{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SQ3J6NB6S5E3THIZ7URG5RTDQI","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":"d485c099f454cc0177b97bd16715c52dfc9f90901e71f3203f85562146a124e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-21T03:46:48Z","title_canon_sha256":"d0eb160800d4e1851ab637fe541b3ab20cee3c8a7cb1e501d386370955c60d09"},"schema_version":"1.0","source":{"id":"2410.15619","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.15619","created_at":"2026-07-05T09:24:39Z"},{"alias_kind":"arxiv_version","alias_value":"2410.15619v2","created_at":"2026-07-05T09:24:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.15619","created_at":"2026-07-05T09:24:39Z"},{"alias_kind":"pith_short_12","alias_value":"SQ3J6NB6S5E3","created_at":"2026-07-05T09:24:39Z"},{"alias_kind":"pith_short_16","alias_value":"SQ3J6NB6S5E3THIZ","created_at":"2026-07-05T09:24:39Z"},{"alias_kind":"pith_short_8","alias_value":"SQ3J6NB6","created_at":"2026-07-05T09:24:39Z"}],"graph_snapshots":[{"event_id":"sha256:8b092a27c5a8aebd6122ac7a5bd58939abe206a8185d088210887d377b538cba","target":"graph","created_at":"2026-07-05T09:24:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.15619/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove blowup for the defocusing septic complex-valued nonlinear wave equation in $\\mathbb{R}^{4+1}$. This work builds on the earlier results of Shao, Wei, and Zhang [SWZ2024a,SWZ2024b], reducing the order of the nonlinearity from $29$ to $7$ in $\\mathbb{R}^{4+1}$. As in [SWZ2024a,SWZ2024b], the proof hinges on a connection between solutions to the nonlinear wave equation and the relativistic Euler equations via a front compression blowup mechanism. More specifically, the problem is reduced to constructing smooth, radially symmetric, self-similar imploding profiles for the rel","authors_text":"Jiajie Chen, Tristan Buckmaster","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-21T03:46:48Z","title":"Blowup for the defocusing septic complex-valued nonlinear wave equation in $\\mathbb{R}^{4+1}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.15619","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:fadb4ffc1549c9e5f5b664f2c8a2adac2d482a3285c4facc30cc23791731b05c","target":"record","created_at":"2026-07-05T09:24:39Z","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":"d485c099f454cc0177b97bd16715c52dfc9f90901e71f3203f85562146a124e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-21T03:46:48Z","title_canon_sha256":"d0eb160800d4e1851ab637fe541b3ab20cee3c8a7cb1e501d386370955c60d09"},"schema_version":"1.0","source":{"id":"2410.15619","kind":"arxiv","version":2}},"canonical_sha256":"94369f343e9749b99d19fd226ec6638203437bdb011252af88d22a499ba9e48d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94369f343e9749b99d19fd226ec6638203437bdb011252af88d22a499ba9e48d","first_computed_at":"2026-07-05T09:24:39.822405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:24:39.822405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1gH3zZJQWDUBqekFVCEUOeyHWQg2FkvAoa+TDVfExfIBJtCYjRgmmAvB1nqneXlULvS6lIhPGsNcGzE18jxFBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:24:39.822915Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.15619","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fadb4ffc1549c9e5f5b664f2c8a2adac2d482a3285c4facc30cc23791731b05c","sha256:8b092a27c5a8aebd6122ac7a5bd58939abe206a8185d088210887d377b538cba"],"state_sha256":"3e4d6b49e35382c96343b8ad8909a21ae0f4cfd62de5e3dabfcaeb2bb44e6409"}