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Conditional Geometric Relational Diagnostics (c-GRD): Constraint Topology and Duality in String-Theoretic Frameworks

Authors: De Jesus, Elias;

Conditional Geometric Relational Diagnostics (c-GRD): Constraint Topology and Duality in String-Theoretic Frameworks

Abstract

Related Work: De Jesus, Elias. (2026). Diagnostic Map of Constraint-Coupled Vacua in String-Inspired Models. Zenodo. https://doi.org/10.5281/zenodo.18320070 This technical note introduces and empirically validates Conditional Geometric Relational Diagnostics (c-GRD), a falsifiable diagnostic framework for analyzing constraint topology in complex physical systems. c-GRD extends Two-Boundary Inference (TBI) by generating conditional, pre-registrable predictions of three types: (I) relational invariance, (II) forbidden regions, and (III) regime transitions, expressed through a signed radial coordinate \rho = \ln(R/\sqrt{e}) constructed from dimensionless observable ratios. The framework is validated using galaxy dynamics data from the Radial Acceleration Relation (RAR) and low-multipole CMB power spectra. Results show: (i) a localized and asymmetric regime transition in RAR at \rho = 0, coincident with the empirically established MOND acceleration scale; (ii) a correct null result for CMB low-\ell data where no transition is physically expected; (iii) strong relational variance suppression (≈90%) in acceleration ratios relative to null expectation; and (iv) strict or marginal compliance with pre-registered forbidden regions consistent with measurement scatter. c-GRD is explicitly diagnostic, not predictive of numerical constants, and does not advocate any specific theory of gravity or cosmology. Its relevance to string theory lies in providing a constraint-topology and duality-oriented diagnostic language for large theory spaces and landscapes, clarifying why predictivity may be structurally limited in the absence of boundary accessibility or global compression constraints.

Keywords

Constraint topology Two-Boundary Inference (TBI) Geometric Relational Diagnostics (GRD) Conditional diagnostics String theory landscape Duality Swampland Predictivity Radial Acceleration Relation (RAR) Galaxy dynamics Cosmic microwave background (CMB) Relational invariance Forbidden regions Regime transitions Information geometry

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
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