{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZDMR3EWRPBYJBOW7UGI3MYNZS4","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":"2c40ca352034af4c2cf673fa70b7c7f70e03827003dad8c2104643cbe968cf36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-30T13:33:37Z","title_canon_sha256":"0dd7825eb9bfb29782a81e9b93e025b5e2faa8d427601182e1358f0c6677f69f"},"schema_version":"1.0","source":{"id":"1106.6221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.6221","created_at":"2026-05-18T02:53:54Z"},{"alias_kind":"arxiv_version","alias_value":"1106.6221v1","created_at":"2026-05-18T02:53:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6221","created_at":"2026-05-18T02:53:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZDMR3EWRPBYJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZDMR3EWRPBYJBOW7","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZDMR3EWR","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:b5d448c417b4ae82d164cc850a71ad6269aff6b86e553312368f7b352dc43ce2","target":"graph","created_at":"2026-05-18T02:53:54Z","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":"In this paper we prove the blow-up theorem in the critical case for weakly coupled systems of semilinear wave equations in high dimensions. The upper bound of the lifespan of the solution is precisely clarified.","authors_text":"Hiroyuki Takamura, Kyouhei Wakasa, Yuki Kurokawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-30T13:33:37Z","title":"The blow-up and lifespan of solutions to systems of semilinear wave equation with critical exponents in high dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6221","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:f6f9ea127b27385d73a7e2c35922056188d2123ec823fb4efbb9563fa1aaf16b","target":"record","created_at":"2026-05-18T02:53:54Z","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":"2c40ca352034af4c2cf673fa70b7c7f70e03827003dad8c2104643cbe968cf36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-30T13:33:37Z","title_canon_sha256":"0dd7825eb9bfb29782a81e9b93e025b5e2faa8d427601182e1358f0c6677f69f"},"schema_version":"1.0","source":{"id":"1106.6221","kind":"arxiv","version":1}},"canonical_sha256":"c8d91d92d1787090badfa191b661b99706476bb3f997701d0b6573f2b9e6d799","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8d91d92d1787090badfa191b661b99706476bb3f997701d0b6573f2b9e6d799","first_computed_at":"2026-05-18T02:53:54.400646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:54.400646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Egwfe8/r+J0lGswA9nx2u5zCF3XQ3+EmqneuHEgRCnfWwD4CHML7nJCaAvXbS91Mwt3I0OpJWyXNc+PAZyZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:54.401511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.6221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6f9ea127b27385d73a7e2c35922056188d2123ec823fb4efbb9563fa1aaf16b","sha256:b5d448c417b4ae82d164cc850a71ad6269aff6b86e553312368f7b352dc43ce2"],"state_sha256":"b09a27a7a4bb1fcaaa2bba193cea1d040cf2a19ad69846e6ba87944b3cb638f1"}