{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RTQDVLNXZFGMRWJAC325RBMPYQ","short_pith_number":"pith:RTQDVLNX","canonical_record":{"source":{"id":"1606.08481","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-27T20:47:14Z","cross_cats_sorted":[],"title_canon_sha256":"6b19cd57a3a5fe0fa77118aca4c12b95601b6d297ad866111f69a99f50faf5c7","abstract_canon_sha256":"778d9684f1c37f43a71fae57da8cff956387c351da01fe7d50c7c01c91873276"},"schema_version":"1.0"},"canonical_sha256":"8ce03aadb7c94cc8d92016f5d8858fc43422fb296df7517b75f629ea2b725ef3","source":{"kind":"arxiv","id":"1606.08481","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08481","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08481v2","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08481","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"pith_short_12","alias_value":"RTQDVLNXZFGM","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RTQDVLNXZFGMRWJA","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RTQDVLNX","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RTQDVLNXZFGMRWJAC325RBMPYQ","target":"record","payload":{"canonical_record":{"source":{"id":"1606.08481","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-27T20:47:14Z","cross_cats_sorted":[],"title_canon_sha256":"6b19cd57a3a5fe0fa77118aca4c12b95601b6d297ad866111f69a99f50faf5c7","abstract_canon_sha256":"778d9684f1c37f43a71fae57da8cff956387c351da01fe7d50c7c01c91873276"},"schema_version":"1.0"},"canonical_sha256":"8ce03aadb7c94cc8d92016f5d8858fc43422fb296df7517b75f629ea2b725ef3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:24.620145Z","signature_b64":"ORvpiO6zuvkYIrbSBvAGm+1tFtu45CKGKa1sSD2pqOo3HAJMCgfl6l0tQ2dKwN6x230LsERn70BbfAhbm8WzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ce03aadb7c94cc8d92016f5d8858fc43422fb296df7517b75f629ea2b725ef3","last_reissued_at":"2026-05-18T00:59:24.619519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:24.619519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.08481","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":"2026-05-18T00:59:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kmplA981B16Zghf5+oK5ksb65WGRHdeqgKeO98lFAlEoKv8pv0e9+aBtu6lyffLBQL3bwe6N4My0pS2wFaVjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:17:12.245911Z"},"content_sha256":"00280d8a3d0776a8f936fcb8b5b9ba72f701671f4fea0ac5ddc19190b089ad7b","schema_version":"1.0","event_id":"sha256:00280d8a3d0776a8f936fcb8b5b9ba72f701671f4fea0ac5ddc19190b089ad7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RTQDVLNXZFGMRWJAC325RBMPYQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Terence Tao","submitted_at":"2016-06-27T20:47:14Z","abstract_excerpt":"In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as \\begin{align*} \\partial_t \\omega + {\\mathcal L}_u \\omega &= 0\\\\ u &= \\delta \\tilde \\eta^{-1} \\Delta^{-1} \\omega \\end{align*} where $\\omega$ is the vorticity $2$-form, ${\\mathcal L}_u$ denotes the Lie derivative with respect to the velocity field $u$, $\\Delta$ is the Hodge Laplacian, $\\delta$ is the codifferential (the negative of the divergence operator), and $\\tilde \\eta^{-1}$ is the canonical map from $2$-forms to $2$-vector fields induced by the Euclidea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08481","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":"2026-05-18T00:59:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rYYSlfSVoUPRpJFIXjNgwKWakqtVTuXtb4VRAvzpsjp/BWGq0w4jJAb8KPH6qkFKS6vtlcIm788t0Y77Y/lGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:17:12.246269Z"},"content_sha256":"79596dac6f1d54e4436edab52c7e285bee4356d8012a43d6e468a963878f5dfe","schema_version":"1.0","event_id":"sha256:79596dac6f1d54e4436edab52c7e285bee4356d8012a43d6e468a963878f5dfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RTQDVLNXZFGMRWJAC325RBMPYQ/bundle.json","state_url":"https://pith.science/pith/RTQDVLNXZFGMRWJAC325RBMPYQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RTQDVLNXZFGMRWJAC325RBMPYQ/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":"2026-06-04T18:17:12Z","links":{"resolver":"https://pith.science/pith/RTQDVLNXZFGMRWJAC325RBMPYQ","bundle":"https://pith.science/pith/RTQDVLNXZFGMRWJAC325RBMPYQ/bundle.json","state":"https://pith.science/pith/RTQDVLNXZFGMRWJAC325RBMPYQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RTQDVLNXZFGMRWJAC325RBMPYQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RTQDVLNXZFGMRWJAC325RBMPYQ","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":"778d9684f1c37f43a71fae57da8cff956387c351da01fe7d50c7c01c91873276","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-27T20:47:14Z","title_canon_sha256":"6b19cd57a3a5fe0fa77118aca4c12b95601b6d297ad866111f69a99f50faf5c7"},"schema_version":"1.0","source":{"id":"1606.08481","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08481","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08481v2","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08481","created_at":"2026-05-18T00:59:24Z"},{"alias_kind":"pith_short_12","alias_value":"RTQDVLNXZFGM","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RTQDVLNXZFGMRWJA","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RTQDVLNX","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:79596dac6f1d54e4436edab52c7e285bee4356d8012a43d6e468a963878f5dfe","target":"graph","created_at":"2026-05-18T00:59:24Z","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 the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as \\begin{align*} \\partial_t \\omega + {\\mathcal L}_u \\omega &= 0\\\\ u &= \\delta \\tilde \\eta^{-1} \\Delta^{-1} \\omega \\end{align*} where $\\omega$ is the vorticity $2$-form, ${\\mathcal L}_u$ denotes the Lie derivative with respect to the velocity field $u$, $\\Delta$ is the Hodge Laplacian, $\\delta$ is the codifferential (the negative of the divergence operator), and $\\tilde \\eta^{-1}$ is the canonical map from $2$-forms to $2$-vector fields induced by the Euclidea","authors_text":"Terence Tao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-27T20:47:14Z","title":"Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08481","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":"sha256:00280d8a3d0776a8f936fcb8b5b9ba72f701671f4fea0ac5ddc19190b089ad7b","target":"record","created_at":"2026-05-18T00:59:24Z","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":"778d9684f1c37f43a71fae57da8cff956387c351da01fe7d50c7c01c91873276","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-27T20:47:14Z","title_canon_sha256":"6b19cd57a3a5fe0fa77118aca4c12b95601b6d297ad866111f69a99f50faf5c7"},"schema_version":"1.0","source":{"id":"1606.08481","kind":"arxiv","version":2}},"canonical_sha256":"8ce03aadb7c94cc8d92016f5d8858fc43422fb296df7517b75f629ea2b725ef3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ce03aadb7c94cc8d92016f5d8858fc43422fb296df7517b75f629ea2b725ef3","first_computed_at":"2026-05-18T00:59:24.619519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:24.619519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ORvpiO6zuvkYIrbSBvAGm+1tFtu45CKGKa1sSD2pqOo3HAJMCgfl6l0tQ2dKwN6x230LsERn70BbfAhbm8WzAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:24.620145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08481","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00280d8a3d0776a8f936fcb8b5b9ba72f701671f4fea0ac5ddc19190b089ad7b","sha256:79596dac6f1d54e4436edab52c7e285bee4356d8012a43d6e468a963878f5dfe"],"state_sha256":"6463526069e8dcc730ebf6b4062cfeefc23ad1e937dbb2adffedd3fed5d56e76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47nrUk/Luytp1Gt3x+VXDBllnwKhKtHYkFmstNEhw8JnyCnT0WOGtWtkcHihLX3dXs5ojnX9+xbyOGhlDeQiCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:17:12.248464Z","bundle_sha256":"071950a3ded18199370f512bd1abbf65e38db096f7ba875d6214c94390911b97"}}