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They interact via Newtonian potential. $Q_3$ is captured by $Q_2$, and $Q_4$ travels back and forth between two centers. Based on a model of Gerver, we prove that there is a Cantor set of initial conditions which lead to solutions of the Hamiltonian system whose velocities are accelerated to infinity within finite time avoiding all early collisions."},"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":"1307.2645","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-10T01:41:17Z","cross_cats_sorted":[],"title_canon_sha256":"5a0da9dd82cef1adce538c749f955e49279ef6ab0222c05ee876563927b880a9","abstract_canon_sha256":"7e4091eabbfb121a66da4252348ac12d9602b861a5e6a68ecd6fbaa5782334cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:05.408274Z","signature_b64":"g5n5WPocsRd4epNjtSHmeH1TeHd1jezZ4HRdhBMMKltFUk4Fwl1gIisYNSp2nOir39wLNxzFaW3IcdrTF7+sDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71393dd00760eb4ed497133ed8465b0f495146dfb9afea9c2a64859f92033730","last_reissued_at":"2026-05-18T01:11:05.407784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:05.407784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Collision singularities in the Planar two-Center-two-Body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dmitry Dolgopyat, Jinxin Xue","submitted_at":"2013-07-10T01:41:17Z","abstract_excerpt":"In this paper, we study a model of simplified four-body problem called planar two-center-two-body problem. 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