{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2QLDLVBXBQ5EZFLQ3XMGSKBMMJ","short_pith_number":"pith:2QLDLVBX","canonical_record":{"source":{"id":"1303.6823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-27T13:22:13Z","cross_cats_sorted":[],"title_canon_sha256":"5bbb8fd4ff18fb0eab3accb18367dd451e357ca16b25d4fcf7409d2f936b9b1d","abstract_canon_sha256":"f3546c9f4906ef29eb1d44e1f8994e30e0cd0e487a3417e06e3888d1b896ac24"},"schema_version":"1.0"},"canonical_sha256":"d41635d4370c3a4c9570ddd869282c624c326e2e969f8a91e398dbad65b7a8fa","source":{"kind":"arxiv","id":"1303.6823","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6823","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6823v1","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6823","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"2QLDLVBXBQ5E","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2QLDLVBXBQ5EZFLQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2QLDLVBX","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2QLDLVBXBQ5EZFLQ3XMGSKBMMJ","target":"record","payload":{"canonical_record":{"source":{"id":"1303.6823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-27T13:22:13Z","cross_cats_sorted":[],"title_canon_sha256":"5bbb8fd4ff18fb0eab3accb18367dd451e357ca16b25d4fcf7409d2f936b9b1d","abstract_canon_sha256":"f3546c9f4906ef29eb1d44e1f8994e30e0cd0e487a3417e06e3888d1b896ac24"},"schema_version":"1.0"},"canonical_sha256":"d41635d4370c3a4c9570ddd869282c624c326e2e969f8a91e398dbad65b7a8fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:39.619769Z","signature_b64":"R34pL7iSOgzFTC522687jvfexdR8nar9LELf/pn61ETiaFgKTaAY54MKrKZstarjhNGqHgLZ/2WGMMcvQcWoDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d41635d4370c3a4c9570ddd869282c624c326e2e969f8a91e398dbad65b7a8fa","last_reissued_at":"2026-05-18T03:29:39.619354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:39.619354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.6823","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":"2026-05-18T03:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cztiAM8fldVhgusSvzWoVehgFf5NjDtWHAeKTKRkIO42ca29oOlUxdghOQM1F6tKGlsHbg0/QPhGilXniMCBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:29:14.668178Z"},"content_sha256":"97a450f66fc982a5d8cca6d8aed22c4940f4f3f281a0647872a5caf9f1ae053d","schema_version":"1.0","event_id":"sha256:97a450f66fc982a5d8cca6d8aed22c4940f4f3f281a0647872a5caf9f1ae053d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2QLDLVBXBQ5EZFLQ3XMGSKBMMJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Fisher-KPP equation with nonlinear fractional diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diana Stan, Juan Luis V\\'azquez","submitted_at":"2013-03-27T13:22:13Z","abstract_excerpt":"We study the propagation properties of nonnegative and bounded solutions of the class of reaction-diffusion equations with nonlinear fractional diffusion: $u_{t} + (-\\Delta)^s (u^m)=f(u)$. For all $0<s<1$ and $m> m_c=(N-2s)_+/N $, we consider the solution of the initial-value problem with initial data having fast decay at infinity and prove that its level sets propagate exponentially fast in time, in contradiction to the traveling wave behaviour of the standard KPP case, which corresponds to putting $s=1$, $m=1$ and $f(u)=u(1-u)$. The proof of this fact uses as an essential ingredient the rece"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6823","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":"2026-05-18T03:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owWSmzrwgbKdL3kM/te/IdmUS879BKoksI3C861YjlSB31KZ9gHnvF6OP7LyXgVg/0cs9vBy323J6Vgy34S4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:29:14.668542Z"},"content_sha256":"8b81b78f9b7b7692ed2ea5728b3c6752982f7faafaa57236a159ab97f9374f5e","schema_version":"1.0","event_id":"sha256:8b81b78f9b7b7692ed2ea5728b3c6752982f7faafaa57236a159ab97f9374f5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2QLDLVBXBQ5EZFLQ3XMGSKBMMJ/bundle.json","state