Dual Closure on the Thales Partition Manifold: Empirical Test of Local Rapidity Closure and Global Ratio Closure on 4,124 SXS Binary Black Hole Simulations
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2026
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| _version_ | 1866901669507235840 |
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| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| contents | <p class="p1">This technical note tests a proposed <span class="s1"><strong>dual-closure architecture</strong></span> on the SXS Collaboration catalog of binary black hole simulations. The observable is the radiated-energy fraction,</p> <p class="p2">Y = E_{\mathrm{rad}}/M,</p> <p class="p1">computed from 4,124 cleaned SXS binary black hole simulations.</p> <p class="p1">The framework separates closure into two mechanisms. <span class="s1"><strong>Local rapidity closure</strong></span> asks whether residuals from a mass-partition backbone decay exponentially in the mass rapidity</p> <p class="p2">|\xi_{\mathrm{mass}}|=\left|\frac12\ln(m_1/m_2)\right|.</p> <p class="p1"><strong>Global ratio closure</strong> asks whether a finite ratio basis remains stable across spin regimes, with regime changes expressed mainly through coefficient shifts rather than changes in basis content.</p> <p class="p1">Three pre-specified empirical tests were performed. First, within low-, mid-, and high-spin strata, residuals from a mass-partition backbone decay exponentially in <span class="s1">|\xi_{\mathrm{mass}}|</span>, with decay rates <span class="s1">\lambda\in[1.39,1.95]</span>, <span class="s1">R^2_{\mathrm{fit}}\in[0.89,0.97]</span>, and <span class="s1">p\leq 5\times10^{-5}</span>. Second, residuals from a fuller mass+spin+binding model vary sharply across the effective-spin axis <span class="s1">\chi_{\mathrm{eff}}</span>, with a deep trough near <span class="s1">|\chi_{\mathrm{eff}}|\approx0.15\text{--}0.20</span> and a roughly sevenfold increase toward extreme spins, identifying <span class="s1">\chi_{\mathrm{eff}}</span> as a regime-boundary coordinate. Third, a seven-ratio basis,</p> <p class="p2">\{\eta,\eta^2,\chi_{\mathrm{eff}},\chi_{\mathrm{eff}}^2, b_{\mathrm{bind}},b_{\mathrm{bind}}^2,1/D\},</p> <p class="p1">remains broadly stable across spin regimes, while candidate mass-ratio variables outside the basis are statistically redundant.</p> <p class="p3">The results support the interpretation that BBH radiated energy is organized by <span class="s1"><strong>local rapidity closure within spin regimes</strong></span> and <span class="s1"><strong>global ratio-basis stability across regimes</strong></span>. The note does not propose a new phenomenological fitting formula for radiated energy and does not replace existing numerical-relativity remnant fits. Its contribution is diagnostic: it tests whether residual structure, regime dependence, and ratio-basis stability exhibit the dual-closure pattern predicted by the partition-framework architecture.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19736696 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Dual Closure on the Thales Partition Manifold: Empirical Test of Local Rapidity Closure and Global Ratio Closure on 4,124 SXS Binary Black Hole Simulations De Jesus, Elias binary black holes; SXS catalog; numerical relativity; radiated energy; remnant mass; effective spin; \chi_{\mathrm{eff}}; mass ratio; symmetric mass ratio; partition rapidity; ratio closure; rapidity closure; Thales partition manifold; backbone plus context; residual analysis; regime boundaries; gravitational waves; BBH merger; empirical model comparison; partition geometry; SXS simulations. <p class="p1">This technical note tests a proposed <span class="s1"><strong>dual-closure architecture</strong></span> on the SXS Collaboration catalog of binary black hole simulations. The observable is the radiated-energy fraction,</p> <p class="p2">Y = E_{\mathrm{rad}}/M,</p> <p class="p1">computed from 4,124 cleaned SXS binary black hole simulations.</p> <p class="p1">The framework separates closure into two mechanisms. <span class="s1"><strong>Local rapidity closure</strong></span> asks whether residuals from a mass-partition backbone decay exponentially in the mass rapidity</p> <p class="p2">|\xi_{\mathrm{mass}}|=\left|\frac12\ln(m_1/m_2)\right|.</p> <p class="p1"><strong>Global ratio closure</strong> asks whether a finite ratio basis remains stable across spin regimes, with regime changes expressed mainly through coefficient shifts rather than changes in basis content.</p> <p class="p1">Three pre-specified empirical tests were performed. First, within low-, mid-, and high-spin strata, residuals from a mass-partition backbone decay exponentially in <span class="s1">|\xi_{\mathrm{mass}}|</span>, with decay rates <span class="s1">\lambda\in[1.39,1.95]</span>, <span class="s1">R^2_{\mathrm{fit}}\in[0.89,0.97]</span>, and <span class="s1">p\leq 5\times10^{-5}</span>. Second, residuals from a fuller mass+spin+binding model vary sharply across the effective-spin axis <span class="s1">\chi_{\mathrm{eff}}</span>, with a deep trough near <span class="s1">|\chi_{\mathrm{eff}}|\approx0.15\text{--}0.20</span> and a roughly sevenfold increase toward extreme spins, identifying <span class="s1">\chi_{\mathrm{eff}}</span> as a regime-boundary coordinate. Third, a seven-ratio basis,</p> <p class="p2">\{\eta,\eta^2,\chi_{\mathrm{eff}},\chi_{\mathrm{eff}}^2, b_{\mathrm{bind}},b_{\mathrm{bind}}^2,1/D\},</p> <p class="p1">remains broadly stable across spin regimes, while candidate mass-ratio variables outside the basis are statistically redundant.</p> <p class="p3">The results support the interpretation that BBH radiated energy is organized by <span class="s1"><strong>local rapidity closure within spin regimes</strong></span> and <span class="s1"><strong>global ratio-basis stability across regimes</strong></span>. The note does not propose a new phenomenological fitting formula for radiated energy and does not replace existing numerical-relativity remnant fits. Its contribution is diagnostic: it tests whether residual structure, regime dependence, and ratio-basis stability exhibit the dual-closure pattern predicted by the partition-framework architecture.</p> |
| title | Dual Closure on the Thales Partition Manifold: Empirical Test of Local Rapidity Closure and Global Ratio Closure on 4,124 SXS Binary Black Hole Simulations |
| topic | binary black holes; SXS catalog; numerical relativity; radiated energy; remnant mass; effective spin; \chi_{\mathrm{eff}}; mass ratio; symmetric mass ratio; partition rapidity; ratio closure; rapidity closure; Thales partition manifold; backbone plus context; residual analysis; regime boundaries; gravitational waves; BBH merger; empirical model comparison; partition geometry; SXS simulations. |
| url | https://doi.org/10.5281/zenodo.19736696 |