{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GVPRN5T5N3RGADGDGEVOXZM5T2","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":"137b1b7782a8e081d3d44e29d0bb3671d2c54deaf9bd18ae6b1c0a9f65263bf0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-03T15:44:42Z","title_canon_sha256":"5a8009bb0462a6eec1c12341c5057c0ceec73c8d80b21913a80cdc8136070c1a"},"schema_version":"1.0","source":{"id":"1508.00456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00456","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00456v1","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00456","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"pith_short_12","alias_value":"GVPRN5T5N3RG","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GVPRN5T5N3RGADGD","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GVPRN5T5","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:2dd1afb2b5d3aa559bd1418489c06e9803213c9b19a60db89e754f97a04c40cb","target":"graph","created_at":"2026-05-18T01:35:58Z","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":"We address the problem of understanding the dynamics around typical singular points of $3D$ piecewise smooth vector fields. A model $Z_0$ in $3D$ presenting a T-singularity is considered and a complete picture of its dynamics is obtained in the following way: \\textit{(i)} $Z_0$ has an invariant plane $\\pi_0$ filled up with periodic orbits (this means that the restriction $Z_0 |_{\\pi_0}$ is a center around the singularity), \\textit{(ii)} All trajectories of $Z_0$ converge to the surface $\\pi_0$, and such attraction occurs in a very non-usual and amazing way, \\textit{(iii)} given an arbitrary in","authors_text":"Marco Antonio Teixeira, Tiago De Carvalho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-03T15:44:42Z","title":"Attractivity, degeneracy and codimension of a typical singularity in 3D piecewise smooth vector fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00456","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":"sha256:8410bc8fed3c2a561f8eece43ee412b7462b8258aaa329450733dddfb633f6cb","target":"record","created_at":"2026-05-18T01:35:58Z","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":"137b1b7782a8e081d3d44e29d0bb3671d2c54deaf9bd18ae6b1c0a9f65263bf0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-03T15:44:42Z","title_canon_sha256":"5a8009bb0462a6eec1c12341c5057c0ceec73c8d80b21913a80cdc8136070c1a"},"schema_version":"1.0","source":{"id":"1508.00456","kind":"arxiv","version":1}},"canonical_sha256":"355f16f67d6ee2600cc3312aebe59d9e854da6ef61554b317aa8cd27b85c799c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"355f16f67d6ee2600cc3312aebe59d9e854da6ef61554b317aa8cd27b85c799c","first_computed_at":"2026-05-18T01:35:58.080573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:58.080573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dWCyprcvuBrcI+dUONPiLfwdjRLVpT89o05E7/sCVXHJuS6ELfZqq+dBf/GJ2H6/afJvSRnq1iscVHvQXBv1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:58.081149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8410bc8fed3c2a561f8eece43ee412b7462b8258aaa329450733dddfb633f6cb","sha256:2dd1afb2b5d3aa559bd1418489c06e9803213c9b19a60db89e754f97a04c40cb"],"state_sha256":"287766d53d66a7c4ac19293bfe23471a8e45636e1b5e8d4a14a28d11fadb415c"}