DOI: 10.5281/zenodo.18640504
title: Galactic Resonance: Scale Brahim Lattice to Astronomical Scales

description: An empirical large-scale test of the Brahim Lattice—a deterministic quantization map applied to 52,511 astronomical observables across five independent domains. This repository contains the open-source reproducibility archive for the research paper: "Galactic Resonance: Scaling the Brahim Lattice to Astronomical Observables Across Five Domains."

🌌 Overview

The Brahim lattice is a discrete quantization map defined by the function:
$$\mathcal{D}(x) = \frac{-\ln x}{\ln \varphi}$$

where $\varphi = (1 + \sqrt{5})/2$ is the golden ratio. This project maps dimensionless astronomical ratios (periods, masses, temperatures, frequencies) through $\mathcal{D}(x)$ and tests for statistically significant clustering against a 206-point lattice.

Key Contributions





Scale: Analysis of 52,511 values from NASA, ESA, LIGO, and Breakthrough Listen APIs.




Significance: Rejection of the null hypothesis at $p < 10^{-300}$ (Fisher combined $Z=38.45$).




Predictions: 6,942 blind astronomical predictions (5,712 exoplanets, 1,230 stellar companions).




SETI: Proposal for the Brahim Beacon, a self-verifying interstellar protocol.



📊 Domain Results

The analysis spans five major astronomical datasets:




Domain
Records
Z-score
p-value




NASA Exoplanets



21,370



85.10



$< 10^{-1573}$





ESA Gaia DR3



30,000



77.67



$< 10^{-1200}$





LIGO/Virgo GW



1,062



14.78



$< 10^{-49}$





Breakthrough Listen



60



4.95



$< 3.7 \times 10^{-7}$





Planck CMB



19



0.24



0.406





Fisher Combined



52,619



38.45



$< 10^{-300}$





🛠 Project Structure

Data & Database (galaxy.db)

The project utilizes a 8.12 MB SQLite database containing:





observables: Raw and normalized data points.




lattice_hits: Mapping of data to the 206 lattice sites.




planet_predictions: Full physical prognosis for 5,712 predicted worlds.




stellar_predictions: 1,230 companion predictions.




seti_signals: Analysis of 30 curated candidate signals.



Software Packages





brahim-hermes v0.5.0: Core mathematical library for lattice construction, dimension mapping, and null-model generation.




galactic-resonance v0.1.0: Domain-specific fetchers (ADQL/TAP), normalizers, and the prediction engine.



📡 Brahim Beacon Protocol

The paper proposes a SETI handshake referenced to the hydrogen 21 cm line ($f_0 = 1.420405751 \text{ GHz}$):





Carrier: $f_0$.




Companion Tones: $f_n = f_0 \cdot \varphi^{-n}$ for $n = 1 \dots 10$.




Handshake: Three tones satisfying the polynomial $\beta^2 + 4\beta - 1 = 0$, where $\beta = \sqrt{5}-2$.



🚀 Reproducibility

To reproduce the Z-scores and predictions:





Environment: Ensure Python 3.9+ and IEEE 754 arithmetic compliance.




Dependencies: numpy, scipy, astropy, pyvo, sqlite3.




Seed: All Monte Carlo trials use seed=42.




Hardware: Statistical tests are CPU-bound; frequency scanning utilizes CUDA (optimized for NVIDIA RTX 40-series).



# Example: Running the lattice scanner
python -m galactic_resonance.scanner --domain exoplanets --quantize


📜 References

If using this data or methodology, please cite:



Brahim, E. O. (2026). Galactic Resonance: Scaling the Brahim Lattice to Astronomical Observables Across Five Domains. DOI: 10.5281/zenodo.18640504.


This research utilizes data from NASA Exoplanet Archive, ESA Gaia, and the LIGO Scientific Collaboration.