{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SJF7DNGW5U3TICRABK7O4WGP5U","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":"901564dcb5c271289e64232a7dabb3848d78a63084507c03e41ca6467d32646a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-30T15:30:26Z","title_canon_sha256":"2c66ef061d4ceb2354966de5f2edca3dd2ca100f9dafddc45b06beae735ed27d"},"schema_version":"1.0","source":{"id":"1111.7208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7208","created_at":"2026-05-18T04:07:18Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7208v1","created_at":"2026-05-18T04:07:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7208","created_at":"2026-05-18T04:07:18Z"},{"alias_kind":"pith_short_12","alias_value":"SJF7DNGW5U3T","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SJF7DNGW5U3TICRA","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SJF7DNGW","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:2719a6dd7b6b866af8656fb13461fc94bf53ecbfa4ba27c86368def729c71821","target":"graph","created_at":"2026-05-18T04:07:18Z","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 the asymptotics of blowup for nonlinear heat equations with superlinear power nonlinearities in arbitrary dimensions and we estimate the remainders.","authors_text":"D. Egli, I. M. Sigal, W. Kong, Z. Gang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-30T15:30:26Z","title":"On Blowup in Nonlinear Heat Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7208","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":"sha256:3ed30430665d8df16565a60e56b1447dd6e902a2bf3d4d23e69641e704a74f96","target":"record","created_at":"2026-05-18T04:07:18Z","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":"901564dcb5c271289e64232a7dabb3848d78a63084507c03e41ca6467d32646a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-30T15:30:26Z","title_canon_sha256":"2c66ef061d4ceb2354966de5f2edca3dd2ca100f9dafddc45b06beae735ed27d"},"schema_version":"1.0","source":{"id":"1111.7208","kind":"arxiv","version":1}},"canonical_sha256":"924bf1b4d6ed37340a200abeee58cfed2f64ef1c6d6a530c3a0e12c68163f470","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"924bf1b4d6ed37340a200abeee58cfed2f64ef1c6d6a530c3a0e12c68163f470","first_computed_at":"2026-05-18T04:07:18.463977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:18.463977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CQJ02HcPfnDJBNzKp1e0HeDhPW6nyP6H0EDTJkKa9+k1+RS3ruIwOVSDQf3knyXGSMdkZWKr8u4+jV5pikB7Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:18.464771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.7208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ed30430665d8df16565a60e56b1447dd6e902a2bf3d4d23e69641e704a74f96","sha256:2719a6dd7b6b866af8656fb13461fc94bf53ecbfa4ba27c86368def729c71821"],"state_sha256":"53c745389e23ea19519598419afce5a6f0e49d27ff278aabdd32e3f4cae927cb"}