{"paper":{"title":"Symplectic mechanics of relativistic spinning compact bodies. III. quadratic-in-spin integrability in Type-D Einstein spacetimes: persistence and breakdown","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"gr-qc","authors_text":"Adrien Druart, Paul Ramond, Soichiro Isoyama","submitted_at":"2026-01-10T03:48:10Z","abstract_excerpt":"We investigate the integrability of spinning compact body dynamics at quadratic order in spin in four-dimensional Einstein spacetimes admitting a non-degenerate Killing--Yano tensor. Working within the Mathisson--Papapetrou--Tulczyjew--Dixon framework under the Tulczyjew--Dixon spin supplementary condition, we model the spin-induced quadrupole with a deformability parameter $\\kappa$, where $\\kappa=1$ corresponds to black holes. The dynamics is formulated as a Hamiltonian system on a 10-dimensional physical phase space obtained by Dirac--Bergmann reduction. For $\\kappa=1$, we establish Liouvill"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.06416","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.06416/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}