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QO+R Framework: From String Theory to Galactic Observations

A Novel Two-Field Modified Gravity Framework with Empirical Validation

Author: Jonathan Edouard Slama Affiliation: Metafund Research Division, Strasbourg, France Contact: jonathan@metafund.in ORCID: 0009-0002-1292-4350 Version: 4.0 Date: January 2026

DOI License: MIT

📋 Nature Submission Guide (Manuscript #2025-12-33523)

Title: A non-monotonic environmental signature in galaxy dynamics suggests dual scalar fields

This repository supports the Nature Article submission. Reviewers should focus on the following directories:

Manuscript Section Repository Location Key Files
Figure 1 (U-shape discovery) Paper1-BTFR-UShape/figures/ fig06_replicability.png
Figure 2 (Sign inversion) Paper1-BTFR-UShape/figures/ fig11_tng_multiscale.png
Figure 3 (Robustness) Paper1-BTFR-UShape/figures/ fig05_robustness.png
Figure 4 (Screening) Paper1-BTFR-UShape/figures/ fig09_solar_system.png
SPARC analysis Paper1-BTFR-UShape/tests/03_ushape_discovery/ discover_ushape.py
ALFALFA analysis Paper1-BTFR-UShape/tests/06_replicability/ Scripts in folder
TNG sign inversion Paper1-BTFR-UShape/tests/10_tng_validation/ Scripts in folder
Statistical robustness Paper1-BTFR-UShape/tests/05_robustness/ Scripts in folder
Multi-scale validation Paper4-QOR-Validation/tests/ Full test suite
Methods details Paper4-QOR-Validation/experimental/ Complete methodology

Quick Reproduction

# Figure 1A: SPARC U-shape discovery
cd Paper1-BTFR-UShape/tests/03_ushape_discovery
python discover_ushape.py

# Figure 1B: ALFALFA replication  
cd ../06_replicability
python *.py

# Figure 2: TNG sign inversion
cd ../10_tng_validation
python *.py

# Figure 3: Statistical robustness
cd ../05_robustness
python *.py

Papers NOT directly part of Nature submission

  • Paper2-Residual-Diagnostics/ — Medical extension (separate research line)
  • Paper3-ToE/ — String theory derivation (theoretical background, not submitted)

System Requirements

Software Dependencies

  • Python 3.9+ (tested on 3.9, 3.10, 3.11)
  • See requirements.txt for complete list with version numbers

Operating System

Tested on:

  • Windows 10/11 (64-bit)
  • Ubuntu 20.04/22.04
  • macOS 12+ (Intel and Apple Silicon)

Hardware

  • No special hardware required
  • Standard desktop computer with 8GB+ RAM
  • ~5GB disk space for full data downloads

Installation Time

  • Dependencies installation: ~5 minutes on normal desktop
  • Data downloads (optional): ~30 minutes for complete dataset (~2GB)

Demo Run Time

  • Quick demo (SPARC only): ~30 seconds
  • Full validation suite: ~5 minutes
  • Complete reproduction with downloads: ~2 hours

Overview

This repository contains the complete QO+R (Quotient Ontologique + Reliquat) research framework, including:

  • Theoretical derivation from Type IIB string theory
  • Empirical validation on 1,219,410+ objects across 8 datasets
  • Medical extension demonstrating universal residual methodology
  • Discovery of a hidden conservation law of gravity
  • Full reproducibility with scripts, data, and documentation

The Four Papers

Paper Title Key Result Objects PDF
Paper 1 Environmental Modulation of the BTFR: Discovery of a U-Shaped Pattern U-shape detection (4.4 sigma) 24,056 paper1_qor_btfr_v3.pdf
Paper 2 Residual Diagnostic Methodology: From Galaxies to Biomarkers 85% significant ratios 9,254 paper2_residuals_v3.pdf
Paper 3 From String Theory to Galactic Observations lambda_QR ~ 1 confirmed 708,086 paper3_string_theory_v2.pdf
Paper 4 A Hidden Conservation Law of Gravity QO+R Conservation Law 1,219,410 paper4_qor_validation.pdf

Key Discoveries

The QO+R Conservation Law

rho * G_eff(rho) = constant

The product of matter density and effective gravitational strength is conserved across cosmic environments. This is a hidden symmetry of gravity, analogous to energy conservation in mechanics.

The QO+R Density-Screening Relation

G_eff(rho) = G_N * [1 + lambda_QR * alpha_0 / (1 + (rho/rho_c)^delta)]

Parameters:
- lambda_QR = 1.23 +/- 0.35 (universal coupling)
- alpha_0 = 0.05 (bare amplitude)
- rho_c = 10^-25 g/cm^3 (critical density)
- delta = 1.0 (screening exponent)

Summary of Evidence

Discovery Evidence Significance
U-shape in BTFR 6 datasets, 1.2M objects >10 sigma
Sign inversion (killer prediction) Q-dom vs R-dom populations 26 sigma
Universal coupling constant Stable across 14 orders of magnitude lambda_QR = 1.23 +/- 0.35
Chameleon screening GC, WB null results Confirmed
Low-density signal UDG, filaments Detected
Alternative theories eliminated WDM, SIDM, f(R), Fuzzy DM String Theory only compatible

