Graph-Schur Stability and Certified Rank Selection for Dipole–Quadrupole–Octupole BBGKY Correctors
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2026
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| _version_ | 1866902026741350400 |
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| author | Panasenko, Dmytro |
| author_facet | Panasenko, Dmytro |
| contents | <p>This preprint presents a finite-block spectral certification method for density-selected BBGKY response correctors. The unconditional layer is a three-block graph-Schur theorem: a cumulative rank-fifteen dipole–quadrupole–octupole Gram matrix is coercive whenever the diagonal response blocks have spectral gaps and the normalized off-diagonal coupling graph has spectral radius below one.</p> <p> </p> <p>The BBGKY-facing layer is deliberately conditional. The abstract block matrix is realized as an observable-dual Gram matrix of finite multiple response tests, and closure estimates are stated under explicit cutoff, response-map, residual-tail, source, and scale-gate hypotheses. This separation keeps the graph-Schur result a finite-dimensional spectral theorem while making the kinetic-response application model-dependent and checkable.</p> <p> </p> <p>The manuscript also introduces a hysteresis-controlled certified selector over the finite-rank menu {3,8,15}. A reproducible manufactured benchmark on the three-dimensional torus illustrates the certification pipeline using explicit trigonometric response cells, a generated 15 x 15 Gram certification table, a trajectory-derived selector table, and one diagnostic figure.</p> <p> </p> <p>This is the author-submitted manuscript version associated with the submission to Mathematical Methods in the Applied Sciences, manuscript ID 1622935. The preprint was made available after journal submission for transparency.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20364198 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Graph-Schur Stability and Certified Rank Selection for Dipole–Quadrupole–Octupole BBGKY Correctors Panasenko, Dmytro BBGKY hierarchy mean-field limit density-selected phase dynamics finite-rank tensor correctors graph-Schur stability Schur complement block Gram matrix dipole-quadrupole-octupole coupling rank selection hysteresis mathematical physics <p>This preprint presents a finite-block spectral certification method for density-selected BBGKY response correctors. The unconditional layer is a three-block graph-Schur theorem: a cumulative rank-fifteen dipole–quadrupole–octupole Gram matrix is coercive whenever the diagonal response blocks have spectral gaps and the normalized off-diagonal coupling graph has spectral radius below one.</p> <p> </p> <p>The BBGKY-facing layer is deliberately conditional. The abstract block matrix is realized as an observable-dual Gram matrix of finite multiple response tests, and closure estimates are stated under explicit cutoff, response-map, residual-tail, source, and scale-gate hypotheses. This separation keeps the graph-Schur result a finite-dimensional spectral theorem while making the kinetic-response application model-dependent and checkable.</p> <p> </p> <p>The manuscript also introduces a hysteresis-controlled certified selector over the finite-rank menu {3,8,15}. A reproducible manufactured benchmark on the three-dimensional torus illustrates the certification pipeline using explicit trigonometric response cells, a generated 15 x 15 Gram certification table, a trajectory-derived selector table, and one diagnostic figure.</p> <p> </p> <p>This is the author-submitted manuscript version associated with the submission to Mathematical Methods in the Applied Sciences, manuscript ID 1622935. The preprint was made available after journal submission for transparency.</p> |
| title | Graph-Schur Stability and Certified Rank Selection for Dipole–Quadrupole–Octupole BBGKY Correctors |
| topic | BBGKY hierarchy mean-field limit density-selected phase dynamics finite-rank tensor correctors graph-Schur stability Schur complement block Gram matrix dipole-quadrupole-octupole coupling rank selection hysteresis mathematical physics |
| url | https://doi.org/10.5281/zenodo.20364198 |