📄 Cite the Paper (OSF DOI): 10.17605/OSF.IO/YHDMZ 💻 Cite the Code (Zenodo DOI): 10.5281/zenodo.20225304

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🌌 GEO — Hidden Geometry Framework

GEO (Hidden Geometry Framework) is an exploratory mathematical and cosmological framework investigating whether stable geometric transfer relations can reproduce selected observational structures through an internal operator architecture.

The framework explores geometric operators, transfer structures, hidden efficiency relations, cosmological applications, planetary architectures, and reproducible numerical experiments.

This repository contains the public GEO framework, mathematical notes, validation studies, experimental results, and GEO-Lens applications.

Update: ESP Version

For a cleaner, organized, and Spanish-language reconstruction of this experimental framework, please visit our dedicated technical repository: [GEO-Geometria-Oculta-ESP] https://github.com/LeoTorreblanca/GEO-Geometria-Oculta-ESP

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🛠️ Technical Validation Kit (CLASS Patch)

The official implementation of the GEO framework for CLASS v3.x is now available. This kit includes the necessary source patches and diagnostic scripts to reproduce the $H_0 = 73.04$ result.

👉 Access the Kit here: https://github.com/LeoTorreblanca/GEO_Launch_Kit

The GEO Launch Kit is released under the MIT License and is provided as a public validation environment for independent inspection, reproduction, testing, and scientific discussion of GEO-Lens calculations and associated Hubble examples.

CLASS-GEO-Lens

Public implementation:

https://github.com/LeoTorreblanca/CLASS-GEO-Lens

DOI:

https://doi.org/10.5281/zenodo.20529415

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🌐 Official Channels

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🌌 GEO-Lens Application to the Hubble Tension

This section presents the GEO-Lens application to the Hubble tension and summarizes the operator chain used to reconstruct the numerical scale of the discrepancy between early-universe and local measurements of the Hubble constant.

The associated mathematical derivations, operator definitions, validation materials, and closure documents are provided below for independent inspection, reproduction, and evaluation.

📐 Core Mathematical Derivation (Strong Prediction)

The intensity factor $\alpha$ is derived autonomously from the internal harmonic geometry without external data calibration:

$$\alpha = \frac{\Phi \times (1 - \eta)}{\sqrt{2}} \approx 0.534463$$

Where $\eta = 0.6$ represents the GEO Partition Constant and harmonic link rule.

When coupled with the internal operator $\delta_R$ under the partition constant $\eta = 0.6$, it precisely reconstructs the local expansion rate:

• $H_0$ Planck (Base): $67.40 \text{ km/s/Mpc}$
• $H_0$ GEO (Predicted): $73.040000 \text{ km/s/Mpc}$
• Relative Error: $+0.0000e+00$

📂 Scientific Documentation

The full mathematical proofs and framework bridges are structured across 5 core technical sheets available in this repository:

• PDF 1: Hubble Tension 12-Digit Auditing
• PDF 2: Reconstructive vs Strong Prediction Levels
• PDF 3: GEO Bridge & Coupling Metrics
• PDF 4: Universal Alpha Derivation Thesis
• PDF 5: Final Cosmological Closure Report

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🌐 Context & Observational Discrepancy References

This geometric resolution addresses the current core observational conflicts debated by the international physics community:

• The Hubble Wars Framework: Museum of Science Analysis — Reviewing the baseline tension between Planck ($67.4$) and SH0ES ($73.04 \text{ km/s/Mpc}$) measurements.
• Active Academic Review (2026): arXiv:2505.24743v1 — Documenting active space telescope data-fitting and systematic constraints.
• The Call for New Physics: CERN Courier Report — Outlining the theoretical necessity for zero-relative-error structural and harmonic operators.

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🪐 Multi-Planetary Empirical Validation (NASA Data Bridge)

The geometric rules of the GEO Framework are not limited to large-scale cosmological structures; they scale invariantly down to planetary system architectures.

An automated empirical validation has been performed against the official NASA Exoplanet Archive, tracking how orbital focus and structural fractures occur across 2,099 multi-planetary systems ($N \geq 3$).

👉 Explore the Data Suite: GEO-Exoplanets-Validation

📈 Planetary Critical Thresholds & The $N=5$ Step

When applying the GEO Critical Discontinuity Operator with a threshold of $2.2$ on semi-major axis ratios ($a_{i+1}/a_i$), the universe reveals three geometric laws:

• 98.09% Coherence Rate: Planetary architectures strictly minimize chaos, restricting themselves to 0 or 1 major transition jump.
• The $N=5$ Geometric Saturation: The probability of structural fracture behaves like a quantum step-function, jumping from 9.58% to 26.67% exactly at the 5th body, confirming the packing limits of a single harmonic resonance shell.
• Internal Node Protection: Inner nodes remain tightly locked. In high-complexity systems ($N=7$), internal fractures drop to zero, concentrating a prominent 41.7% of the focus jumps exactly between Node 3 and Node 4.

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🌌 GEO — Hidden Geometry Framework

Author: Leonel Hernan Torreblanca

📋 Overview

GEO (Geometría Oculta / Hidden Geometry Framework) is an exploratory cosmological framework proposing that part of the observed suppression of large-scale structure growth may emerge from an underlying geometric transfer architecture.

The framework investigates whether stable geometric relations can reproduce effective cosmological growth suppression without introducing arbitrary free modifications.

The project explores the emergence of:

• Effective active fractions
• Complementary transfer sectors
• Geometric node structures
• Stable predictive relations

This repository contains reproducible Python scripts, generated figures, numerical outputs, and the first GEO exploratory test series.

📐 Central Hypothesis

The framework investigates whether cosmological growth suppression can be interpreted as a consequence of a hidden geometric transfer structure. Instead of treating suppression as an arbitrary correction, GEO explores the possibility that observable growth evolves inside a constrained geometric architecture.

Several recurring relations emerged during testing:

$$f_c$$ $$f_{out} = 1 - f_c$$ $$\eta = f_c^2$$ $$R = \mu^{1/3}$$

The framework does not claim a confirmed physical theory. This repository represents an exploratory mathematical/cosmological framework, numerical tests, geometric interpretations, and reproducible experimental analysis.

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🧪 GEO Test Series

PRUEBA 1 — SOP Emergence

Initial emergence of effective suppression and active geometric fraction:

• Growth suppression
• Stable $S_8$
• Emergence of $f_c$
• Complementary sector interpretation

PRUEBA 2 — Geometric Node Analysis

Analysis of preferred geometric regions:

• $3/4$
• $\sqrt{3/5}$
• $\pi/4$
• Emergence of effective geometric bands

PRUEBA 3 — Architectural Transfer Structure

Investigation of:

• Geometric partition
• Active/complementary transfer
• Efficiency structure
• Architectural consistency

PRUEBA 4 — Prediction Law

Exploration of predictive relations:

$$R = \mu^{1/3}$$

and geometric transfer consistency.

PRUEBA 5 — Final Prediction Consistency

Final observational consistency analysis involving:

• $S_8$
• Effective suppression
• $E_G$ ratio
• Geometric prediction stability

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📂 Repository Structure

scripts/  -> Reproducible GEO scripts
figures/  -> Generated plots and visual outputs
results/  -> Numerical outputs and console logs
pdf/      -> Individual PDF reports
paper/    -> GEO preprint versions