Repository Structure

QO-R-JEDSLAMA/
|
+-- Paper1-BTFR-UShape/           # Discovery paper
|   +-- manuscript/               # LaTeX + PDF
|   +-- figures/                  # 13 publication figures
|   +-- data/                     # SPARC processed data
|   +-- tests/                    # 13 validation scripts
|
+-- Paper2-Residual-Diagnostics/  # Medical extension
|   +-- nhanes_extension/         # NHANES analysis
|   +-- data/                     # Clinical datasets
|
+-- Paper3-ToE/                   # String theory paper
|   +-- manuscript/               # LaTeX + PDF
|   +-- tests/                    # TNG validation scripts
|
+-- Paper4-QOR-Validation/        # Conservation law paper (NEW)
|   +-- manuscript/               # LaTeX + PDF + theory docs
|   +-- experimental/             # Complete research documentation
|   +-- tests/                    # 14-test validation suite
|   +-- data/                     # Multi-context datasets
|
+-- DATA_SOURCES.md               # How to obtain all datasets
+-- PUBLICATION_AUDIT.md          # Quality checklist
+-- REPLICABILITY_AUDIT.md        # Reproducibility checklist
+-- LICENSE                       # MIT License
+-- requirements.txt              # Python dependencies
+-- README.md                     # This file

Data Sources

Dataset Type N Source Papers
SPARC Observation 181 Lelli+ 2016 1, 3, 4
ALFALFA Observation 19,222 Haynes+ 2018 1, 3, 4
WALLABY Observation 2,047 ASKAP 3, 4
KiDS DR4 Observation ~1,000,000 ESO 4
Planck PSZ2 Observation 1,653 ESA 4
Gaia DR3 Observation Wide binaries ESA 4
TNG50/100/300 Simulation 685,030 IllustrisTNG 3, 4
NHANES Medical 9,254 CDC 2

See DATA_SOURCES.md for complete download instructions.

Quick Start

1. Clone the repository

git clone https://github.com/JonathanSlama/QO-R-JEDSLAMA.git
cd QO-R-JEDSLAMA

2. Install dependencies

pip install -r requirements.txt

3. Run Paper 4 validation suite (14 tests)

cd Paper4-QOR-Validation/tests
python run_all_tests.py

4. Compile manuscripts

cd Paper1-BTFR-UShape/manuscript && pdflatex paper1_qor_btfr_v3.tex
cd ../../Paper3-ToE/manuscript && pdflatex paper3_string_theory_v2.tex
cd ../../Paper4-QOR-Validation/manuscript && pdflatex paper4_qor_validation.tex

Theoretical Framework

The QO+R Lagrangian

L = sqrt(-g) [ (M_P^2/2) F(chi) R - (1/2)(d phi)^2 - (Z(chi)/2)(d chi)^2 - V(phi,chi) ]
  + L_matter[A^2(phi,chi) g_mu_nu, psi]

Where:

  • phi (Q-field): Couples to gas via electromagnetic interactions
  • chi (R-field): Couples to stars via gravitational interactions
  • A(phi,chi) = exp[beta(phi - kappa*chi)/M_P]: Conformal coupling

String Theory Origin

10D Type IIB Supergravity
         |
         v
Calabi-Yau Compactification (Quintic P^4[5])
         |
         v
4D Effective Theory (dilaton phi, Kahler modulus chi)
         |
         v
KKLT Moduli Stabilization
         |
         v
QO+R with lambda_QR ~ O(1)
         |
         v
QO+R Conservation Law: rho * G_eff = constant

Citation

If you use this work, please cite:

@software{slama2025qor,
  author       = {Slama, Jonathan Edouard},
  title        = {{QO+R Framework: From String Theory to Galactic
                   Observations - A Hidden Conservation Law of Gravity}},
  year         = 2025,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.17943132},
  url          = {https://github.com/JonathanSlama/QO-R-JEDSLAMA}
}

License

This project is licensed under the MIT License - see LICENSE for details.

Acknowledgments

  • SPARC Team (Lelli, McGaugh, Schombert) for the galaxy database
  • IllustrisTNG Collaboration for simulation data access
  • ALFALFA Team (Haynes et al.) for the HI survey
  • KiDS Collaboration for optical photometry
  • Planck Collaboration for SZ cluster catalog
  • Gaia Collaboration for astrometric data
  • Emmy Noether for the theorem connecting symmetries to conservation laws
  • All pioneers of gravity theory: Newton, Einstein, Hilbert, Schwarzschild
  • Iris - An AI assistant trained with my reasoning methodology, for invaluable help with manuscript drafting, test design, and iterative refinement of the scientific arguments

Important Caveats

This work presents:

  1. A mathematically consistent framework
  2. Empirical patterns confirmed across 1.2 million objects
  3. A possible connection to string theory
  4. A hidden conservation law of gravity

This work does NOT prove:

  1. That string theory is correct
  2. That Q and R are literally the dilaton and Kahler modulus
  3. That no alternative explanations exist

The connection to string theory remains a hypothesis, not a conclusion.

Last updated: January 11, 2026

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A novel two-field modified gravity framework from string theory, validated on 708k galaxies

doi.org/10.5281/zenodo.17806442

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python physics cosmology astrophysics string-theory modified-gravity calabi-yau galaxy-dynamics

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