{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PEJESQQY7XN3OEJCQDKJNT3YH6","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":"dbdf1dc776e1350f0dd6a3d8d3df1cdf66221772d21d040c9240ecb86a98d125","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-23T14:00:59Z","title_canon_sha256":"428f5a1d065bc70f6b9c0034016cf6f7a9bd9879352b796c9fc27f3b1ab92bd4"},"schema_version":"1.0","source":{"id":"1701.06394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06394","created_at":"2026-05-18T00:28:46Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06394v1","created_at":"2026-05-18T00:28:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06394","created_at":"2026-05-18T00:28:46Z"},{"alias_kind":"pith_short_12","alias_value":"PEJESQQY7XN3","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PEJESQQY7XN3OEJC","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PEJESQQY","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:ed8a1d4b89647fe3bb5caf2c3594be3f4a718068f00f2a39e91341897a58b47d","target":"graph","created_at":"2026-05-18T00:28:46Z","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 consider a bistable ($0\\textless{}\\theta\\textless{}1$ being the three constant steady states) delayed reaction diffusion equation, which serves as a model in population dynamics. The problem does not admit any comparison principle. This prevents the use of classical technics and, as a consequence, it is far from obvious to understand the behaviour of a possible travelling wave in $+\\infty$. Combining refined {\\it a priori} estimates and a Leray Schauder topological degree argument, we construct a travelling wave connecting 0 in $-\\infty$ to \\lq\\lq something\" which is strictly above the unst","authors_text":"Arnaud Ducrot (IMB), Matthieu Alfaro (IMAG), Thomas Giletti (IECL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-23T14:00:59Z","title":"Travelling waves for a non-monotone bistable equation with delay: existence and oscillations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06394","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":"sha256:7ee11295bd6d130d44f25292d242b596daee889a0b0e8299926708551a93af09","target":"record","created_at":"2026-05-18T00:28:46Z","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":"dbdf1dc776e1350f0dd6a3d8d3df1cdf66221772d21d040c9240ecb86a98d125","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-23T14:00:59Z","title_canon_sha256":"428f5a1d065bc70f6b9c0034016cf6f7a9bd9879352b796c9fc27f3b1ab92bd4"},"schema_version":"1.0","source":{"id":"1701.06394","kind":"arxiv","version":1}},"canonical_sha256":"7912494218fddbb7112280d496cf783fbd26b00a4b72ad631eaaf9fde8a9ba2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7912494218fddbb7112280d496cf783fbd26b00a4b72ad631eaaf9fde8a9ba2c","first_computed_at":"2026-05-18T00:28:46.876208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:46.876208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zHNdcN4dLC46dEPTI2dyXtlSGCJnoDCP3eUboFs6NTEAwPXgu/vW9ey+KMIXZOLgzLMuQ6PQ8Dp6xCbklk/DDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:46.876895Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ee11295bd6d130d44f25292d242b596daee889a0b0e8299926708551a93af09","sha256:ed8a1d4b89647fe3bb5caf2c3594be3f4a718068f00f2a39e91341897a58b47d"],"state_sha256":"18088b472c69372296836370d0b519d70724ad933df844287150fe9004fd0810"}