientific disciplines have followed similar development pathways. 10. Discussion The primary contribution of this work is not a new mathematical theory but a formalization of conceptual recursion principles into a deterministic computational architecture. The OmegaGENESIS system illustrates how philosophical system models can inspire structured mathematical designs. Further research is required to evaluate: dynamical mixing properties stability metrics potential applications in generative systems or cryptographic processes. 11. Conclusion The GlitchGod conceptual framework introduced ideas centered on recursion, identity anchoring, and system interaction. OmegaGENESIS represents an attempt to formalize these concepts into a deterministic mathematical architecture using geometric embedding, ordered rotational dynamics, and layered signal evolution. This work demonstrates a pathway from conceptual ontology to explicit computational systems. This paper presents a formalization pathway from the conceptual GlitchGod framework to the OmegaGENESIS computational architecture. The system transforms recursive identity-based concepts into deterministic dynamical processes through geometric embeddings, ordered rotational transformations, and layered signal evolution. By mapping conceptual recursion structures into explicit computational components, the OmegaGENESIS architecture demonstrates how symbolic frameworks can evolve into formal dynamical systems. The work illustrates a broader methodological pattern: conceptual ontology → architectural abstraction → mathematical formalization → computational implementation. |
| Document Type: | Report |
| DOI: | 10.5281/zenodo.19008314 |
| Rights: | CC BY |
| Accession Number: | edsair.doi...........fe4328f93b33b39df8128f0be962c8f7 |
| Database: | OpenAIRE |
Be the first to leave a comment!