Relational and Logical Geometry Across Scales: The RTLI Book of Principles, Methods, and Tests
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| Natura: | Recurso digital |
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Zenodo
2025
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| _version_ | 1866901946534723584 |
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| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| contents | <p>This book presents the <span><strong>Relational Thermodynamic Layered Index (RTLI)</strong></span> framework as a methods-first, open-science approach to understanding coherence across physical systems and scales. RTLI is built on a small set of relational and geometric principles that constrain how systems distribute variance, achieve stability, and transition between regimes. Rather than introducing new forces or fields, the framework focuses on <span><strong>logical–relational geometry</strong></span>, where coherence corridors, stability thresholds, and coupling costs emerge from distributed constraints and efficient packing.</p> <p>The book develops the core principles of RTLI, including impedance-based geometry, quadratic coupling (rectification) costs, and the Relational Vortex Principle (RVP), which predicts that disorder and scatter peak at marginal stability rather than at extremes. These principles lead to explicit, falsifiable predictions—such as universal coherence angles, bounded coherence ratios, and transition-localized suppression signals—that can be tested directly against data.</p> <p>Detailed analytical methods are provided for applying RTLI to real systems, including galaxy dynamics, cross-scale correlations, and harmonic and PCA-based diagnostics. Worked examples demonstrate how the same relational structure manifests differently depending on physical context, while remaining constrained by the same underlying geometry. The framework is presented as modular and extensible, with clear falsification criteria and an explicit invitation for independent testing, extension, and remixing under an open-science license.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17915576 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Relational and Logical Geometry Across Scales: The RTLI Book of Principles, Methods, and Tests De Jesus, Elias Relational coherence RTLI framework Relational geometry Distributed constraint Marginal stability Coherence corridors Quadratic coupling cost Rectification Relational Vortex Principle Galaxy dynamics Structure formation Information geometry Cross-scale physics Open science methods Falsifiable frameworks <p>This book presents the <span><strong>Relational Thermodynamic Layered Index (RTLI)</strong></span> framework as a methods-first, open-science approach to understanding coherence across physical systems and scales. RTLI is built on a small set of relational and geometric principles that constrain how systems distribute variance, achieve stability, and transition between regimes. Rather than introducing new forces or fields, the framework focuses on <span><strong>logical–relational geometry</strong></span>, where coherence corridors, stability thresholds, and coupling costs emerge from distributed constraints and efficient packing.</p> <p>The book develops the core principles of RTLI, including impedance-based geometry, quadratic coupling (rectification) costs, and the Relational Vortex Principle (RVP), which predicts that disorder and scatter peak at marginal stability rather than at extremes. These principles lead to explicit, falsifiable predictions—such as universal coherence angles, bounded coherence ratios, and transition-localized suppression signals—that can be tested directly against data.</p> <p>Detailed analytical methods are provided for applying RTLI to real systems, including galaxy dynamics, cross-scale correlations, and harmonic and PCA-based diagnostics. Worked examples demonstrate how the same relational structure manifests differently depending on physical context, while remaining constrained by the same underlying geometry. The framework is presented as modular and extensible, with clear falsification criteria and an explicit invitation for independent testing, extension, and remixing under an open-science license.</p> |
| title | Relational and Logical Geometry Across Scales: The RTLI Book of Principles, Methods, and Tests |
| topic | Relational coherence RTLI framework Relational geometry Distributed constraint Marginal stability Coherence corridors Quadratic coupling cost Rectification Relational Vortex Principle Galaxy dynamics Structure formation Information geometry Cross-scale physics Open science methods Falsifiable frameworks |
| url | https://doi.org/10.5281/zenodo.17915576 |