{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CXXTJVYJWK2PDTXKFSRCYQ7UO5","short_pith_number":"pith:CXXTJVYJ","canonical_record":{"source":{"id":"1802.10161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-27T21:03:15Z","cross_cats_sorted":[],"title_canon_sha256":"4851fa4e593e815622ea4eae4142a39662943c1eb31e2fdb50bfb1e10cd97e4e","abstract_canon_sha256":"fc828703fec179fdbaa420bbfd8c2f7381477a5c5dac5bbb7a13e1a5bbf6f0e0"},"schema_version":"1.0"},"canonical_sha256":"15ef34d709b2b4f1ceea2ca22c43f47777ab234ba1a0ff93eff650286bafd390","source":{"kind":"arxiv","id":"1802.10161","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.10161","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1802.10161v1","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10161","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"CXXTJVYJWK2P","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CXXTJVYJWK2PDTXK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CXXTJVYJ","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CXXTJVYJWK2PDTXKFSRCYQ7UO5","target":"record","payload":{"canonical_record":{"source":{"id":"1802.10161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-27T21:03:15Z","cross_cats_sorted":[],"title_canon_sha256":"4851fa4e593e815622ea4eae4142a39662943c1eb31e2fdb50bfb1e10cd97e4e","abstract_canon_sha256":"fc828703fec179fdbaa420bbfd8c2f7381477a5c5dac5bbb7a13e1a5bbf6f0e0"},"schema_version":"1.0"},"canonical_sha256":"15ef34d709b2b4f1ceea2ca22c43f47777ab234ba1a0ff93eff650286bafd390","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:17.969042Z","signature_b64":"EZsfGMdczZTnZhP/pN/azLDj9XXjKosmpGzqSw3tbEKQ8AMvv+I1ZOk8X5cNhZ0aUI5dWXaJeSkB0RdtENFBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15ef34d709b2b4f1ceea2ca22c43f47777ab234ba1a0ff93eff650286bafd390","last_reissued_at":"2026-05-18T00:22:17.968399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:17.968399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.10161","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lUQMAjAZp/L9Faf4HlT+qGCO74J7jn/nQlKSRJSxwVUqJaaq304MIWKKoYapJQqfSuzNQAvunqoDLrMidikFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:14:14.042148Z"},"content_sha256":"c46fbe0feb79d5a174c193f2ad77cbdc156ab21f14abd750829a93c0b4ecaea0","schema_version":"1.0","event_id":"sha256:c46fbe0feb79d5a174c193f2ad77cbdc156ab21f14abd750829a93c0b4ecaea0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CXXTJVYJWK2PDTXKFSRCYQ7UO5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Confinement of vorticity for the 2D Euler-alpha equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David Ambrose, Helena Nussenzveig Lopes, Milton Lopes Filho","submitted_at":"2018-02-27T21:03:15Z","abstract_excerpt":"In this article we consider weak solutions of the Euler-$\\alpha$ equations in the full plane. We take, as initial unfiltered vorticity, an arbitrary nonnegative, compactly supported, bounded Radon measure. Global well-posedness for the corresponding initial value problem is due M. Oliver and S. Shkoller. We show that, for all time, the support of the unfiltered vorticity is contained in a disk whose radius grows no faster than $\\mathcal{O}((t\\log t)^{1/4})$. This result is an adaptation of the corresponding result for the incompressible 2D Euler equations with initial vorticity compactly suppo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10161","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"urIOLHNlD+T/uKIPc6ainLUh4THf2b7vkLcpvhQSNhTau7Xd7dPywZuDOOKWIDP6/F6feQ5RQw9fPVa44Hx3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:14:14.042808Z"},"content_sha256":"dc0a100f9bdc23fd4e84ded49aaf2559ef2d6e03f6ee6e9d845e93a30547d784","schema_version":"1.0","event_id":"sha256:dc0a100f9bdc23fd4e84ded49aaf2559ef2d6e03f6ee6e9d845e93a30547d784"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CXXTJVYJWK2PDTXKFSRCYQ7UO5/bundle.json","state_url":"https://pith.science/pith/CXXTJVYJWK2PDTXKFSRCYQ7UO5