{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RNAGPG47BLIHBK7MYPR5MJ742I","short_pith_number":"pith:RNAGPG47","canonical_record":{"source":{"id":"1605.05506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-18T10:21:19Z","cross_cats_sorted":[],"title_canon_sha256":"982e55380ce77076de851c6aba03855bee52c90d689ac995a9d06b386bf40745","abstract_canon_sha256":"70538b58c2f898561054ed3d87a874684206010f1b27cd40c7c051c73c8aab4f"},"schema_version":"1.0"},"canonical_sha256":"8b40679b9f0ad070abecc3e3d627fcd231eec286ec3df340fb44a21a43791fbc","source":{"kind":"arxiv","id":"1605.05506","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RNAGPG47BLIHBK7MYPR5MJ742I","target":"record","payload":{"canonical_record":{"source":{"id":"1605.05506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-18T10:21:19Z","cross_cats_sorted":[],"title_canon_sha256":"982e55380ce77076de851c6aba03855bee52c90d689ac995a9d06b386bf40745","abstract_canon_sha256":"70538b58c2f898561054ed3d87a874684206010f1b27cd40c7c051c73c8aab4f"},"schema_version":"1.0"},"canonical_sha256":"8b40679b9f0ad070abecc3e3d627fcd231eec286ec3df340fb44a21a43791fbc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:34.745218Z","signature_b64":"ZHarwL0W1LYY1FHDpup8M9nMvlcQq88d+wP5aBTlq5a2t519Ee6CxRBBZsK2L2zogB2NLUB5I6xtStcAxE4hDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b40679b9f0ad070abecc3e3d627fcd231eec286ec3df340fb44a21a43791fbc","last_reissued_at":"2026-05-18T01:14:34.744552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:34.744552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.05506","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O/NmCQhKeisBgUX1QpyBTBWKRtGX2VDKbmH3eGtUyyoGKC/MNhnqvS+FCBNOduhxLwk38XZcRY2gx6DwDQjiDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:57:30.852945Z"},"content_sha256":"8bcfc5bba8848f48eb0c2be5d4e46d7a9a64da91af419a89d825ca662b1ddfeb","schema_version":"1.0","event_id":"sha256:8bcfc5bba8848f48eb0c2be5d4e46d7a9a64da91af419a89d825ca662b1ddfeb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RNAGPG47BLIHBK7MYPR5MJ742I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence to traveling waves in the Fisher-Kolmogorov equation with a non-Lipschitzian reaction term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pavel Dr\\'abek, Peter Tak\\'a\\v{c}","submitted_at":"2016-05-18T10:21:19Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05506","kind":"arxiv","version":1},"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":"2026-05-18T01:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1dBeEcYDP1ORPkknw1hI439grY2wQ+EmTvstE6iDQQxHLJX47UuInkHFUTngq2742KmFFe7MfigH+KZAK4GDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:57:30.853344Z"},"content_sha256":"69c4aec74f7c00984d067c5ad94cad32bbddbe30d65c0a8860b7061d79b24bd3","schema_version":"1.0","event_id":"sha256:69c4aec74f7c00984d067c5ad94cad32bbddbe30d65c0a8860b7061d79b24bd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RNAGPG47BLIHBK7MYPR5MJ742I/bundle.json","state_url":"https://pith.science/pith/RNAGPG47BLIHBK7MYPR5MJ742I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RNAGPG47BLIHBK7MYPR5MJ742I/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":"2026-06-03T13:57:30Z","links":{"resolver":"https://pith.science/pith/RNAGPG47BLIHBK7MYPR5MJ742I","bundle":"https://pith.science/pith/RNAGPG47BLIHBK7MYPR5MJ742I/bundle.json","state":"https://pith.science/pith/RNAGPG47BLIHBK7MYPR5MJ742I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RNAGPG47BLIHBK7MYPR5MJ742I/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BIgGTl+1U6v6g/fMNTIhvn71xJmRIivc5SV+MW48alfms6xiXgxiDDh0vew5Y4FzLEFWvQWANfxlov56pR+1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:57:30.855382Z","bundle_sha256":"9f75d60b24db6289009b380fa85e8a3bf909b57a57f06b08e650dc0244dbccea"}}