_url":"https://pith.science/pith/2QLDLVBXBQ5EZFLQ3XMGSKBMMJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2QLDLVBXBQ5EZFLQ3XMGSKBMMJ/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":"2026-05-22T11:29:14Z","links":{"resolver":"https://pith.science/pith/2QLDLVBXBQ5EZFLQ3XMGSKBMMJ","bundle":"https://pith.science/pith/2QLDLVBXBQ5EZFLQ3XMGSKBMMJ/bundle.json","state":"https://pith.science/pith/2QLDLVBXBQ5EZFLQ3XMGSKBMMJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2QLDLVBXBQ5EZFLQ3XMGSKBMMJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2QLDLVBXBQ5EZFLQ3XMGSKBMMJ","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":"f3546c9f4906ef29eb1d44e1f8994e30e0cd0e487a3417e06e3888d1b896ac24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-27T13:22:13Z","title_canon_sha256":"5bbb8fd4ff18fb0eab3accb18367dd451e357ca16b25d4fcf7409d2f936b9b1d"},"schema_version":"1.0","source":{"id":"1303.6823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6823","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6823v1","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6823","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"2QLDLVBXBQ5E","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2QLDLVBXBQ5EZFLQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2QLDLVBX","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:8b81b78f9b7b7692ed2ea5728b3c6752982f7faafaa57236a159ab97f9374f5e","target":"graph","created_at":"2026-05-18T03:29:39Z","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 the propagation properties of nonnegative and bounded solutions of the class of reaction-diffusion equations with nonlinear fractional diffusion: $u_{t} + (-\\Delta)^s (u^m)=f(u)$. For all $0<s<1$ and $m> m_c=(N-2s)_+/N $, we consider the solution of the initial-value problem with initial data having fast decay at infinity and prove that its level sets propagate exponentially fast in time, in contradiction to the traveling wave behaviour of the standard KPP case, which corresponds to putting $s=1$, $m=1$ and $f(u)=u(1-u)$. The proof of this fact uses as an essential ingredient the rece","authors_text":"Diana Stan, Juan Luis V\\'azquez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-27T13:22:13Z","title":"The Fisher-KPP equation with nonlinear fractional diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6823","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":"sha256:97a450f66fc982a5d8cca6d8aed22c4940f4f3f281a0647872a5caf9f1ae053d","target":"record","created_at":"2026-05-18T03:29:39Z","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":"f3546c9f4906ef29eb1d44e1f8994e30e0cd0e487a3417e06e3888d1b896ac24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-27T13:22:13Z","title_canon_sha256":"5bbb8fd4ff18fb0eab3accb18367dd451e357ca16b25d4fcf7409d2f936b9b1d"},"schema_version":"1.0","source":{"id":"1303.6823","kind":"arxiv","version":1}},"canonical_sha256":"d41635d4370c3a4c9570ddd869282c624c326e2e969f8a91e398dbad65b7a8fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d41635d4370c3a4c9570ddd869282c624c326e2e969f8a91e398dbad65b7a8fa","first_computed_at":"2026-05-18T03:29:39.619354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:39.619354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R34pL7iSOgzFTC522687jvfexdR8nar9LELf/pn61ETiaFgKTaAY54MKrKZstarjhNGqHgLZ/2WGMMcvQcWoDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:39.619769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97a450f66fc982a5d8cca6d8aed22c4940f4f3f281a0647872a5caf9f1ae053d","sha256:8b81b78f9b7b7692ed2ea5728b3c6752982f7faafaa57236a159ab97f9374f5e"],"state_sha256":"f145861a767fa80180915135e962645b8ecbe046339a44710484c1dcc13a5acd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XyCHsP7gk/onew1vNS3OEyW8/3/UmJnXuvkc15XxA3VIuyJeWKO7ILljpC9AjbNXd9ixyq8E7rBHHzFjr2jnAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T11:29:14.670614Z","bundle_sha256":"914d900e01d848a6a9181efcf27d63f7ffde6d66c720394a1cdeeaa4d87711c6"}}