{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RGWKQCTKO6Y2ZK3KLTPLADP2I5","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":"6bfef72d7f890225e2c0f00c6ee817b1788e64c2a01e38babc3aeb090c4b5b37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-30T04:59:16Z","title_canon_sha256":"9488e3c1f841bdea324bfe40dda5271906ae2ac87020bc86154c3d397768a4df"},"schema_version":"1.0","source":{"id":"1503.08532","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08532","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08532v3","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08532","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"pith_short_12","alias_value":"RGWKQCTKO6Y2","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RGWKQCTKO6Y2ZK3K","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RGWKQCTK","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:4fb5d04db6710068897dad53b902235be148401ef9331cb7c9122ecdaa166cba","target":"graph","created_at":"2026-05-18T01:33:33Z","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 admissible growth at infinity of initial data of positive solutions of $\\prt\\_t u-\\Gd u+f(u)=0$ in $\\BBR\\_+\\ti\\BBR^N$ when $f(u)$ is a continuous  function, {\\it mildly} superlinear at infinity, the model case being $f(u)=u\\ln^\\ga (1+u)$ with $1\\textless{}\\ga\\textless{}2$. We prove in particular that if the growth of the initial data at infinity  is too strong, there is no more diffusion and the corresponding solution satisfies the ODE problem $\\prt\\_t \\gf+f(\\gf)=0$ on $\\BBR\\_+$ with $\\gf(0)=\\infty$.","authors_text":"Andrey Shishkov (IAMM), Laurent V\\'eron (LMPT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-30T04:59:16Z","title":"Admissible initial growth for diffusion equations with weakly superlinear absorption"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08532","kind":"arxiv","version":3},"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:cfcf3b3dabbc8c0e95456554506ceb280f1965b4e263980c5f555d35afb2d1a8","target":"record","created_at":"2026-05-18T01:33:33Z","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":"6bfef72d7f890225e2c0f00c6ee817b1788e64c2a01e38babc3aeb090c4b5b37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-30T04:59:16Z","title_canon_sha256":"9488e3c1f841bdea324bfe40dda5271906ae2ac87020bc86154c3d397768a4df"},"schema_version":"1.0","source":{"id":"1503.08532","kind":"arxiv","version":3}},"canonical_sha256":"89aca80a6a77b1acab6a5cdeb00dfa475dc9bd4f03be8c717d3b838b0d83880d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89aca80a6a77b1acab6a5cdeb00dfa475dc9bd4f03be8c717d3b838b0d83880d","first_computed_at":"2026-05-18T01:33:33.734060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:33.734060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YKEXE7xiYIYoPxu9FgZ9dujThNp14lW5TI7EOfLVUA6v2fNqbRA98N+OoNY52paY30+Bg601+mpWOk2i9g2WDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:33.734562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08532","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfcf3b3dabbc8c0e95456554506ceb280f1965b4e263980c5f555d35afb2d1a8","sha256:4fb5d04db6710068897dad53b902235be148401ef9331cb7c9122ecdaa166cba"],"state_sha256":"2ed7d21a099d6414930fcae12a5a7cba214e4fadea720b7369d62152f1106553"}