{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HLV3XO7CTWW2LEUJA7EO63LHLE","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":"5f5f28ae9eb6c998063d8168976f031af3ad5617b42062b38bad693a1884b00b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-24T20:48:47Z","title_canon_sha256":"916023b240b3ceb5dd27b463915a032ead19b7448c070bba675cd4fdf000107d"},"schema_version":"1.0","source":{"id":"1010.5001","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5001","created_at":"2026-05-18T04:33:04Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5001v2","created_at":"2026-05-18T04:33:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5001","created_at":"2026-05-18T04:33:04Z"},{"alias_kind":"pith_short_12","alias_value":"HLV3XO7CTWW2","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HLV3XO7CTWW2LEUJ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HLV3XO7C","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:67446e7b90566338fd76801c9d0bc155c3bc8df46184553bb915bc15730e9e6b","target":"graph","created_at":"2026-05-18T04:33:04Z","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 use a Leibnitz rule type inequality for fractional derivatives to prove conditions under which a solution $u(x,t)$ of the k-generalized KdV equation is in the space $L^2(|x|^{2s}\\,dx)$ for $s \\in \\mathbb R_{+}$.","authors_text":"Joules Nahas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-24T20:48:47Z","title":"A decay property of solutions to the k-generalized KdV equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5001","kind":"arxiv","version":2},"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:e19b63005b7df16abc709d34933fd42e580786a344fa60eff1a02d3d3eda39d9","target":"record","created_at":"2026-05-18T04:33:04Z","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":"5f5f28ae9eb6c998063d8168976f031af3ad5617b42062b38bad693a1884b00b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-24T20:48:47Z","title_canon_sha256":"916023b240b3ceb5dd27b463915a032ead19b7448c070bba675cd4fdf000107d"},"schema_version":"1.0","source":{"id":"1010.5001","kind":"arxiv","version":2}},"canonical_sha256":"3aebbbbbe29dada5928907c8ef6d67592dedadd56de58b0f4af3fe08a06e517a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aebbbbbe29dada5928907c8ef6d67592dedadd56de58b0f4af3fe08a06e517a","first_computed_at":"2026-05-18T04:33:04.065521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:04.065521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CsRus/Qdv+1vVLVUUugmYjwx14GyCYJCFp8+/0bKFq+Jgmi6ELEuJI/Ljm0CnDdqXMccNrTqus9hbsifVq+DCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:04.066254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5001","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e19b63005b7df16abc709d34933fd42e580786a344fa60eff1a02d3d3eda39d9","sha256:67446e7b90566338fd76801c9d0bc155c3bc8df46184553bb915bc15730e9e6b"],"state_sha256":"87ddf2dbc3454b2530aa970897925b3b20e99c1d819ab1c3f958d80f336b95bc"}