{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OBIZ2FEFJFFBDZMLS4Q5HE5454","short_pith_number":"pith:OBIZ2FEF","canonical_record":{"source":{"id":"1111.0217","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-01T15:15:06Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"be826aced54fbb6ca6307143def7f3db0534c2aebcb0ca058813415265db7f88","abstract_canon_sha256":"4be88503b5e21ebfce6709a54a89288c14a9f6c3e7bbea8724869dbc065ec427"},"schema_version":"1.0"},"canonical_sha256":"70519d1485494a11e58b9721d393bcef00811616001d55c502b1da4315d46c1a","source":{"kind":"arxiv","id":"1111.0217","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0217","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0217v5","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0217","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"OBIZ2FEFJFFB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OBIZ2FEFJFFBDZML","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OBIZ2FEF","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OBIZ2FEFJFFBDZMLS4Q5HE5454","target":"record","payload":{"canonical_record":{"source":{"id":"1111.0217","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-01T15:15:06Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"be826aced54fbb6ca6307143def7f3db0534c2aebcb0ca058813415265db7f88","abstract_canon_sha256":"4be88503b5e21ebfce6709a54a89288c14a9f6c3e7bbea8724869dbc065ec427"},"schema_version":"1.0"},"canonical_sha256":"70519d1485494a11e58b9721d393bcef00811616001d55c502b1da4315d46c1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:20.348462Z","signature_b64":"dvblGt/S8bk95OawXOUtTtzrSFYMlrx6vrvRbWZJcAc+3kJHZWVopWcyGLJ74PtTIyaDGgQq8902DYEgvA3RCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70519d1485494a11e58b9721d393bcef00811616001d55c502b1da4315d46c1a","last_reissued_at":"2026-05-18T03:41:20.348000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:20.348000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.0217","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:41:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LCRiZ/Iiecqs9Wns5v9/AAX1wtN6e9mKLi+3SwWMZSIPl9Nzr26K4sqzUe6JaBNA5FWCfQiTJmFiXqNxxYyHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:00:58.215344Z"},"content_sha256":"e6d1bb0f2d7d25a0bbecdde38226864d21d12d56a068a6cf4b236814f733b2e8","schema_version":"1.0","event_id":"sha256:e6d1bb0f2d7d25a0bbecdde38226864d21d12d56a068a6cf4b236814f733b2e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OBIZ2FEFJFFBDZMLS4Q5HE5454","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A geometric measure-type regularity criterion for solutions to the 3D Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Zoran Grujic","submitted_at":"2011-11-01T15:15:06Z","abstract_excerpt":"A local anisotropic geometric measure-type condition on the super-level sets of solutions to the 3D NSE preventing the formation of finite-time singularity is presented; essentially, local one-dimensional sparseness of the regions of intense fluid activity in a very weak sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0217","kind":"arxiv","version":5},"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":"2026-05-18T03:41:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQIhmNbc/99BtxGbwto3YHTcndWmB6v3+A+zLVR8ELBJiCkE7JlUimbiQaxFbs2itNfYiINFDP4nuk1AyMlNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:00:58.215706Z"},"content_sha256":"ab2c04e867b3f14f5a479144ecf6deebdb0fde48fd6aea073a4f60d0da3a1ded","schema_version":"1.0","event_id":"sha256:ab2c04e867b3f14f5a479144ecf6deebdb0fde48fd6aea073a4f60d0da3a1ded"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OBIZ2FEFJFFBDZMLS4Q5HE5454/bundle.json","state_url":"https://pith.science/pith/OBIZ2FEFJFFBDZMLS4Q5HE5454/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OBIZ2FEFJFFBDZMLS4Q5HE5454/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":"2026-06-04T19:00:58Z","links":{"resolver":"https://pith.science/pith/OBIZ2FEFJFFBDZMLS4Q5HE5454","bundle":"https://pith.science/pith/OBIZ2FEFJFFBDZMLS4Q5HE5454/bundle.json","state":"https://pith.science/pith/OBIZ2FEFJFFBDZMLS4Q5HE5454/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OBIZ2FEFJFFBDZMLS4Q5HE5454/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OBIZ2FEFJFFBDZMLS4Q5HE5454","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":"4be88503b5e21ebfce6709a54a89288c14a9f6c3e7bbea8724869dbc065ec427","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-01T15:15:06Z","title_canon_sha256":"be826aced54fbb6ca6307143def7f3db0534c2aebcb0ca058813415265db7f88"},"schema_version":"1.0","source":{"id":"1111.0217","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0217","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0217v5","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0217","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"OBIZ2FEFJFFB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OBIZ2FEFJFFBDZML","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OBIZ2FEF","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:ab2c04e867b3f14f5a479144ecf6deebdb0fde48fd6aea073a4f60d0da3a1ded","target":"graph","created_at":"2026-05-18T03:41:20Z","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":"A local anisotropic geometric measure-type condition on the super-level sets of solutions to the 3D NSE preventing the formation of finite-time singularity is presented; essentially, local one-dimensional sparseness of the regions of intense fluid activity in a very weak sense.","authors_text":"Zoran Grujic","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-01T15:15:06Z","title":"A geometric measure-type regularity criterion for solutions to the 3D Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0217","kind":"arxiv","version":5},"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:e6d1bb0f2d7d25a0bbecdde38226864d21d12d56a068a6cf4b236814f733b2e8","target":"record","created_at":"2026-05-18T03:41:20Z","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":"4be88503b5e21ebfce6709a54a89288c14a9f6c3e7bbea8724869dbc065ec427","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-01T15:15:06Z","title_canon_sha256":"be826aced54fbb6ca6307143def7f3db0534c2aebcb0ca058813415265db7f88"},"schema_version":"1.0","source":{"id":"1111.0217","kind":"arxiv","version":5}},"canonical_sha256":"70519d1485494a11e58b9721d393bcef00811616001d55c502b1da4315d46c1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70519d1485494a11e58b9721d393bcef00811616001d55c502b1da4315d46c1a","first_computed_at":"2026-05-18T03:41:20.348000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:20.348000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dvblGt/S8bk95OawXOUtTtzrSFYMlrx6vrvRbWZJcAc+3kJHZWVopWcyGLJ74PtTIyaDGgQq8902DYEgvA3RCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:20.348462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0217","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6d1bb0f2d7d25a0bbecdde38226864d21d12d56a068a6cf4b236814f733b2e8","sha256:ab2c04e867b3f14f5a479144ecf6deebdb0fde48fd6aea073a4f60d0da3a1ded"],"state_sha256":"acd809402b094ffe6461591dcdd58d10f5d789bdd5deb02beae15ceb9ae3d0aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K8SDBGLJiP0MO1cW3nkZF/gWNNZPcjgDFijIc9JR/FI6hm5CAlLZHE6y6yP7N7cwmTitWw+IBUQaSs4H3CVJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:00:58.217646Z","bundle_sha256":"7fa97dc2537eaf3e91c60159995545e02ffae7bd554c81cd8330241cefe9d301"}}