{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FN7M33XEAMR7WNTRU7XM5A4ZXC","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":"0f76331d50085ff629b61138307c9eadbdefc9bc1200e67a6eb0c374c822d1ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-30T17:23:23Z","title_canon_sha256":"69746cc481a8edee4d496eecd306fc1fb76aee24eee3ca3e5baabcafedc8f108"},"schema_version":"1.0","source":{"id":"1708.09372","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09372","created_at":"2026-05-18T00:27:19Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09372v2","created_at":"2026-05-18T00:27:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09372","created_at":"2026-05-18T00:27:19Z"},{"alias_kind":"pith_short_12","alias_value":"FN7M33XEAMR7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FN7M33XEAMR7WNTR","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FN7M33XE","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:33be4a984eead7a9f9cacc549b56bc453d65388525306dec320587c5c262b3bc","target":"graph","created_at":"2026-05-18T00:27:19Z","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 and the companion paper [EJE2], we establish finite-time singularity formation for finite-energy strong solutions to the axi-symmetric $3D$ Euler equations in the domain $\\{(x,y,z)\\in\\mathbb{R}^3:z^2\\leq c(x^2+y^2)\\}$ for some $c>0$. In the spirit of our previous works, [EJSI] and [EJB], we do this by first studying scale-invariant solutions which satisfy a one dimensional PDE system and proving that they may become singular in finite time for properly chosen initial data. We then prove local well-posedness for the $3D$ Euler equations in a natural regularity class which includes","authors_text":"In-Jee Jeong, Tarek M. Elgindi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-30T17:23:23Z","title":"Finite-time Singularity Formation for Strong Solutions to the $3D$ Euler Equations, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09372","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:bfab42c62fde7a34a90c711c3adf29e5114ad06d83bf43e9a73244252e12a9d3","target":"record","created_at":"2026-05-18T00:27:19Z","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":"0f76331d50085ff629b61138307c9eadbdefc9bc1200e67a6eb0c374c822d1ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-30T17:23:23Z","title_canon_sha256":"69746cc481a8edee4d496eecd306fc1fb76aee24eee3ca3e5baabcafedc8f108"},"schema_version":"1.0","source":{"id":"1708.09372","kind":"arxiv","version":2}},"canonical_sha256":"2b7ecdeee40323fb3671a7eece8399b8945a7ade97d3aee9badb3c3b2e43ee09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b7ecdeee40323fb3671a7eece8399b8945a7ade97d3aee9badb3c3b2e43ee09","first_computed_at":"2026-05-18T00:27:19.096701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:19.096701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zgCd/GiXQ5NYyYcPBs/jhCMY5ZmCYMkZbivrMjyg9erLE7aOLr2oRnBLsc6pYnhwVKAtM7TMlngb/eY4xFdSAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:19.097200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09372","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfab42c62fde7a34a90c711c3adf29e5114ad06d83bf43e9a73244252e12a9d3","sha256:33be4a984eead7a9f9cacc549b56bc453d65388525306dec320587c5c262b3bc"],"state_sha256":"ee223a0030f926a5d75d499fc05fc57d55125138349d0ab79e41ff683b8c3528"}