{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FPZXUXO7J7TSDYJ3FOX6LUYARK","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":"2e1048422a5d9f6c02d35337f64db4f1e8258c54f4515cc3c8351160447c1ff7","cross_cats_sorted":["math.AP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-02T18:22:19Z","title_canon_sha256":"45049dccf0b1186098012d9868a5a628c715dc3f45d90d53d864cf2a5a9f996e"},"schema_version":"1.0","source":{"id":"1702.00772","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00772","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00772v2","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00772","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"FPZXUXO7J7TS","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FPZXUXO7J7TSDYJ3","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FPZXUXO7","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:387f03dad24b070d5d823e293e7a53a46fb0be410767a9bb49e0762e13c6cf05","target":"graph","created_at":"2026-05-18T00:09:31Z","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 develop a new homological invariant for the dynamics of the bounded solutions to the travelling wave PDE \\[ \\left\\{ \\begin{array}{l l}\n  \\partial_t^2 u - c \\partial_t u + \\Delta u + f(x,u) = 0 \\qquad & t \\in \\mathbf{R},\\; x \\in \\Omega, \\newline\n  B(u) = 0 & t \\in \\mathbf{R},\\; x \\in \\partial \\Omega, \\end{array} \\right. \\] where $c \\neq 0$, $\\Omega \\subset \\mathbf{R}^d$ is a bounded domain, $\\Delta$ is the Laplacian on $\\Omega$, and $B$ denotes Dirichlet, Neumann, or periodic boundary data. Restrictions on the nonlinearity $f$ are kept to a minimum, for instance, any nonlinearity exhibiting ","authors_text":"Bente Bakker, Jan Bouwe van den Berg, Rob Vandervorst","cross_cats":["math.AP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-02T18:22:19Z","title":"A Floer homology approach to travelling waves in reaction-diffusion equations on cylinders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00772","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":"sha256:8b933804577f3fc29cbe58dec86eddcc388734062d915faef2f4894693ff9491","target":"record","created_at":"2026-05-18T00:09:31Z","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":"2e1048422a5d9f6c02d35337f64db4f1e8258c54f4515cc3c8351160447c1ff7","cross_cats_sorted":["math.AP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-02T18:22:19Z","title_canon_sha256":"45049dccf0b1186098012d9868a5a628c715dc3f45d90d53d864cf2a5a9f996e"},"schema_version":"1.0","source":{"id":"1702.00772","kind":"arxiv","version":2}},"canonical_sha256":"2bf37a5ddf4fe721e13b2bafe5d3008a847633766d35aafc6f8b75768f23d10f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bf37a5ddf4fe721e13b2bafe5d3008a847633766d35aafc6f8b75768f23d10f","first_computed_at":"2026-05-18T00:09:31.422780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:31.422780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0RRNwU44PE+W+uSdQ1hYC1+c02dIXEhheLO2fabVkq/hFMTlHTY+vgwnE/ZOF9xlBmFiMHsyDbQdFn0qxZVgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:31.423472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00772","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b933804577f3fc29cbe58dec86eddcc388734062d915faef2f4894693ff9491","sha256:387f03dad24b070d5d823e293e7a53a46fb0be410767a9bb49e0762e13c6cf05"],"state_sha256":"026112acf92d8fe2b4643efb1aa745083a6d08591763919f2d13df83e5483910"}