{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FH76A2DLGD5N7YI4JKCKWRY4XZ","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":"250c879107d3aad6f84112c79c3916363640b87cf85590aad6a9fb777d662589","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-22T04:05:11Z","title_canon_sha256":"0ab8b591f637880175dd928918a202a99b03bb8bcc37183042413ec69ef3cf61"},"schema_version":"1.0","source":{"id":"1806.08487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08487","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08487v1","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08487","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"FH76A2DLGD5N","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FH76A2DLGD5N7YI4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FH76A2DL","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:e15aa151557f74ba5ca1c2f6444ff310558b6d5f4acef1fe20892237ce3e34e5","target":"graph","created_at":"2026-05-18T00:12:37Z","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":"Geometric treatments of blow-up solutions for autonomous ordinary differential equations and their blow-up rates are concerned. Our approach focuses on the type of invariant sets at infinity via compactifications of phase spaces, and dynamics on their center-stable manifolds. In particular, we show that dynamics on center-stable manifolds of invariant sets at infinity with appropriate time-scale desingularizations as well as blowing-up of singularities characterize dynamics of blow-up solutions as well as their rigorous blow-up rates.","authors_text":"Kaname Matsue","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-22T04:05:11Z","title":"Geometric treatments and a common mechanism in finite-time singularities for autonomous ODEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08487","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":"sha256:593b26361fc41a1d96137fc045fd63e8c413f68e913299b37b68914f5f186ddc","target":"record","created_at":"2026-05-18T00:12:37Z","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":"250c879107d3aad6f84112c79c3916363640b87cf85590aad6a9fb777d662589","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-22T04:05:11Z","title_canon_sha256":"0ab8b591f637880175dd928918a202a99b03bb8bcc37183042413ec69ef3cf61"},"schema_version":"1.0","source":{"id":"1806.08487","kind":"arxiv","version":1}},"canonical_sha256":"29ffe0686b30fadfe11c4a84ab471cbe444c7da09ad2711beb3d126cd970a2da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29ffe0686b30fadfe11c4a84ab471cbe444c7da09ad2711beb3d126cd970a2da","first_computed_at":"2026-05-18T00:12:37.111143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:37.111143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a1GRnin2fwFwVbZTBTJYedZksMp+BwSBAu0knbHegH+nnZsEHd5H+SZbrchJDwOfXSdjYi14+b/6oT22vlO5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:37.111835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.08487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:593b26361fc41a1d96137fc045fd63e8c413f68e913299b37b68914f5f186ddc","sha256:e15aa151557f74ba5ca1c2f6444ff310558b6d5f4acef1fe20892237ce3e34e5"],"state_sha256":"e3ca25fd5a585a503c57a0cc38c0e723b986ae5739a36c0b9cac32b38a3daba3"}