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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.18315249 |
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Table of Contents:
- <p>This technical note introduces and empirically validates <span><strong>Conditional Geometric Relational Diagnostics (c-GRD)</strong></span>, a falsifiable diagnostic framework for analyzing <span><strong>constraint topology</strong></span> in complex physical systems. c-GRD extends Two-Boundary Inference (TBI) by generating conditional, pre-registrable predictions of three types: <span><strong>(I) relational invariance</strong></span>, <span><strong>(II) forbidden regions</strong></span>, and <span><strong>(III) regime transitions</strong></span>, expressed through a signed radial coordinate <span>\rho = \ln(R/\sqrt{e})</span> constructed from dimensionless observable ratios.</p> <p>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 <span>\rho = 0</span>, coincident with the empirically established MOND acceleration scale; (ii) a correct null result for CMB low-<span>\ell</span> 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.</p> <p>c-GRD is explicitly <span><strong>diagnostic, not predictive</strong></span> of numerical constants, and does not advocate any specific theory of gravity or cosmology. Its relevance to string theory lies in providing a <span><strong>constraint-topology and duality-oriented diagnostic language</strong></span> for large theory spaces and landscapes, clarifying why predictivity may be structurally limited in the absence of boundary accessibility or global compression constraints.</p>