{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C44FV4MFCPP6S6JYBPYR64H4L3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"92b321b1ecd63546e1c5ba1fc2c3c9a407023af51ad46ef81a0c478a4a0363b3","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-09T08:36:01Z","title_canon_sha256":"f2859ab152ebcb8ba0ad4daa0cf902af15bb21275c46fc890096e1586b797c49"},"schema_version":"1.0","source":{"id":"1602.02897","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02897","created_at":"2026-05-18T00:48:09Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02897v1","created_at":"2026-05-18T00:48:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02897","created_at":"2026-05-18T00:48:09Z"},{"alias_kind":"pith_short_12","alias_value":"C44FV4MFCPP6","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C44FV4MFCPP6S6JY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C44FV4MF","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:e4556096f7ff3a921d8ee4c2ca335c4c35d5592301e2c68c0a9f7d996369e2d3","target":"graph","created_at":"2026-05-18T00:48:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For the $N$-centre problem in the three dimensional space, $$ \\ddot x = -\\sum_{i=1}^{N} \\frac{m_i \\,(x-c_i)}{\\vert x - c_i \\vert^{\\alpha+2}}, \\qquad x \\in \\mathbb{R}^3 \\setminus \\{c_1,\\ldots,c_N\\}, $$ where $N \\geq 2$, $m_i > 0$ and $\\alpha \\in [1,2)$, we prove the existence of entire parabolic trajectories having prescribed asymptotic directions. The proof relies on a variational argument of min-max type. Morse index estimates and regularization techniques are used in order to rule out the possible occurrence of collisions.","authors_text":"Alberto Boscaggin, Susanna Terracini, Walter Dambrosio","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-09T08:36:01Z","title":"Scattering parabolic solutions for the spatial N-centre problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02897","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6c38df48b877a8218fe86e7caa6170058648b9192ce546bab33db1ad3a75dcd8","target":"record","created_at":"2026-05-18T00:48:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"92b321b1ecd63546e1c5ba1fc2c3c9a407023af51ad46ef81a0c478a4a0363b3","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-09T08:36:01Z","title_canon_sha256":"f2859ab152ebcb8ba0ad4daa0cf902af15bb21275c46fc890096e1586b797c49"},"schema_version":"1.0","source":{"id":"1602.02897","kind":"arxiv","version":1}},"canonical_sha256":"17385af18513dfe979380bf11f70fc5ec1ba80bd349eeb9a3bf0a007ddf0e11e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17385af18513dfe979380bf11f70fc5ec1ba80bd349eeb9a3bf0a007ddf0e11e","first_computed_at":"2026-05-18T00:48:09.943191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:09.943191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kwaRd9nDEoyTCo+nYLbWZkC2fMq3YKl0rII4uKXE7+VQOyYjpblegfBo5QBrz8+GK1eI9bwRVLfxKUPKuSSXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:09.943754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02897","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c38df48b877a8218fe86e7caa6170058648b9192ce546bab33db1ad3a75dcd8","sha256:e4556096f7ff3a921d8ee4c2ca335c4c35d5592301e2c68c0a9f7d996369e2d3"],"state_sha256":"dab70a3764698fe5437b5bbbb0c50ed7ae3c9a50537fdbbb23ec83ee30ded8e0"}