Conditional Geometric Relational Diagnostics (c-GRD): Constraint Topology and Duality in String-Theoretic Frameworks
Fuente:
Zenodo
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Recurso digital |
| Publicado: |
Zenodo
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866901909229535232 |
|---|---|
| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18315249 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Conditional Geometric Relational Diagnostics (c-GRD): Constraint Topology and Duality in String-Theoretic Frameworks De Jesus, Elias 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 <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> |
| title | Conditional Geometric Relational Diagnostics (c-GRD): Constraint Topology and Duality in String-Theoretic Frameworks |
| topic | 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 |
| url | https://doi.org/10.5281/zenodo.18315249 |