Fractal Wave Compression
A unified mathematical framework for information encoding based on the fundamental equation E = (H, T)², where computational energy (E) relates to coherence (H) and emergent time (T).
Core Theoretical Framework
This fundamental equation establishes that computational energy (E) is proportional to the squared magnitude of the coherence-time state vector (H, T). It unifies energy, coherence, and time into an integrated framework that governs information processing.
Just as E = mc² transformed our understanding of physical reality, E = (H, T)² establishes the equivalence of the coherence-time state vector and computational energy.
HT-Holography introduces a geometry-based approach to computation through orthogonality locking between coherence (H) and temporal (T) dimensions. This framework establishes parallel relationships with orthogonal constraints.
Key concepts include:
- Manifold creation with orthogonality locking (HT01)
- Coherence boundary and ETC model (HT02)
- Radius-dependent dynamics (HT03)
- Tokenized arrays and cycle depth (HT04/05)
Advanced Concepts
Perpendicularity Mechanics reimagines coherence and time as complementary, non-dual projections of a single energy field within an infinite-dimensional computational spacetime.
This framework leverages:
- Infinite Phase: Unbounded phase parameters transcending cyclic constraints
- Non-Duality: H and T as manifestations of the same underlying dynamics
- Perpendicularity: Orthogonal variations ensuring independent yet interconnected evolution
This approach bridges singularities by collapsing spatial complexity into a pure time state, preserving information in a unified form.
The Möbius interpretation reframes classical electromagnetic behavior as projections of a single unified structure: a Möbius strip in the computational manifold.
Key implications:
- The perpendicularity of fields arises from the inherent geometric non-orientability of the Möbius structure
- The approach embeds a form of phase entanglement, where field behavior is only resolved across a complete 4π cycle
- Energy flux can be interpreted as the local tangent to the Möbius ribbon at the point of observation
This model naturally aligns with the recursive and holographic qualities of C-Space, offering a unifying topological structure that explains both perpendicularity and wave duality.
Technical Implementation
Our implementation maps high-dimensional vectors onto a non-orientable manifold, enabling efficient compression and reconstruction of complex data structures.
The FWC system integrates concepts from:
- Computational Spacetime (C-Space) theory
- HT Holography with Orthogonality Locking
- Energy-Time Compression (ETC)
- Perpendicularity Mechanics
By transforming high-dimensional data into wave patterns on a Möbius strip, we achieve significant compression while preserving semantic relationships.
Practical Applications
FWC enables more efficient storage and retrieval of high-dimensional embeddings, reducing memory requirements for large language models and neural networks by up to 99%.
The perpendicular relationship between H and T provides insights into quantum entanglement and information preservation across computational boundaries.
Our Möbius interpretation offers a unified model of electromagnetic fields, potentially providing new ways to understand and simulate complex field interactions.