{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:23NSOM55CYTZDDUPRAUAJSCQHR","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":"6c8a86f8e1621923937514a530a82fae8ee5ccb7a649235d309eb5b20eec820b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-11T00:53:17Z","title_canon_sha256":"14208687bba751f4d577428d5e1690ed910d8972be85ffc0fa099d21cfed5781"},"schema_version":"1.0","source":{"id":"1403.2449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2449","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2449v1","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2449","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"pith_short_12","alias_value":"23NSOM55CYTZ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"23NSOM55CYTZDDUP","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"23NSOM55","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:0ac9edff7cfa80269c74fc688c58acc9bfd6c490c0186c811999afe0c97f1034","target":"graph","created_at":"2026-05-18T02:56:43Z","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 study a version of the Keller-Segel model for bacterial chemotaxis, for which exact travelling wave solutions are explicitly known in the zero attractant diffusion limit. Using geometric singular perturbation theory, we construct travelling wave solutions in the small diffusion case that converge to these exact solutions in the singular limit.","authors_text":"Graeme Pettet, Kristen Harley, Peter van Heijster","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-11T00:53:17Z","title":"A geometric construction of travelling wave solutions to the Keller-Segel model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2449","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":"sha256:713edd7a586c8e11f7e9517eea8c85e75e80d62b9b09d582b06fb44c5ae8253c","target":"record","created_at":"2026-05-18T02:56:43Z","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":"6c8a86f8e1621923937514a530a82fae8ee5ccb7a649235d309eb5b20eec820b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-11T00:53:17Z","title_canon_sha256":"14208687bba751f4d577428d5e1690ed910d8972be85ffc0fa099d21cfed5781"},"schema_version":"1.0","source":{"id":"1403.2449","kind":"arxiv","version":1}},"canonical_sha256":"d6db2733bd1627918e8f882804c8503c4174af892d98a89a0f1927a381c4eab1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6db2733bd1627918e8f882804c8503c4174af892d98a89a0f1927a381c4eab1","first_computed_at":"2026-05-18T02:56:43.298582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:43.298582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PHFw4usiYGsNA0Wakl0Cg9HpgydziIh3kMJbTysm0q6Bebl7H/CqpqqHsK+ie3SSxgtcAMEZk5awe7Q6KkobCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:43.298973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:713edd7a586c8e11f7e9517eea8c85e75e80d62b9b09d582b06fb44c5ae8253c","sha256:0ac9edff7cfa80269c74fc688c58acc9bfd6c490c0186c811999afe0c97f1034"],"state_sha256":"d20723eb14397f4e98a5df04f94694acadadf5bf6988c5aed9cd1b9facdd5612"}