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CXXTJVYJWK2PDTXKFSRCYQ7UO5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T06:14:14Z","links":{"resolver":"https://pith.science/pith/CXXTJVYJWK2PDTXKFSRCYQ7UO5","bundle":"https://pith.science/pith/CXXTJVYJWK2PDTXKFSRCYQ7UO5/bundle.json","state":"https://pith.science/pith/CXXTJVYJWK2PDTXKFSRCYQ7UO5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CXXTJVYJWK2PDTXKFSRCYQ7UO5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CXXTJVYJWK2PDTXKFSRCYQ7UO5","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":"fc828703fec179fdbaa420bbfd8c2f7381477a5c5dac5bbb7a13e1a5bbf6f0e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-27T21:03:15Z","title_canon_sha256":"4851fa4e593e815622ea4eae4142a39662943c1eb31e2fdb50bfb1e10cd97e4e"},"schema_version":"1.0","source":{"id":"1802.10161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.10161","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1802.10161v1","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10161","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"CXXTJVYJWK2P","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CXXTJVYJWK2PDTXK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CXXTJVYJ","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:dc0a100f9bdc23fd4e84ded49aaf2559ef2d6e03f6ee6e9d845e93a30547d784","target":"graph","created_at":"2026-05-18T00:22:17Z","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 article we consider weak solutions of the Euler-$\\alpha$ equations in the full plane. We take, as initial unfiltered vorticity, an arbitrary nonnegative, compactly supported, bounded Radon measure. Global well-posedness for the corresponding initial value problem is due M. Oliver and S. Shkoller. We show that, for all time, the support of the unfiltered vorticity is contained in a disk whose radius grows no faster than $\\mathcal{O}((t\\log t)^{1/4})$. This result is an adaptation of the corresponding result for the incompressible 2D Euler equations with initial vorticity compactly suppo","authors_text":"David Ambrose, Helena Nussenzveig Lopes, Milton Lopes Filho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-27T21:03:15Z","title":"Confinement of vorticity for the 2D Euler-alpha equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10161","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:c46fbe0feb79d5a174c193f2ad77cbdc156ab21f14abd750829a93c0b4ecaea0","target":"record","created_at":"2026-05-18T00:22:17Z","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":"fc828703fec179fdbaa420bbfd8c2f7381477a5c5dac5bbb7a13e1a5bbf6f0e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-27T21:03:15Z","title_canon_sha256":"4851fa4e593e815622ea4eae4142a39662943c1eb31e2fdb50bfb1e10cd97e4e"},"schema_version":"1.0","source":{"id":"1802.10161","kind":"arxiv","version":1}},"canonical_sha256":"15ef34d709b2b4f1ceea2ca22c43f47777ab234ba1a0ff93eff650286bafd390","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15ef34d709b2b4f1ceea2ca22c43f47777ab234ba1a0ff93eff650286bafd390","first_computed_at":"2026-05-18T00:22:17.968399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:17.968399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EZsfGMdczZTnZhP/pN/azLDj9XXjKosmpGzqSw3tbEKQ8AMvv+I1ZOk8X5cNhZ0aUI5dWXaJeSkB0RdtENFBBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:17.969042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.10161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c46fbe0feb79d5a174c193f2ad77cbdc156ab21f14abd750829a93c0b4ecaea0","sha256:dc0a100f9bdc23fd4e84ded49aaf2559ef2d6e03f6ee6e9d845e93a30547d784"],"state_sha256":"6e58440ce272e46e5eefe46c090cff71fd11377e4fa2c37df06718ba898c606b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GVAtgRk7vV3trPgtfGcrnxUl9TVdZlaKs2qza8Q0TF90ZFJLaLLPWX/lcKQrgRUTXZ2gMhuFWY4Tx2pBuBohDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:14:14.046289Z","bundle_sha256":"0ddf7b2ddf5b13204a7c74cf2718dcb5e7457eaed5da955e0b8232169f1691c1"}}