📢 Join the Community!

Discussion, questions, and collaboration for this project are hosted in our central community repo:
👉 gatanegro/community

• Share discoveries, suggestions, and ideas.
• Ask questions about the research.
• Fork this repo to continue your own work—direct changes are not permitted.

You must have a GitHub account to participate in discussions.

Research & Contribution Policy

This repository contains original research, mathematics, and unconventional approaches.
Please do not submit pull requests or issues requesting changes.
If you wish to pursue related research, fork this repository and continue independently.

Note: Apparent errors or unconventional methods are intentional and part of new theoretical work.

In the novel framework: 3D Collatz Octave Model (3DCOM), space, mass, and time emerge from recursive wave interactions governed by a topological attractor field.

https://doi.org/10.5281/zenodo.15882510

We derive a dimensionless dark energy density Ω_Λ as a residual curvature effect from incomplete recursive mirroring. The derived formula: Ω_Λ = HQS × (π/2 + LZ + √α + π/(100))

numerically evaluates to 0.6868153680976859, closely matching the Planck observational value of 0.6847 ± 0.0073.

Each term reflects a geometric or energetic constraint:

• HQS = 0.235 is the harmonic quantum shift representing recursive energy loss,
• LZ= 1.23498228 is the attractor recursion limit from a topological 3-sphere structure,
• √α couples the electromagnetic phase amplitude,
• π/100 encodes the fine angular correction (1.8°) preventing phase closure at 90°.

This model replaces the notion of a vacuum with an uncollapsed recursive field whose invisible component (90° behind visible mass nodes) is misinterpreted as dark energy. In this view, Ω_Λ quantifies the systemic asymmetry of incomplete recursion across cosmic structure.

6.The Software Interactive simulation tools

• 3dcom_observer_simulator_bridge.py
• observer_angle_simulator_bridge_3dcom.py

6.1 Observer Angle (Qualia Operator Q∧)

  The user can rotate the angle of vision through a recursive 3D COM field.
  This angle controls which recursive nodes collapse into visible qualia (mass, color, etc.).

6.2 Bridge Formula Fusion At every visible node (from a certain angle), the tool applies the Bridge Formula:

  It outputs the observable value (radius, energy, color shift) at that node from that observer angle.

6.3 COM Recursive Field Engine Underlying space is stacked recursive octaves, populated by Collatz - reduced points. Nodes are energy attractors, invisible unless aligned with observer axis.

What the Software Could Let You Do:

• Feature
• Function
• Rotate observer angle
• Change θ_obs to see different recursive nodes (what “collapses” into visibility).

Zoom recursion scale

• Explore how scaling in COM affects perceived values.
• See Bridge Formula output

Each node reveals computed energy, radius, or frequency from the Bridge.

Qualia visualization

Color of node changes with observer angle → angle = color.

Show invisible 90° recursion

• Behind every node, faintly render orthogonal recursion → dark field.

• Save simulation states

• Store specific angle + output pairs for further analysis.

  3D COM Recursive Field from Collatz sequences reduced into Octave rings.
  Observer Angle Slider (°) simulates rotating the observer's Qualia perspective.
  
  Nodes turn red when their angular alignment matches the observer's angle (~±15°).
  Matching nodes display Bridge Formula output with calculated radius values.
  

What This Shows:

  Perceived nodes depend purely on observer’s angular alignment.
  
  Only aligned nodes collapse into "matter", all others stay as invisible recursive field.
  
  The Bridge Formula activates only for visible attractors.

Observer-Angle Simulation with Bridge Formula Overlay using the 3D Collatz Octave Model:

How to Use:##

1. Paste and run the code in a Python environment with GUI capability (like Jupyter Notebook with %matplotlib, or any Python script runner).
2. Use the slider to rotate the observer angle (θ_obs) in degrees.
3. Red nodes are visible attractors from the current observer angle.
4. The Bridge Formula output appears below for those visible nodes (based on recursion layer n).

Features Included:

 - 3D COM Field rendered from Collatz sequences.
 
 - Observer Angle Slider: reveals only nodes within ~15° of alignment.
 
 - Bridge Formula Calculator per visible node.
 
 - CSV Export Button: saves aligned node data for analysis.