Compactness, Coupling Density, and Entropy-Like Organization on the Thales Partition Manifold: A Conservative Scalar Diagnostic for Equipartition, Horizon Response, and Cosmic-Web Local Modes
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2026
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| _version_ | 1866901997022609408 |
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| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| contents | <p class="p1">This technical note introduces a conservative scalar diagnostic for comparing compactness, entropy saturation, coupling organization, and density-like structure in gravitational systems. The construction uses the constrained binary partition <span class="s1">a+b=1</span> and associated Thales variables <span class="s1">h=\sqrt{ab}</span>, <span class="s1">\chi=|a-b|</span>, and <span class="s1">R_{\rm part}=1/(4ab)</span> to measure departure from balanced coupling.</p> <p class="p1">The main physical motivation is Padmanabhan’s equipartition view of gravitational dynamics. The note does not derive or replace the Einstein field equation, nor does it claim to prove thermodynamic gravity. Instead, it provides a normalized scalar language for identifying how far a system lies from two-channel equipartition once physically meaningful channels are defined.</p> <p class="p1">For compact gravitating systems, the compactness parameter <span class="s1">C=2GM/(rc^2)</span> is read as the partition <span class="s1">C+(1-C)=1</span>. Using standard formulas, the note records the exact identities <span class="s1">S_B/S_{BH}=C</span>, <span class="s1">T_{\rm screen}/T_H=C</span>, and <span class="s1">T_{\rm prop}/T_H=C/\sqrt{1-C}</span>, while carefully distinguishing the physical Schwarzschild horizon response <span class="s1">R_H=(1-C)^{-1}</span> from the symmetric partition response <span class="s1">R_{\rm part}=[4C(1-C)]^{-1}</span>.</p> <p class="p1">The note also separates ordinary material density, coupling density, and rational-state density, arguing that material concentration and coupling organization should not be conflated. A pilot cosmic-web local-mode analysis based on the SDSS-IV Cosmic Web Catalog finds that local gradient partitions are dominated by near-equipartition states, while higher-<span class="s1">R</span> regimes show weaker balanced gradient participation and mildly higher ordinary density. This supports the use of <span class="s1">R_{\rm part}</span> as a diagnostic coordinate for entropy-like organization, while leaving physical interpretation to domain-specific gravitational theory.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20208935 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Compactness, Coupling Density, and Entropy-Like Organization on the Thales Partition Manifold: A Conservative Scalar Diagnostic for Equipartition, Horizon Response, and Cosmic-Web Local Modes De Jesus, Elias Thales partition; compactness; entropy saturation; Padmanabhan equipartition; holographic equipartition; gravitational thermodynamics; Bekenstein bound; Bekenstein-Hawking entropy; Unruh temperature; Hawking temperature; horizon response; coupling density; rational-state density; cosmic web; SDSS-IV Cosmic Web Catalog; SPARC; binary partition; thermodynamic gravity; scalar diagnostic; bulk-boundary thermodynamics. <p class="p1">This technical note introduces a conservative scalar diagnostic for comparing compactness, entropy saturation, coupling organization, and density-like structure in gravitational systems. The construction uses the constrained binary partition <span class="s1">a+b=1</span> and associated Thales variables <span class="s1">h=\sqrt{ab}</span>, <span class="s1">\chi=|a-b|</span>, and <span class="s1">R_{\rm part}=1/(4ab)</span> to measure departure from balanced coupling.</p> <p class="p1">The main physical motivation is Padmanabhan’s equipartition view of gravitational dynamics. The note does not derive or replace the Einstein field equation, nor does it claim to prove thermodynamic gravity. Instead, it provides a normalized scalar language for identifying how far a system lies from two-channel equipartition once physically meaningful channels are defined.</p> <p class="p1">For compact gravitating systems, the compactness parameter <span class="s1">C=2GM/(rc^2)</span> is read as the partition <span class="s1">C+(1-C)=1</span>. Using standard formulas, the note records the exact identities <span class="s1">S_B/S_{BH}=C</span>, <span class="s1">T_{\rm screen}/T_H=C</span>, and <span class="s1">T_{\rm prop}/T_H=C/\sqrt{1-C}</span>, while carefully distinguishing the physical Schwarzschild horizon response <span class="s1">R_H=(1-C)^{-1}</span> from the symmetric partition response <span class="s1">R_{\rm part}=[4C(1-C)]^{-1}</span>.</p> <p class="p1">The note also separates ordinary material density, coupling density, and rational-state density, arguing that material concentration and coupling organization should not be conflated. A pilot cosmic-web local-mode analysis based on the SDSS-IV Cosmic Web Catalog finds that local gradient partitions are dominated by near-equipartition states, while higher-<span class="s1">R</span> regimes show weaker balanced gradient participation and mildly higher ordinary density. This supports the use of <span class="s1">R_{\rm part}</span> as a diagnostic coordinate for entropy-like organization, while leaving physical interpretation to domain-specific gravitational theory.</p> |
| title | Compactness, Coupling Density, and Entropy-Like Organization on the Thales Partition Manifold: A Conservative Scalar Diagnostic for Equipartition, Horizon Response, and Cosmic-Web Local Modes |
| topic | Thales partition; compactness; entropy saturation; Padmanabhan equipartition; holographic equipartition; gravitational thermodynamics; Bekenstein bound; Bekenstein-Hawking entropy; Unruh temperature; Hawking temperature; horizon response; coupling density; rational-state density; cosmic web; SDSS-IV Cosmic Web Catalog; SPARC; binary partition; thermodynamic gravity; scalar diagnostic; bulk-boundary thermodynamics. |
| url | https://doi.org/10.5281/zenodo.20208935 |