{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2HYVO6XO6S4IDFZTMZVCWITIQE","short_pith_number":"pith:2HYVO6XO","canonical_record":{"source":{"id":"1506.00845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-02T11:35:02Z","cross_cats_sorted":[],"title_canon_sha256":"993fdf5b302c1b943c44b5483c0c28e368d5bafafffd2b1b0eceda62791ecc32","abstract_canon_sha256":"bc573d2743438508b2f097b544717c3c98b913ef9da335808c148fcee6851fbe"},"schema_version":"1.0"},"canonical_sha256":"d1f1577aeef4b8819733666a2b2268810b983e08fd9d260ac31c97e11d7b0237","source":{"kind":"arxiv","id":"1506.00845","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00845","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00845v1","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00845","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"2HYVO6XO6S4I","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2HYVO6XO6S4IDFZT","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2HYVO6XO","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2HYVO6XO6S4IDFZTMZVCWITIQE","target":"record","payload":{"canonical_record":{"source":{"id":"1506.00845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-02T11:35:02Z","cross_cats_sorted":[],"title_canon_sha256":"993fdf5b302c1b943c44b5483c0c28e368d5bafafffd2b1b0eceda62791ecc32","abstract_canon_sha256":"bc573d2743438508b2f097b544717c3c98b913ef9da335808c148fcee6851fbe"},"schema_version":"1.0"},"canonical_sha256":"d1f1577aeef4b8819733666a2b2268810b983e08fd9d260ac31c97e11d7b0237","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:34.341747Z","signature_b64":"NvCjTFuoL3jPR/D7dBbJQ5XDxcU4bO1ffOF0SHwvRtkUV+p3zbgcnI4QO2VX+8TzVhiEYmsLqhCgQuWvVFK/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1f1577aeef4b8819733666a2b2268810b983e08fd9d260ac31c97e11d7b0237","last_reissued_at":"2026-05-18T01:59:34.341078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:34.341078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.00845","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UVanYj/0XG56FQVUuYyD6l9j7TxqsTAgDw+QyI872AI4PJHT2hywqYJyodsFuKBFuEWA3t/v4ppv4icMQT4KCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:01:44.404424Z"},"content_sha256":"1dc05433751b66223fe5e7c609e248c8ceaa1d4c9ae42bc695059575b5fc2c27","schema_version":"1.0","event_id":"sha256:1dc05433751b66223fe5e7c609e248c8ceaa1d4c9ae42bc695059575b5fc2c27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2HYVO6XO6S4IDFZTMZVCWITIQE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fold singularities of nonsmooth and slow-fast dynamical systems -- equivalence through regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mike R. Jeffrey","submitted_at":"2015-06-02T11:35:02Z","abstract_excerpt":"The two-fold singularity has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous at some hypersurface, it can become tangent to that surface from one side or the other, and tangency from both sides creates a two-fold singularity. The local flow bears a superficial resemblance to so-called {\\it folded singularities} in (smooth) slow-fast systems, which arise at the intersection of attractive and repelling branches of slow invariant manifolds, important in the local study of canards and mixed mode "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00845","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jS8ltoEC80YfXW6dA+W+ShaK3weboCuJk1roMXmo1sWn5MEUWw609RR9yZd9CiGJVS78hhs0eDXEXj8J9t/RAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:01:44.404778Z"},"content_sha256":"22712a15e4c8176ea7b7b39d5838174cec92d4570b415e7fd746a803c8d660b3","schema_version":"1.0","event_id":"sha256:22712a15e4c8176ea7b7b39d5838174cec92d4570b415e7fd746a803c8d660b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2HYVO6XO6S4IDFZTMZVCWITIQE/bundle.json","state_url":"https://pith.science/pith/2HYVO6XO6S4IDFZTMZVCWITIQE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2HYVO6XO6S4IDFZTMZVCWITIQE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T00:01:44Z","links":{"resolver":"https://pith.science/pith/2HYVO6XO6S4IDFZTMZVCWITIQE","bundle":"https://pith.science/pith/2HYVO6XO6S4IDFZTMZVCWITIQE/bundle.json","state":"https://pith.science/pith/2HYVO6XO6S4IDFZTMZVCWITIQE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2HYVO6XO6S4IDFZTMZVCWITIQE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2HYVO6XO6S4IDFZTMZVCWITIQE","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":"bc573d2743438508b2f097b544717c3c98b913ef9da335808c148fcee6851fbe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-02T11:35:02Z","title_canon_sha256":"993fdf5b302c1b943c44b5483c0c28e368d5bafafffd2b1b0eceda62791ecc32"},"schema_version":"1.0","source":{"id":"1506.00845","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00845","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00845v1","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00845","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"2HYVO6XO6S4I","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2HYVO6XO6S4IDFZT","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2HYVO6XO","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:22712a15e4c8176ea7b7b39d5838174cec92d4570b415e7fd746a803c8d660b3","target":"graph","created_at":"2026-05-18T01:59:34Z","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 two-fold singularity has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous at some hypersurface, it can become tangent to that surface from one side or the other, and tangency from both sides creates a two-fold singularity. The local flow bears a superficial resemblance to so-called {\\it folded singularities} in (smooth) slow-fast systems, which arise at the intersection of attractive and repelling branches of slow invariant manifolds, important in the local study of canards and mixed mode ","authors_text":"Mike R. Jeffrey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-02T11:35:02Z","title":"Fold singularities of nonsmooth and slow-fast dynamical systems -- equivalence through regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00845","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":"sha256:1dc05433751b66223fe5e7c609e248c8ceaa1d4c9ae42bc695059575b5fc2c27","target":"record","created_at":"2026-05-18T01:59:34Z","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":"bc573d2743438508b2f097b544717c3c98b913ef9da335808c148fcee6851fbe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-02T11:35:02Z","title_canon_sha256":"993fdf5b302c1b943c44b5483c0c28e368d5bafafffd2b1b0eceda62791ecc32"},"schema_version":"1.0","source":{"id":"1506.00845","kind":"arxiv","version":1}},"canonical_sha256":"d1f1577aeef4b8819733666a2b2268810b983e08fd9d260ac31c97e11d7b0237","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1f1577aeef4b8819733666a2b2268810b983e08fd9d260ac31c97e11d7b0237","first_computed_at":"2026-05-18T01:59:34.341078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:34.341078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NvCjTFuoL3jPR/D7dBbJQ5XDxcU4bO1ffOF0SHwvRtkUV+p3zbgcnI4QO2VX+8TzVhiEYmsLqhCgQuWvVFK/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:34.341747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00845","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dc05433751b66223fe5e7c609e248c8ceaa1d4c9ae42bc695059575b5fc2c27","sha256:22712a15e4c8176ea7b7b39d5838174cec92d4570b415e7fd746a803c8d660b3"],"state_sha256":"8f39df4fa7fb8e377ee0b3ab71d2cbfb2738a585e4ed1b106f06a439718cfbfd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PP21EuifHD9MKajxvlRErtfRamHlPVr7avaSFFtsXEkaN7W+DXoQlxXCWGXyQ6+TYHPXAvSnFt/+QTVZUWyDAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:01:44.406759Z","bundle_sha256":"b0f16b1ee144addeb1353962b8b48e6cec089872f5003cc9274608c0abc06d32"}}