Emergent Geometry from Lyapunov Stability: Effective Metric Structure from the Second Variation of the RMB Stability Functional
Fuente:
Zenodo
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Recurso digital |
| Lenguaje: | inglés |
| Publicado: |
Zenodo
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866901450594975744 |
|---|---|
| author | Dellomonaco, Davide |
| author_facet | Dellomonaco, Davide |
| contents | <p>This note develops a minimal and background-independent mechanism for emergent geometric description within the Space–Matter–Motion (RMB) theory.<br>Starting from the RMB stability functional, it is shown that Lyapunov-stable attractors naturally induce an effective metric-like structure through the second variation. The resulting positive-definite quadratic form defines a stability metric on the configuration space of organized motion.</p> <p>The construction is pre-dynamical and does not assume a spacetime manifold, metric, or geometric postulates. Instead, geometric notions arise as secondary diagnostic structures encoding local stability properties of motion. Under fluctuations, the inverse stability operator admits a statistical interpretation in terms of perturbation correlations.</p> <p>This mechanism links directly to the RMB stability functional (Stability Principle Note) and to the master equation derived in the RMB Mathematical Core Note, providing a coherent bridge between stability, variational structure, and emergent geometry within the RMB framework. The work serves as a foundational note complementing the canonical RMB formulation and its subsequent dynamical and phenomenological applications.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18391786 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Emergent Geometry from Lyapunov Stability: Effective Metric Structure from the Second Variation of the RMB Stability Functional Dellomonaco, Davide Space–Matter–Motion theory RMB theory emergent geometry Lyapunov stability variational methods second variation configuration space background-independent physics RMB stability functional pre-dynamical framework <p>This note develops a minimal and background-independent mechanism for emergent geometric description within the Space–Matter–Motion (RMB) theory.<br>Starting from the RMB stability functional, it is shown that Lyapunov-stable attractors naturally induce an effective metric-like structure through the second variation. The resulting positive-definite quadratic form defines a stability metric on the configuration space of organized motion.</p> <p>The construction is pre-dynamical and does not assume a spacetime manifold, metric, or geometric postulates. Instead, geometric notions arise as secondary diagnostic structures encoding local stability properties of motion. Under fluctuations, the inverse stability operator admits a statistical interpretation in terms of perturbation correlations.</p> <p>This mechanism links directly to the RMB stability functional (Stability Principle Note) and to the master equation derived in the RMB Mathematical Core Note, providing a coherent bridge between stability, variational structure, and emergent geometry within the RMB framework. The work serves as a foundational note complementing the canonical RMB formulation and its subsequent dynamical and phenomenological applications.</p> |
| title | Emergent Geometry from Lyapunov Stability: Effective Metric Structure from the Second Variation of the RMB Stability Functional |
| topic | Space–Matter–Motion theory RMB theory emergent geometry Lyapunov stability variational methods second variation configuration space background-independent physics RMB stability functional pre-dynamical framework |
| url | https://doi.org/10.5281/zenodo.18391786 |