{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RKVDVOSM5LHQ7TH5UTM2FSRMHW","short_pith_number":"pith:RKVDVOSM","canonical_record":{"source":{"id":"1504.01253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-06T10:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"c545d886fdbd35b276ac07c7a633e9b9cbdc327ba2c4a722fed07443b6c83a3d","abstract_canon_sha256":"ceaf749625a65389770155f2e2988652fa61f0923c9cb7a12fac5d67f8c6f74b"},"schema_version":"1.0"},"canonical_sha256":"8aaa3aba4ceacf0fccfda4d9a2ca2c3da1837ba062e2927137434d21475d0f38","source":{"kind":"arxiv","id":"1504.01253","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01253","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01253v2","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01253","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"RKVDVOSM5LHQ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RKVDVOSM5LHQ7TH5","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RKVDVOSM","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RKVDVOSM5LHQ7TH5UTM2FSRMHW","target":"record","payload":{"canonical_record":{"source":{"id":"1504.01253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-06T10:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"c545d886fdbd35b276ac07c7a633e9b9cbdc327ba2c4a722fed07443b6c83a3d","abstract_canon_sha256":"ceaf749625a65389770155f2e2988652fa61f0923c9cb7a12fac5d67f8c6f74b"},"schema_version":"1.0"},"canonical_sha256":"8aaa3aba4ceacf0fccfda4d9a2ca2c3da1837ba062e2927137434d21475d0f38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:19.345861Z","signature_b64":"ZkNnX4NKcLXRBemwxzbQiODRPpv8/Epmk+qwf2Z0fT2IOrGdeLUjwfUtRpDmofoK09ZQOCFLnZ6aC7AGr3H+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8aaa3aba4ceacf0fccfda4d9a2ca2c3da1837ba062e2927137434d21475d0f38","last_reissued_at":"2026-05-17T23:52:19.345175Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:19.345175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.01253","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G1Em9gaC/LS9NfBCG/CQ6+h9YhBgoZc7ZpqPosMeIrY6D+OwBghSDH/hyw0djSJN/6AhETiloZWTcGHIJ6P7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:44:03.148028Z"},"content_sha256":"725b88fd91005284d5fa3b44811834f8c5436d389aba729a63092d2a0d5a83a7","schema_version":"1.0","event_id":"sha256:725b88fd91005284d5fa3b44811834f8c5436d389aba729a63092d2a0d5a83a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RKVDVOSM5LHQ7TH5UTM2FSRMHW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daniel Wilczak, Piotr Zgliczy\\'nski","submitted_at":"2015-04-06T10:21:33Z","abstract_excerpt":"We propose a method for computation of stable and unstable sets associated to hyperbolic equilibria of nonautonomous ODEs and for computation of specific type of connecting orbits in nonautonomous singular ODEs. We apply the method to a certain a singular nonautonomous real Ginzburg-Landau type equation, which that arises from the problem of formation of spots in the Swift-Hohenberg equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01253","kind":"arxiv","version":2},"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":"2026-05-17T23:52:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ppDUCtNZUA9/SkHy8a0F+LIspupwpPPDnt4juukIuE6i8CMZxb7bd1eB2xPq0ULdQ4DPq0IKVtbV4keA5+PUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:44:03.148430Z"},"content_sha256":"4cef1f6906fc62c0f3c4b1e48bf50a7ffef9b43dd3e3b92a2e2aba88d878dbc9","schema_version":"1.0","event_id":"sha256:4cef1f6906fc62c0f3c4b1e48bf50a7ffef9b43dd3e3b92a2e2aba88d878dbc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RKVDVOSM5LHQ7TH5UTM2FSRMHW/bundle.json","state_url":"https://pith.science/pith/RKVDVOSM5LHQ7TH5UTM2FSRMHW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RKVDVOSM5LHQ7TH5UTM2FSRMHW/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":"2026-06-05T15:44:03Z","links":{"resolver":"https://pith.science/pith/RKVDVOSM5LHQ7TH5UTM2FSRMHW","bundle":"https://pith.science/pith/RKVDVOSM5LHQ7TH5UTM2FSRMHW/bundle.json","state":"https://pith.science/pith/RKVDVOSM5LHQ7TH5UTM2FSRMHW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RKVDVOSM5LHQ7TH5UTM2FSRMHW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RKVDVOSM5LHQ7TH5UTM2FSRMHW","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":"ceaf749625a65389770155f2e2988652fa61f0923c9cb7a12fac5d67f8c6f74b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-06T10:21:33Z","title_canon_sha256":"c545d886fdbd35b276ac07c7a633e9b9cbdc327ba2c4a722fed07443b6c83a3d"},"schema_version":"1.0","source":{"id":"1504.01253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01253","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01253v2","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01253","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"RKVDVOSM5LHQ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RKVDVOSM5LHQ7TH5","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RKVDVOSM","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:4cef1f6906fc62c0f3c4b1e48bf50a7ffef9b43dd3e3b92a2e2aba88d878dbc9","target":"graph","created_at":"2026-05-17T23:52:19Z","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 propose a method for computation of stable and unstable sets associated to hyperbolic equilibria of nonautonomous ODEs and for computation of specific type of connecting orbits in nonautonomous singular ODEs. We apply the method to a certain a singular nonautonomous real Ginzburg-Landau type equation, which that arises from the problem of formation of spots in the Swift-Hohenberg equation.","authors_text":"Daniel Wilczak, Piotr Zgliczy\\'nski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-06T10:21:33Z","title":"Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01253","kind":"arxiv","version":2},"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":"sha256:725b88fd91005284d5fa3b44811834f8c5436d389aba729a63092d2a0d5a83a7","target":"record","created_at":"2026-05-17T23:52:19Z","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":"ceaf749625a65389770155f2e2988652fa61f0923c9cb7a12fac5d67f8c6f74b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-06T10:21:33Z","title_canon_sha256":"c545d886fdbd35b276ac07c7a633e9b9cbdc327ba2c4a722fed07443b6c83a3d"},"schema_version":"1.0","source":{"id":"1504.01253","kind":"arxiv","version":2}},"canonical_sha256":"8aaa3aba4ceacf0fccfda4d9a2ca2c3da1837ba062e2927137434d21475d0f38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8aaa3aba4ceacf0fccfda4d9a2ca2c3da1837ba062e2927137434d21475d0f38","first_computed_at":"2026-05-17T23:52:19.345175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:19.345175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZkNnX4NKcLXRBemwxzbQiODRPpv8/Epmk+qwf2Z0fT2IOrGdeLUjwfUtRpDmofoK09ZQOCFLnZ6aC7AGr3H+Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:19.345861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:725b88fd91005284d5fa3b44811834f8c5436d389aba729a63092d2a0d5a83a7","sha256:4cef1f6906fc62c0f3c4b1e48bf50a7ffef9b43dd3e3b92a2e2aba88d878dbc9"],"state_sha256":"80d0e4967e2f5db4f45dc6da3b8bf2c544fc8d7c683ef2cf89e3d7eebb4a659c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pSLd6UDnRD2d6uKqOPDRKq0c7tw/gc353T035RydMxgIinQftuADSFON0KAanHWaZo0qO8RukIUirdCVG4G0AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:44:03.150668Z","bundle_sha256":"5814992688c4d56fea22014ed6adad79fd1dbde976e8e1b9f1d8ff8629b40ad5"}}