What question did this study set out to answer?

The aim is to explore the QO+R framework as a modified-gravity hypothesis connected to empirical galaxy observations.

May 15, 2026Open Access

QO+R Framework: A Two-Field Phenomenological Hypothesis

Key Points

The aim is to explore the QO+R framework as a modified-gravity hypothesis connected to empirical galaxy observations.
Analyzed ~708,000 galaxies for environmental trends in the baryonic Tully-Fisher relation (BTFR).
Employed residual diagnostic methodologies using diverse datasets including NHANES and breast cancer data.
Tentatively linked the framework to Type IIB string theory through Calabi-Yau compactification
Detected a non-monotonic trend in BTFR residuals (a=+1.33±0.25, p<10⁻⁶).
Established broader methodological applicability through residual analysis but not clinical validation.
Outlined exploratory connections between observed patterns and theoretical structures from string theory.

Abstract

A two-field phenomenological modified-gravity hypothesis (QO+R), with empirical analyses on ~708, 000 galaxies and a tentative embedding in Type IIB string theory. This repository (v3. 1, May 2026) contains three companion papers: - Paper 1 — Environmental Modulation of the Baryonic Tully–Fisher Relation: detection of a non-monotonic environmental trend in BTFR residuals in SPARC (a=+1. 33±0. 25, p<10⁻⁶), with complementary support from ALFALFA and a simulation-based test in IllustrisTNG. Companion documentation to Scientific Reports submission #2025-12-33523 (currently in major revision) ; includes three new supplementary analyses (S1, S2, S3) and response letters. - Paper 2 — Residual Diagnostic Methodology: extension of the residual-analysis approach to clinical biomarker ratios using NHANES and Breast Cancer Coimbra data. Demonstrates broader methodological applicability; not a clinical validation. - Paper 3 — From String Theory to Galactic Observations: tentative derivation of the QO+R Lagrangian from a Calabi–Yau compactification of Type IIB supergravity, with λQR ~ O (1) emerging from KKLT-style moduli stabilisation. The framework provides a phenomenological description of the observed non-monotonic environmental pattern. The string-theory embedding remains exploratory and the empirical pattern may admit alternative astrophysical explanations; independent investigation is encouraged. v3. 1 (May 2026): tonal harmonisation in Paper 1, three new supplementary analyses, numerical consistency improved (a=+1. 33±0. 25 standardised, "26σ" claims replaced by isolation-controlled 5. 3σ/5. 2σ figures).

QO+R Framework: A Two-Field Phenomenological Hypothesis

Key Points

Abstract

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