{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NOBAHFHJ2Y2J7ZT2JZPHGPDMWR","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":"9b8f74992b4aeccc3d787c71128c70514f24f19a0d30122552c5b6accae1ff95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-16T01:19:38Z","title_canon_sha256":"aa900679fd933d67205e64530f761162fe48a9f47e4c6af3c2c09c56137f5453"},"schema_version":"1.0","source":{"id":"1603.04932","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04932","created_at":"2026-05-18T01:10:06Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04932v1","created_at":"2026-05-18T01:10:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04932","created_at":"2026-05-18T01:10:06Z"},{"alias_kind":"pith_short_12","alias_value":"NOBAHFHJ2Y2J","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NOBAHFHJ2Y2J7ZT2","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NOBAHFHJ","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:49b1d3c0480a0499fb43f14f40fe7ce4c8cf0aed7e0e5346db1c67ba32fe4aa8","target":"graph","created_at":"2026-05-18T01:10:06Z","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":"The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, an invariant set can develop a homoclinic connection when its stable manifold intersects a non-differentiable point of its unstable manifold (or vice-versa). This is a codimension-one bifurcation analogous to a homoclinic tangency of a smooth map, referred to here as a homoclinic corner. This paper presents an unfolding of generic homoclinic corners for saddle fixed points of planar piecewise-smooth continuous maps. I","authors_text":"David J. W. Simpson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-16T01:19:38Z","title":"Unfolding homoclinic connections formed by corner intersections in piecewise-smooth maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04932","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:ee855a7b8315a4f0624e20e267f8eeafdb8ec6fe6b7ce1ab16074006a478768c","target":"record","created_at":"2026-05-18T01:10:06Z","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":"9b8f74992b4aeccc3d787c71128c70514f24f19a0d30122552c5b6accae1ff95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-16T01:19:38Z","title_canon_sha256":"aa900679fd933d67205e64530f761162fe48a9f47e4c6af3c2c09c56137f5453"},"schema_version":"1.0","source":{"id":"1603.04932","kind":"arxiv","version":1}},"canonical_sha256":"6b820394e9d6349fe67a4e5e733c6cb44baff80bc73fdbf4074d5db0252f098e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b820394e9d6349fe67a4e5e733c6cb44baff80bc73fdbf4074d5db0252f098e","first_computed_at":"2026-05-18T01:10:06.367289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:06.367289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bHw0U3x5KelF7G0fKRvp9YOdi59XDsrM40eJtzsTZTR0hHJD1P326F+O3/LLlQthsOAqhOmwWXt3c5vC2NSHBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:06.367941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04932","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee855a7b8315a4f0624e20e267f8eeafdb8ec6fe6b7ce1ab16074006a478768c","sha256:49b1d3c0480a0499fb43f14f40fe7ce4c8cf0aed7e0e5346db1c67ba32fe4aa8"],"state_sha256":"b0c2b411ca75a990992a94a7199ca5098b1168efedde9095cf5089bee2b7d31d"}