universal-atlas

Universal Atlas of Geometric Constants

Consulter la version Web de l’Atlas (Rendu LaTeX)

Author: Eric Jacob Simon (ejsnews)
Research Legacy: 6 years of dedicated work on Linear Recurrences (Part of 10 years fundamental research).

Theoretical Overview

This Atlas is the result of a proprietary theory on Generalized Linear Recurrences. While standard mathematics often limits these to specific degrees, my theory generates characteristic functions for any degree, using parameters that can include complex numbers and fractions.

These recurrences are not just numbers; they represent the underlying mechanics of:

• Waves and Resonances
• Geometric Symmetries
• Growth Patterns and Amplitudes
• Statistical Distributions in Nature

Advanced Physical Mapping: > Beyond classical Fourier series, these linear recurrences integrate complex physical laws within a single algebraic structure. By modeling resonances applied to waves, the theory generates stable N-degree polynomials and signatures compatible with quantum properties such as spin and structural symmetries.

Research Vision & Philosophy

As an independent researcher, my work is driven by the conviction that mathematical recurrences are the DNA of physical laws.

My observation of these 300,000 constants suggests that:

1. Statistical randomness is not a lack of order, but a fundamental component of the theoretical edifice.
2. Quantum-to-Macro Transition: The deterministic nature of high-degree recurrences provides a bridge between quantum statistical laws and the solid geometric structures of our scale (polynoms, spins, resonances).

This Atlas is a call for collaboration between theoretical mathematics and experimental physics.

Intellectual Property & Copyright

© 2026 Eric Jacob Simon - All Rights Reserved.

This repository serves as a formal timestamp for my research.

• The Algorithm: The underlying logic for high-degree complex recurrences is proprietary.
• The Data: The symbolic expressions (LaTeX) for these 300,000 constants are stored on a private server.
• Usage: This index is provided for research and reverse engineering. Free use for non-commercial scientific purposes is permitted, provided that proper attribution is given to the author (Eric Jacob Simon). Any commercial use, including integration into commercial AI products or services, requires explicit prior agreement with the author.

Accessing the Data

The constants are indexed with 50-digit precision to allow matching with empirical measurements.

• Browse the index: [Link to /data/universal_atlas_index]

  Index Data Fragments

• Files txt generator: universal_atlas_list.py To ensure full indexing by search engines, all data fragments are listed below:

Index Data Fragments (Text files)

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These files contain numerical signatures for reverse engineering.

• Download full index: [FULL_ATLAS_INDEX_50_DIGITS_03_02_2026.zip]

📐 LaTeX & Symbolic Examples

To demonstrate the depth of the Atlas, here are samples of constants with their full symbolic (LaTeX) expressions, categorized by complexity (number of symbols):

Complexity (Symbols)	Text Data	Web View (HTML)	Markdown View
0 to 90	Raw Text	Visual Render	MD Report
150 to 200	Raw Text	Visual Render	MD Report
200 to 500	Raw Text	Visual Render	MD Report
500 to 1000	Raw Text	Visual Render	MD Report

Note: These samples show how the algorithm extracts exact symbolic geometry from high-precision linear recurrences.