Prime Geometry and Information Coherence

A framework where prime factorization reveals the geometric structure of information, and phase coherence emerges from the annihilation of noise through recursive interference.

Core Thesis

Information Has Geometric Structure

Every piece of data can be mapped to a coordinate system where prime factors serve as basis vectors. The prime factorization of a number determines its position in this multi-dimensional space, and the "difficulty" of factorization corresponds to geometric distortion or curvature in the local information manifold.

Numbers with small, well-distributed prime factors create regions of low curvature— these are compressible, predictable, and exhibit high internal symmetry. Numbers with large prime factors create regions of high curvature—these resist decomposition and introduce complexity into any system they participate in.

Prime Factor Geometry

Visualization: How numbers map to geometric coordinates based on their prime factorization

Geometric Decomposition

Dimensional Reduction

Factoring out common divisors is equivalent to projecting multiple dimensions onto a common axis. This reduces the degrees of freedom in the system.

Local Curvature

Prime-rich regions create "gravitational" effects in the information space, warping nearby patterns and resisting simplification.

Symmetry Detection

Well-factored regions exhibit repeating patterns and self-similarity, enabling efficient compression and pattern recognition.

Phase Coherence and Interference

Phase Cancellation Mechanism

Signal Coherence: 75
Noise Level: 25
Iterations: 1

Coherent patterns persist while noise self-cancels through destructive interference

Information as Wave Function

SEP treats information streams as complex wave functions where each data point has both magnitude and phase. Through recursive processing:

  • Non-coherent patterns destructively interfere over successive iterations
  • Coherent, self-similar patterns constructively reinforce
  • The system naturally filters signal from noise without explicit classification

This is informational interferometry—using the wave nature of data to extract meaningful patterns through physical principles rather than statistical inference.

The SEP Engine

Real-Time Processing Dashboard

Input Stream Analysis

Prime Density: 0.000
Geometric Distortion: 0.000
Phase Coherence: 0.000

Pattern Extraction

Detected Patterns: 0
Noise Cancelled: 0.0%
Processing Rate: 0 MB/s

The SEP Engine implements these principles in high-performance C++ with CUDA acceleration, processing arbitrary data streams to extract coherent patterns through geometric decomposition and phase interference. Development happens in real-time with continuous integration— productivity verification through live commit tracking.