QO+R Framework

A Two-Field Phenomenological Modified-Gravity Hypothesis

Author: Jonathan Édouard Slama Affiliation: Metafund Research Division, Strasbourg, France Contact: jonathan.slama@outlook.fr · jonathan@metafund.in ORCID: 0009-0002-1292-4350 Version: 3.1 (May 2026)

Concept DOI (all versions, always resolves to latest): 10.5281/zenodo.17806441 Version 3.1 DOI (this release): 10.5281/zenodo.20153973 Version 3.0 DOI (December 2025): 10.5281/zenodo.17806442

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Overview

This repository documents the QO+R framework: a two-field phenomenological modified-gravity hypothesis, with empirical analyses on ~708,000 galaxies across multiple datasets and a tentative theoretical embedding in Type IIB string theory.

The framework provides a phenomenological description of a non-monotonic environmental dependence detected in Baryonic Tully–Fisher residuals. The string-theory embedding remains exploratory, and the observed empirical pattern may admit alternative single-field, baryonic, or population-mixing explanations that have not been exhaustively ruled out. Independent investigation is encouraged.

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📋 Status of the papers in this repository

Paper	Title (short)	Status	Datasets	Key result
Paper 1	A non-monotonic environmental trend in BTFR residuals	Major revision at Scientific Reports (submission #2025-12-33523)	SPARC, ALFALFA, Little THINGS, IllustrisTNG	Non-monotonic trend detected in SPARC: a = +1.33 ± 0.25, p < 10⁻⁶
Paper 2	Residual structure in clinical biomarker ratios	Methodology extension; not a clinical validation	NHANES 2017–2018 (N = 9,254), Breast Cancer Coimbra (N = 116)	72/85 disease–residual combinations show significant distribution differences
Paper 3	From string theory to galactic observations	Theoretical companion (v2, tentative embedding)	Type IIB supergravity → CY₃ (quintic 𝐏⁴[5])	λ_QR ~ 𝒪(1) emerges from KKLT-style moduli stabilisation
Paper 4	QO+R validation suite (experimental)	Experimental, not part of v3.1 Zenodo deposit	Multiple datasets (TNG, KiDS, Planck, Gaia, WALLABY)	Internal validation work; claims have not been harmonised with the prudent tonal framework of the Scientific Reports revision

⚠️ Note on Paper 4. Paper 4 (Paper4-QOR-Validation/) contains earlier-version experimental work whose claims (e.g. a "conservation law of gravity", "26σ significance", "alternative theories eliminated") have not been harmonised with the prudent tonal framework adopted in the v3.1 revision of Paper 1 and the response letters to Scientific Reports. It is preserved in the repository for transparency and to document the research trajectory, but should not be relied upon as part of the v3.1 scientific content. A future v3.2 release will either retire or substantially revise Paper 4.

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🆕 What's new in v3.1 (May 2026)

This release reflects the substantial revision of Paper 1 during the major-revision process at Scientific Reports.

Tonal harmonisation in Paper 1

Approximately forty individual claims have been softened in the manuscript, supplements, and combined documentation. Representative examples:

• "discovery" → "detection" / "evidence for" in section headings, captions, and the summary;
• "confirmed" in IllustrisTNG → "recovered" / "tested" / "supported" (depending on context);
• "independent replication in ALFALFA" → "complementary support from ALFALFA";
• "killer prediction" → "discriminating prediction" (throughout);
• "robustly required by the data" → "strongly favoured by the data within the tested model classes";
• "no single-field theory could reproduce" → "not naturally produced by the simple single-field model tested in the previous section";
• "a discriminating signature of the two-field structure" → "difficult to accommodate within the simple monotonic single-field model considered here … should not be interpreted as excluding all possible single-field, baryonic, or population-mixing alternatives";
• "the model was falsified" → "the simple monotonic single-field model was disfavoured by the data";
• "consistent with all existing precision tests" → "not in obvious conflict with the precision tests considered here; a full constraint analysis across other regimes remains necessary".

Three new supplementary analyses (added to the Scientific Reports submission)

• S1 — Environmental-proxy sensitivity to scale. Fixed-aperture 2MRS density proxies at six radii (1, 2, 3, 5, 7, 10 Mpc) compared with the catalog-based structural classification.
• S2 — Formal model comparison. Five models (flat / linear / quadratic / broken-line / cubic spline) compared on the SPARC sample using AIC, BIC, and Akaike weights. Non-monotonic models strongly favoured over monotonic alternatives (Δ AIC ≈ 39.9 between best non-monotonic model and the linear model).
• S3 — Isolation-controlled re-analysis in IllustrisTNG. Stratification by 5th-nearest-neighbour distance within the R-dominated sample (N = 9,386). Sign inversion concentrated in the densest quartile (Q1: 5.2σ); disappears in the most isolated quartile (Q4: non-significant).

