{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OXRPVZHRPFMF75F4SAN633KZ7T","short_pith_number":"pith:OXRPVZHR","canonical_record":{"source":{"id":"1310.8611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T17:40:05Z","cross_cats_sorted":[],"title_canon_sha256":"b50bb0eeb58426b79c67ecd69d73e3f742116e4d56ed7676d955b32e5afd47d6","abstract_canon_sha256":"e099f5562bc576b7326b5944e9e2f8d0f805565726b4f148a46a18d36a40d481"},"schema_version":"1.0"},"canonical_sha256":"75e2fae4f179585ff4bc901beded59fcf25ae327a3975390c6251bd0b02ec37b","source":{"kind":"arxiv","id":"1310.8611","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8611","created_at":"2026-05-18T02:42:52Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8611v2","created_at":"2026-05-18T02:42:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8611","created_at":"2026-05-18T02:42:52Z"},{"alias_kind":"pith_short_12","alias_value":"OXRPVZHRPFMF","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OXRPVZHRPFMF75F4","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OXRPVZHR","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OXRPVZHRPFMF75F4SAN633KZ7T","target":"record","payload":{"canonical_record":{"source":{"id":"1310.8611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T17:40:05Z","cross_cats_sorted":[],"title_canon_sha256":"b50bb0eeb58426b79c67ecd69d73e3f742116e4d56ed7676d955b32e5afd47d6","abstract_canon_sha256":"e099f5562bc576b7326b5944e9e2f8d0f805565726b4f148a46a18d36a40d481"},"schema_version":"1.0"},"canonical_sha256":"75e2fae4f179585ff4bc901beded59fcf25ae327a3975390c6251bd0b02ec37b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:52.645078Z","signature_b64":"yb+SAQRr+0tX1yiJCulybPR9p3i3EgM5giCCMnTVSIXZvtpf6nvZ7HA3Aj08m2U2mCw7IbKjjDi/LxZOC7okAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75e2fae4f179585ff4bc901beded59fcf25ae327a3975390c6251bd0b02ec37b","last_reissued_at":"2026-05-18T02:42:52.644665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:52.644665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.8611","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DqalZJKPyHLxn6OLoUtvHUAObMuabDcI7lAF0GMeMIcWk6QqaF0/FwpG19ighadk6AfF1DlqHTil7cSf9Q/nBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:26:20.380355Z"},"content_sha256":"49b6912ce12933c52635e42cabff0f0470104f447b0e0424962e5113de46a061","schema_version":"1.0","event_id":"sha256:49b6912ce12933c52635e42cabff0f0470104f447b0e0424962e5113de46a061"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OXRPVZHRPFMF75F4SAN633KZ7T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the energy behavior of locally self-similar blowup for the Euler equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anne Bronzi, Roman Shvydkoy","submitted_at":"2013-10-31T17:40:05Z","abstract_excerpt":"In this note we study locally self-similar blow up for the Euler equation. The main result states that under a mild $L^p$-growth assumption on the profile $v$, namely, $\\int_{|y| \\sim L} |v|^p dy \\lesssim L^{\\g}$ for some $\\g <p-2$, the self-similar solution carries a positive amount of energy up to the time of blow-up $T$, namely, $\\int_{|y| \\sim L} |v|^2 dy \\sim L^{N-2\\a}$. The result implies and extends several previously known exclusion criteria. It also supports a general conjecture relating fractal local dimensions of the energy measure with the rate of velocity growth at the time of pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8611","kind":"arxiv","version":2},"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":"2026-05-18T02:42:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JHQpPoTAfTHoYW0e0lZH3fH3NwBLVlhQilNmtVmQ4ZdlQKA/1/rHTs/8hYXYtBg0S/rvERo2Be6ANy2feNJcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:26:20.380888Z"},"content_sha256":"9c47b6dbbe1df9939f29996071136b33e7273f4df88f697f161de0f2cd7e5194","schema_version":"1.0","event_id":"sha256:9c47b6dbbe1df9939f29996071136b33e7273f4df88f697f161de0f2cd7e5194"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OXRPVZHRPFMF75F4SAN633KZ7T/bundle.json","state_url":"https://pith