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We derive analytical expressions for the magnitude of the eccentricity change and its dependence on the sweep rate and on planetary parameters; the $\\nu_6$ sweeping leads to either an increase or a decrease of eccentricity depending on an asteroid's initial orbit. Based on the slowest rate of $\\nu_6$ sweeping that allows a remnant asteroid belt to survive, we derive a lower limit on Satu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1102.3131","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2011-02-15T17:26:16Z","cross_cats_sorted":[],"title_canon_sha256":"9465f378c440a51c5923dae9a2f9b9fe63f54cda23804319519dba2e519d3cd3","abstract_canon_sha256":"13b5d82d3d39470ed7a1e8120d882ee2a7dc1c7e7b7ec1afbfe0fdcee4bff544"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:10.777852Z","signature_b64":"1qWYRWX9LCRrG24kQ+TMb+fUGbTy2Yh+cOk9tNaKLkBjserO0h9SUOKbJHa8iY9QBGyMs8GWTDozz8xpqKcPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b469075d1e1d6fee9182e8c9792b1c993bf787de77863cd9cc1ac87d7358a72","last_reissued_at":"2026-05-18T02:03:10.777204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:10.777204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Secular resonance sweeping of the main asteroid belt during planet migration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"David A. 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