{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:D2VVJ6WLEIRPQEELFNZTDNOCEW","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":"df0ebe5dfa851b9ff49e792b4937110716753fb12ecf3b1244ef01129aaae0a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-01T20:01:30Z","title_canon_sha256":"e902188490be8439cce1e0979c4e0129e92d5653145fc90f2bcbeba97c58f156"},"schema_version":"1.0","source":{"id":"1603.00430","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00430","created_at":"2026-05-18T01:19:45Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00430v1","created_at":"2026-05-18T01:19:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00430","created_at":"2026-05-18T01:19:45Z"},{"alias_kind":"pith_short_12","alias_value":"D2VVJ6WLEIRP","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D2VVJ6WLEIRPQEEL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D2VVJ6WL","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:1a7cd8eb89993b3d069aea6c420634edd9ca387552e61a4a01c00f882ed5e370","target":"graph","created_at":"2026-05-18T01:19:45Z","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 establish in this article spreading properties for the solutions of equations of the type $\\partial$ t u -- a(x)$\\partial$ xx u -- q(x)$\\partial$ x u = f (x, u), where a, q, f are only assumed to be uniformly continuous and bounded in x, the nonlinearity f is of monostable KPP type between two steady states 0 and 1 and the initial datum is compactly sup-ported. Using homogenization techniques, we construct two speeds w $\\le$ w such that lim t$\\rightarrow$+$\\infty$ sup 0$\\le$x$\\le$wt |u(t, x)--1| = 0 for all w $\\in$ (0, w) and lim t$\\rightarrow$+$\\infty$ sup x$\\ge$wt |u(t, x)| = 0 for all w ","authors_text":"Gr\\'egoire Nadin (LJLL), Henri Berestycki (CAMS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-01T20:01:30Z","title":"Spreading speeds for one-dimensional monostable reaction-diffusion equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00430","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":"sha256:58aaf81ca3846d3ecebb08eb5b75b4d15aee921ff22a7521387eba96220a6d45","target":"record","created_at":"2026-05-18T01:19:45Z","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":"df0ebe5dfa851b9ff49e792b4937110716753fb12ecf3b1244ef01129aaae0a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-01T20:01:30Z","title_canon_sha256":"e902188490be8439cce1e0979c4e0129e92d5653145fc90f2bcbeba97c58f156"},"schema_version":"1.0","source":{"id":"1603.00430","kind":"arxiv","version":1}},"canonical_sha256":"1eab54facb2222f8108b2b7331b5c225a8fbefa0e387de70fd74a5ddf3572e72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1eab54facb2222f8108b2b7331b5c225a8fbefa0e387de70fd74a5ddf3572e72","first_computed_at":"2026-05-18T01:19:45.104724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:45.104724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NOtLhv9Ej2hiTKnbOSeV/iXjp9EoVHyjnvtgXTGnZCMbeKx0l1woz4N0FfYvbsLVluOuDw2anhAgt08GKXPPBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:45.105261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00430","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58aaf81ca3846d3ecebb08eb5b75b4d15aee921ff22a7521387eba96220a6d45","sha256:1a7cd8eb89993b3d069aea6c420634edd9ca387552e61a4a01c00f882ed5e370"],"state_sha256":"62d1b846cfff4bce8fcef614172bedc02c9a885c32b45d6713a5b431f629ed6a"}