.science/pith/OXRPVZHRPFMF75F4SAN633KZ7T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OXRPVZHRPFMF75F4SAN633KZ7T/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":"2026-05-26T07:26:20Z","links":{"resolver":"https://pith.science/pith/OXRPVZHRPFMF75F4SAN633KZ7T","bundle":"https://pith.science/pith/OXRPVZHRPFMF75F4SAN633KZ7T/bundle.json","state":"https://pith.science/pith/OXRPVZHRPFMF75F4SAN633KZ7T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OXRPVZHRPFMF75F4SAN633KZ7T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OXRPVZHRPFMF75F4SAN633KZ7T","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":"e099f5562bc576b7326b5944e9e2f8d0f805565726b4f148a46a18d36a40d481","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T17:40:05Z","title_canon_sha256":"b50bb0eeb58426b79c67ecd69d73e3f742116e4d56ed7676d955b32e5afd47d6"},"schema_version":"1.0","source":{"id":"1310.8611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8611","created_at":"2026-05-18T02:42:52Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8611v2","created_at":"2026-05-18T02:42:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8611","created_at":"2026-05-18T02:42:52Z"},{"alias_kind":"pith_short_12","alias_value":"OXRPVZHRPFMF","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OXRPVZHRPFMF75F4","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OXRPVZHR","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:9c47b6dbbe1df9939f29996071136b33e7273f4df88f697f161de0f2cd7e5194","target":"graph","created_at":"2026-05-18T02:42:52Z","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 note we study locally self-similar blow up for the Euler equation. The main result states that under a mild $L^p$-growth assumption on the profile $v$, namely, $\\int_{|y| \\sim L} |v|^p dy \\lesssim L^{\\g}$ for some $\\g <p-2$, the self-similar solution carries a positive amount of energy up to the time of blow-up $T$, namely, $\\int_{|y| \\sim L} |v|^2 dy \\sim L^{N-2\\a}$. The result implies and extends several previously known exclusion criteria. It also supports a general conjecture relating fractal local dimensions of the energy measure with the rate of velocity growth at the time of pos","authors_text":"Anne Bronzi, Roman Shvydkoy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T17:40:05Z","title":"On the energy behavior of locally self-similar blowup for the Euler equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8611","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":"sha256:49b6912ce12933c52635e42cabff0f0470104f447b0e0424962e5113de46a061","target":"record","created_at":"2026-05-18T02:42:52Z","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":"e099f5562bc576b7326b5944e9e2f8d0f805565726b4f148a46a18d36a40d481","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T17:40:05Z","title_canon_sha256":"b50bb0eeb58426b79c67ecd69d73e3f742116e4d56ed7676d955b32e5afd47d6"},"schema_version":"1.0","source":{"id":"1310.8611","kind":"arxiv","version":2}},"canonical_sha256":"75e2fae4f179585ff4bc901beded59fcf25ae327a3975390c6251bd0b02ec37b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75e2fae4f179585ff4bc901beded59fcf25ae327a3975390c6251bd0b02ec37b","first_computed_at":"2026-05-18T02:42:52.644665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:52.644665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yb+SAQRr+0tX1yiJCulybPR9p3i3EgM5giCCMnTVSIXZvtpf6nvZ7HA3Aj08m2U2mCw7IbKjjDi/LxZOC7okAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:52.645078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49b6912ce12933c52635e42cabff0f0470104f447b0e0424962e5113de46a061","sha256:9c47b6dbbe1df9939f29996071136b33e7273f4df88f697f161de0f2cd7e5194"],"state_sha256":"651a5b22148ecbcfd099e3f7ad158e864b3f284f73ecd1cd9d43e78db90508d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4vLp5+kSHG4e5UNJZQlWfEcgfeOaIZ3ooZ8ZZO1YIFWcKfV/TrqSkoPEfDGFnILzMhakxEJ31qMw/iTe4eYuDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:26:20.384272Z","bundle_sha256":"62c450f7e75bfa7411da1200131a2967fa03bee5722c92b3a995c76303f13927"}}