{"paper":{"title":"Eccentric von Zeipel-Lidov-Kozai effects under mildly hierarchical triple systems: Influence of Brown corrections upon orbit flipping","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.SR"],"primary_cat":"astro-ph.EP","authors_text":"Hanlun Lei, Hao Gao","submitted_at":"2025-07-25T23:03:52Z","abstract_excerpt":"Mildly hierarchical three-body systems are widespread in the Universe, exemplified by planets in stellar binaries and stars in black-hole binaries. In such systems, Brown Hamiltonian corrections play a crucial role in governing the long-term dynamical evolution. In this work, we extend Brown corrections to include octupole-order coupling terms, thereby formulating a more accurate dynamical model for predicting long-term dynamical behaviors. The utilization of the gauge freedom in canonical transformation shows that the quadrupole-octupole coupling term vanishes and the octupole-octupole coupli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19709","kind":"arxiv","version":1},"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/2507.19709/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"}