{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MUB3VEPA5XZADEFKUU6YWDAFGY","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":"3bc3294738344abf8a7bd8062f99abd04447edbe692c9b0de226d3440edf9e42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-16T04:50:15Z","title_canon_sha256":"131e469ca7ca83889203a6efd87cb76d6467c06c585a80e65fc96142a735435f"},"schema_version":"1.0","source":{"id":"1109.3528","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3528","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3528v2","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3528","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"MUB3VEPA5XZA","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MUB3VEPA5XZADEFK","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MUB3VEPA","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:6be8e115f4d39804d26ad6e1d3fba5f4f8b31cc0eaa1894476ca0538049fb832","target":"graph","created_at":"2026-05-18T03:46:18Z","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 consider the Zakharov system in two space dimension with periodic boundary condition. We prove the existence of finite time blow-up solutions. Further, we show there exists no minimal mass blow-up solution.","authors_text":"Masaya Maeda, Nobu Kishimoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-16T04:50:15Z","title":"Construction of blow-up solutions for Zakharov system on $\\mathbb{T}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3528","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":"sha256:50893558ea03d3df93b082538d1fdb2494932e0595337901c057b784800691f1","target":"record","created_at":"2026-05-18T03:46:18Z","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":"3bc3294738344abf8a7bd8062f99abd04447edbe692c9b0de226d3440edf9e42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-16T04:50:15Z","title_canon_sha256":"131e469ca7ca83889203a6efd87cb76d6467c06c585a80e65fc96142a735435f"},"schema_version":"1.0","source":{"id":"1109.3528","kind":"arxiv","version":2}},"canonical_sha256":"6503ba91e0edf20190aaa53d8b0c053605c661f36b1ad1932d835d466f1b98db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6503ba91e0edf20190aaa53d8b0c053605c661f36b1ad1932d835d466f1b98db","first_computed_at":"2026-05-18T03:46:18.581544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:18.581544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DsSK4U7xKZv3KZ+G66Wp5E38QE4v1s90YvgA8dOHa4heaq8QoIO8ggYk20YCPyeajjzGyiO9UCCpMziugIDTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:18.582174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3528","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50893558ea03d3df93b082538d1fdb2494932e0595337901c057b784800691f1","sha256:6be8e115f4d39804d26ad6e1d3fba5f4f8b31cc0eaa1894476ca0538049fb832"],"state_sha256":"1d186369840a53a7717da6cca4398da77621bf7823bfe7f2d737e1abdbe1d778"}