Numerical consistency improvements

• SPARC subsample sizes (N = 181 / 175 / 169) used in different analyses are now explicitly distinguished;
• SPARC curvature coefficient harmonised to a = +1.33 ± 0.25 throughout (previously partially +1.36 ± 0.24);
• All references to "26σ" in TNG removed in favour of the more conservative isolation-controlled 5.3σ (full R-dominated sample) and 5.2σ (densest quartile) figures.

Title change in Paper 1

• v3.0 (December 2025): "A non-monotonic environmental signature in galaxy dynamics suggests dual scalar fields"
• v3.1 (May 2026): "A non-monotonic environmental trend in Baryonic Tully–Fisher residuals: empirical evidence and a two-field phenomenological interpretation"

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📖 Reading order

If you are coming from the Scientific Reports peer review and want to quickly navigate the v3.1 material:

Document	Where to find it
Revised Paper 1 manuscript (PDF)	../Review_Scientific_report/09_Manuscrit_Revise_Final/NATURE_ARTICLE_revised.pdf
Supplementary S1, S2, S3 (PDF)	../Review_Scientific_report/09_Manuscrit_Revise_Final/supplementary/supplementary_material.pdf
Cover letter to the Editor	../Review_Scientific_report/09_Manuscrit_Revise_Final/response_letter/cover_letter.pdf
Response to Referee 1	../Review_Scientific_report/09_Manuscrit_Revise_Final/response_letter/response_letter_R1.pdf
Response to Referee 2	../Review_Scientific_report/09_Manuscrit_Revise_Final/response_letter/response_letter_R2.pdf
Combined Papers 1+2+3 (single PDF, v3.1)	combined_papers/qor_combined_papers_v3_1.pdf
Paper 1 v3.1 standalone	Paper1-BTFR-UShape/manuscript/reviewed_version/paper1_qor_btfr_v3_1.pdf

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Repository structure

QO-R-JEDSLAMA/
├── README.md                       # This file
├── DATA_SOURCES.md                 # How to obtain all datasets
├── PUBLICATION_AUDIT.md            # Quality checklist
├── LICENSE                         # MIT License
├── requirements.txt                # Python dependencies
│
├── Paper1-BTFR-UShape/             # Paper 1: BTFR environmental trend
│   ├── manuscript/                 # v3.0 LaTeX + PDF
│   │   └── reviewed_version/       # v3.1 (current, harmonised tone)
│   ├── figures/                    # 13 publication figures
│   ├── data/                       # SPARC + ALFALFA + 2MRS processed
│   └── tests/                      # 13 reproducibility scripts
│
├── Paper2-Residual-Diagnostics/    # Paper 2: methodology extension
│   ├── nhanes_extension/           # NHANES analysis + manuscript
│   ├── figures/                    # Coimbra figures
│   └── data/                       # Clinical datasets
│
├── Paper3-ToE/                     # Paper 3: theoretical companion
│   ├── manuscript/                 # LaTeX + PDF (v2)
│   ├── figures/                    # 8 figures
│   └── tests/                      # TNG-300 validation scripts
│
├── Paper4-QOR-Validation/          # Paper 4: experimental, see warning above
│   ├── manuscript/                 # LaTeX + PDF (not harmonised v3.1)
│   ├── experimental/               # Research documentation
│   ├── tests/                      # 14-test validation suite
│   └── data/                       # Multi-context datasets
│
└── combined_papers/                # Single combined PDF of Papers 1+2+3 (v3.1)
    ├── qor_combined_papers_v3_1.tex
    ├── qor_combined_papers_v3_1.pdf
    ├── body_paper1.tex
    ├── body_paper2.tex
    ├── body_paper3.tex
    └── figures/                    # Mirror of all figures organised by paper

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Data sources used in v3.1

Dataset	Type	N used	Source	Papers
SPARC	Resolved kinematics	181 (full) / 175 (env-classified) / 169 (2MRS cross-matched)	Lelli et al. 2016	1, 3, 4
ALFALFA α.100	H I linewidths	21,834	Haynes et al. 2018	1, 3, 4
Little THINGS	Dwarf irregulars	40	Hunter et al. 2012	1
IllustrisTNG 50/100/300	Cosmological simulation	~685,000 (combined)	Pillepich et al. 2018 + IllustrisTNG	1, 3, 4
2MRS	Galaxy environments	as catalogue	Huchra et al. 2012	1 (S1)
NHANES 2017–2018	Clinical	9,254	CDC	2
Breast Cancer Coimbra	Clinical	116	Patricio et al. 2018	2
WALLABY, KiDS DR4, Planck PSZ2, Gaia DR3	Various	varies	ASKAP / ESO / ESA	4 (experimental)

See DATA_SOURCES.md for complete download instructions.

