{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RNAGPG47BLIHBK7MYPR5MJ742I","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":"70538b58c2f898561054ed3d87a874684206010f1b27cd40c7c051c73c8aab4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-18T10:21:19Z","title_canon_sha256":"982e55380ce77076de851c6aba03855bee52c90d689ac995a9d06b386bf40745"},"schema_version":"1.0","source":{"id":"1605.05506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05506","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05506v1","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05506","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"RNAGPG47BLIH","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RNAGPG47BLIHBK7M","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RNAGPG47","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:69c4aec74f7c00984d067c5ad94cad32bbddbe30d65c0a8860b7061d79b24bd3","target":"graph","created_at":"2026-05-18T01:14:34Z","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":"We consider the semi linear Fisher-Kolmogorov-Petrovski-Piscounov equation for the advance of an advantageous gene in biology. Its non-smooth reaction function $f(u)$ allows for the introduction of travelling waves with a new profile. We study existence, uniqueness, and long-time asymptotic behavior of the solutions $u(x,t)$, $(x,t)\\in \\mathbb{R}\\times \\mathbb{R}_+$. We prove also the existence and uniqueness (up to a spatial shift) of a travelling wave $U$. Our main result is the uniform convergence (for $x\\in \\mathbb{R}$) of every solution $u(x,t)$ of the Cauchy problem to a single traveling","authors_text":"Pavel Dr\\'abek, Peter Tak\\'a\\v{c}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-18T10:21:19Z","title":"Convergence to traveling waves in the Fisher-Kolmogorov equation with a non-Lipschitzian reaction term"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05506","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":"sha256:8bcfc5bba8848f48eb0c2be5d4e46d7a9a64da91af419a89d825ca662b1ddfeb","target":"record","created_at":"2026-05-18T01:14:34Z","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":"70538b58c2f898561054ed3d87a874684206010f1b27cd40c7c051c73c8aab4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-18T10:21:19Z","title_canon_sha256":"982e55380ce77076de851c6aba03855bee52c90d689ac995a9d06b386bf40745"},"schema_version":"1.0","source":{"id":"1605.05506","kind":"arxiv","version":1}},"canonical_sha256":"8b40679b9f0ad070abecc3e3d627fcd231eec286ec3df340fb44a21a43791fbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b40679b9f0ad070abecc3e3d627fcd231eec286ec3df340fb44a21a43791fbc","first_computed_at":"2026-05-18T01:14:34.744552Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:34.744552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZHarwL0W1LYY1FHDpup8M9nMvlcQq88d+wP5aBTlq5a2t519Ee6CxRBBZsK2L2zogB2NLUB5I6xtStcAxE4hDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:34.745218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bcfc5bba8848f48eb0c2be5d4e46d7a9a64da91af419a89d825ca662b1ddfeb","sha256:69c4aec74f7c00984d067c5ad94cad32bbddbe30d65c0a8860b7061d79b24bd3"],"state_sha256":"a21d94de4e6260ccb6a3ec503e4ebd38851c3d10f9f931a291dfa47c259df119"}