{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z7I7NT34HWJ3YDBYKYUUGTM6M6","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":"e25e697cb8cb6b5150b9a85959e133634d7ec3db36050b4df01c57dc79d5bcf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-17T12:56:08Z","title_canon_sha256":"f8f229ff648f9966a5627e2f4535fd14e7069094b4668992284c2901b0f358cc"},"schema_version":"1.0","source":{"id":"1105.3358","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3358","created_at":"2026-05-18T02:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3358v1","created_at":"2026-05-18T02:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3358","created_at":"2026-05-18T02:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"Z7I7NT34HWJ3","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z7I7NT34HWJ3YDBY","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z7I7NT34","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:77c81deee18ea421ce69e39128506612a8c454fa1512b0330dd585c088aef56a","target":"graph","created_at":"2026-05-18T02:21:59Z","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 class of anisotropic Kepler problems in $\\RR^d\\setminus\\{0\\}$ with homogeneous potentials, we seek parabolic trajectories having prescribed asymptotic directions at infinity and which, in addition, are Morse minimizing geodesics for the Jacobi metric. Such trajectories correspond to saddle heteroclinics on the collision manifold, are structurally unstable and appear only for a codimension-one submanifold of such potentials. We give them a variational characterization in terms of the behavior of the parameter-free minimizers of an associated obstacle problem. We then give a full charact","authors_text":"Gianmaria Verzini, Susanna Terracini, Vivina Barutello","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-17T12:56:08Z","title":"Entire Parabolic Trajectories as Minimal Phase Transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3358","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":"sha256:52cf76e1c3241786629ced0d80be7ab8e3b7f330e78a6cb443f9df5ae1d4b401","target":"record","created_at":"2026-05-18T02:21:59Z","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":"e25e697cb8cb6b5150b9a85959e133634d7ec3db36050b4df01c57dc79d5bcf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-17T12:56:08Z","title_canon_sha256":"f8f229ff648f9966a5627e2f4535fd14e7069094b4668992284c2901b0f358cc"},"schema_version":"1.0","source":{"id":"1105.3358","kind":"arxiv","version":1}},"canonical_sha256":"cfd1f6cf7c3d93bc0c385629434d9e67b272af47055a5c23d996ca1e38a09d54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfd1f6cf7c3d93bc0c385629434d9e67b272af47055a5c23d996ca1e38a09d54","first_computed_at":"2026-05-18T02:21:59.782559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:59.782559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LIGbP8BASQaX91NZGNyXsTw2vVaZFxbJyo4QIBBc4UsyIFnfd2dJqwgjbe5duEqEQodKceajY0cUNJsnCJGRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:59.783284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3358","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52cf76e1c3241786629ced0d80be7ab8e3b7f330e78a6cb443f9df5ae1d4b401","sha256:77c81deee18ea421ce69e39128506612a8c454fa1512b0330dd585c088aef56a"],"state_sha256":"d9b17ee7382fc86535ef1a0c0fadfec14520ad60c985c88e1372ed83159fb7db"}