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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. Reproduce the Paper 1 SPARC detection

cd Paper1-BTFR-UShape/tests/03_ushape_discovery
python discover_ushape.py

4. Compile the combined Papers 1+2+3 (v3.1)

cd combined_papers
pdflatex qor_combined_papers_v3_1.tex
pdflatex qor_combined_papers_v3_1.tex   # Second pass for TOC + bibliography

5. Compile the Scientific Reports revised manuscript and supplements

cd ../Review_Scientific_report/09_Manuscrit_Revise_Final
pdflatex NATURE_ARTICLE_revised.tex
pdflatex NATURE_ARTICLE_revised.tex

cd supplementary
pdflatex supplementary_material.tex
pdflatex supplementary_material.tex

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System requirements

Software dependencies

• Python 3.9+ (tested on 3.9, 3.10, 3.11)
• LaTeX distribution (TeX Live 2023+ or MiKTeX) for manuscript compilation
• See requirements.txt for the full Python package list

Operating systems tested

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

Hardware

• Standard desktop, 8 GB RAM, ~5 GB disk space for full datasets
• No GPU required

Reproduction time (approximate)

• Quick SPARC reproduction: ~30 seconds
• Full validation suite (Paper 1 + 3): ~5 minutes
• Complete reproduction with all downloads: ~2 hours

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Theoretical framework (Paper 3 summary)

The QO+R Lagrangian (effective 4D action)

L = √(-g) [ (M_P²/2) F(χ) R − (1/2)(∂φ)² − (Z(χ)/2)(∂χ)² − V(φ,χ) ]
  + L_matter[ A²(φ,χ) g_μν , ψ ]

Where:

• φ (Q-field): coupled preferentially to gas (electromagnetic);
• χ (R-field): coupled preferentially to stars (gravitational);
• A(φ,χ) = exp[ β (φ − κχ)/M_P ]: conformal coupling to the matter sector.

Tentative string-theory embedding (Paper 3, v2)

10D Type IIB supergravity
         │
         ▼
Calabi–Yau compactification on the quintic 𝐏⁴[5]
         │
         ▼
4D effective theory : dilaton φ ↔ Q ; Kähler modulus T ↔ R
         │
         ▼
KKLT-style moduli stabilisation
         │
         ▼
QO+R effective Lagrangian with λ_QR ~ 𝒪(1)

The string-theory embedding is presented as a tentative phenomenological mapping rather than as a fundamental derivation; alternative origins of the same 4D effective behaviour cannot be excluded.

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How to cite

If you use this work, please cite the v3.1 Zenodo deposit:

@software{slama2026qor_v31,
  author    = {Slama, Jonathan \'Edouard},
  title     = {{QO+R Framework: A Two-Field Phenomenological
                Modified-Gravity Hypothesis (v3.1)}},
  year      = 2026,
  month     = may,
  publisher = {Zenodo},
  version   = {3.1},
  doi       = {10.5281/zenodo.17806441},
  url       = {https://doi.org/10.5281/zenodo.17806441}
}

For the Scientific Reports peer-review record (Paper 1 only), the submission identifier is #2025-12-33523 (currently in major revision).

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License

This project is released under the MIT License — see LICENSE for the full text. The associated datasets retain their original licences (see DATA_SOURCES.md).

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Acknowledgments

• SPARC team (Lelli, McGaugh, Schombert) for the galaxy database;
• IllustrisTNG collaboration for simulation data access;
• ALFALFA team (Haynes et al.) for the H I survey;
• 2MASS Redshift Survey team for the environmental density catalogue;
• Little THINGS team for dwarf-irregular kinematics;
• NHANES / CDC for the clinical biomarker data used in Paper 2;
• The two anonymous referees of Scientific Reports whose careful evaluation substantially improved Paper 1;
• Iris, an AI assistant trained with my reasoning methodology, for invaluable help with manuscript drafting, supplementary-analysis design, and iterative refinement of the scientific arguments throughout this revision cycle.

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Important caveats

This work presents:

1. A phenomenological two-field framework that describes a non-monotonic environmental trend detected in BTFR residuals;
2. Empirical evidence for that trend in SPARC, with complementary linewidth-based support from ALFALFA;
3. A simulation-based test of a discriminating prediction (sign inversion in gas-poor, stellar-massive systems) in IllustrisTNG;
4. A tentative mapping of the framework onto Type IIB string theory via Calabi–Yau compactification.

This work does NOT establish:

1. That string theory is the correct underlying theory of gravity;
2. That the Q and R fields are literally the type-IIB dilaton and the Kähler modulus rather than effective phenomenological proxies;
3. That alternative single-field, baryonic, or population-mixing explanations of the observed pattern have been exhaustively excluded;
4. That the simulation-based sign-inversion test in TNG constitutes an observational confirmation; direct observational follow-up in gas-poor early-type galaxies is the subject of a forthcoming companion paper.

The connection between empirical observation and string-theory phenomenology remains a hypothesis under investigation, not a confirmed result.

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Last updated: 12 May 2026 — version 3.1.