{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:U6ZIXPP4N224VMB37VU6KT6MIX","short_pith_number":"pith:U6ZIXPP4","canonical_record":{"source":{"id":"1007.2587","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2010-07-15T15:26:13Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"01bbd01c6428946b37230f960f1f7728d6fd8457a5de447ac54b4554a9dff961","abstract_canon_sha256":"576b4e3c9a69deb889f38efb37307e2212ed31da4fe0e29702bdae6d8e7a340a"},"schema_version":"1.0"},"canonical_sha256":"a7b28bbdfc6eb5cab03bfd69e54fcc45fec01f6c7ed059dfbc0222b1b8634357","source":{"kind":"arxiv","id":"1007.2587","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2587","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2587v3","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2587","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"U6ZIXPP4N224","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"U6ZIXPP4N224VMB3","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"U6ZIXPP4","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:U6ZIXPP4N224VMB37VU6KT6MIX","target":"record","payload":{"canonical_record":{"source":{"id":"1007.2587","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2010-07-15T15:26:13Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"01bbd01c6428946b37230f960f1f7728d6fd8457a5de447ac54b4554a9dff961","abstract_canon_sha256":"576b4e3c9a69deb889f38efb37307e2212ed31da4fe0e29702bdae6d8e7a340a"},"schema_version":"1.0"},"canonical_sha256":"a7b28bbdfc6eb5cab03bfd69e54fcc45fec01f6c7ed059dfbc0222b1b8634357","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:45.042769Z","signature_b64":"dAsNh5+f17158LNoRxYgte53En5ZkGkUZzjz5UpsiMEcasKkh1rfmoxf7IulLKH85P4RkyXL9ArIzFj+SwsJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7b28bbdfc6eb5cab03bfd69e54fcc45fec01f6c7ed059dfbc0222b1b8634357","last_reissued_at":"2026-05-18T04:18:45.042038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:45.042038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.2587","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U4b5TyTtbAJHb7SV2iIF3qmacN42U3BgR24O0X+3LB5r7lcF2CbfnaUUKnX9+LsiyGPFxF3ZEavWC+ojN5QDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T11:37:16.230035Z"},"content_sha256":"9101dfe500c8ca16b6df0a2b4f81ae38e18c3bf1435590be3dc5f5eb8e28d8ac","schema_version":"1.0","event_id":"sha256:9101dfe500c8ca16b6df0a2b4f81ae38e18c3bf1435590be3dc5f5eb8e28d8ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:U6ZIXPP4N224VMB37VU6KT6MIX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"3D Euler equations and ideal MHD mapped to regular systems: probing the finite-time blowup hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"physics.flu-dyn","authors_text":"Miguel D. Bustamante","submitted_at":"2010-07-15T15:26:13Z","abstract_excerpt":"We prove by an explicit construction that solutions to incompressible 3D Euler equations defined in the periodic cube can be mapped bijectively to a new system of equations whose solutions are globally regular. We establish that the usual Beale-Kato-Majda criterion for finite-time singularity (or blowup) of a solution to the 3D Euler system is equivalent to a condition on the corresponding \\emph{regular} solution of the new system. In the hypothetical case of Euler finite-time singularity, we provide an explicit formula for the blowup time in terms of the regular solution of the new system. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2587","kind":"arxiv","version":3},"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":"2026-05-18T04:18:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qZApaXAbQzj5tL32OI0C8Bk48TRpNEIyfLBlwR8zDnfUJbwCY5HccsDyNbrTMVbc+CcxvNEF0NXrWxohxetODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T11:37:16.230392Z"},"content_sha256":"c52861d2d0f3c079bccae5c6b581465a97d5585876a51d9313b35dab61d45107","schema_version":"1.0","event_id":"sha256:c52861d2d0f3c079bccae5c6b581465a97d5585876a51d9313b35dab61d45107"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U6ZIXPP4N224VMB37VU6KT6MIX/bundle.json","state_url":"https://pith.science/pith/U6ZIXPP4N224VMB37VU6KT6MIX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U6ZIXPP4N224VMB37VU6KT6MIX/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":"2026-05-19T11:37:16Z","links":{"resolver":"https://pith.science/pith/U6ZIXPP4N224VMB37VU6KT6MIX","bundle":"https://pith.science/pith/U6ZIXPP4N224VMB37VU6KT6MIX/bundle.json","state":"https://pith.science/pith/U6ZIXPP4N224VMB37VU6KT6MIX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U6ZIXPP4N224VMB37VU6KT6MIX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:U6ZIXPP4N224VMB37VU6KT6MIX","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":"576b4e3c9a69deb889f38efb37307e2212ed31da4fe0e29702bdae6d8e7a340a","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2010-07-15T15:26:13Z","title_canon_sha256":"01bbd01c6428946b37230f960f1f7728d6fd8457a5de447ac54b4554a9dff961"},"schema_version":"1.0","source":{"id":"1007.2587","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2587","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2587v3","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2587","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"U6ZIXPP4N224","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"U6ZIXPP4N224VMB3","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"U6ZIXPP4","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:c52861d2d0f3c079bccae5c6b581465a97d5585876a51d9313b35dab61d45107","target":"graph","created_at":"2026-05-18T04:18:45Z","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":"We prove by an explicit construction that solutions to incompressible 3D Euler equations defined in the periodic cube can be mapped bijectively to a new system of equations whose solutions are globally regular. We establish that the usual Beale-Kato-Majda criterion for finite-time singularity (or blowup) of a solution to the 3D Euler system is equivalent to a condition on the corresponding \\emph{regular} solution of the new system. In the hypothetical case of Euler finite-time singularity, we provide an explicit formula for the blowup time in terms of the regular solution of the new system. Th","authors_text":"Miguel D. Bustamante","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2010-07-15T15:26:13Z","title":"3D Euler equations and ideal MHD mapped to regular systems: probing the finite-time blowup hypothesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2587","kind":"arxiv","version":3},"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":"sha256:9101dfe500c8ca16b6df0a2b4f81ae38e18c3bf1435590be3dc5f5eb8e28d8ac","target":"record","created_at":"2026-05-18T04:18:45Z","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":"576b4e3c9a69deb889f38efb37307e2212ed31da4fe0e29702bdae6d8e7a340a","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2010-07-15T15:26:13Z","title_canon_sha256":"01bbd01c6428946b37230f960f1f7728d6fd8457a5de447ac54b4554a9dff961"},"schema_version":"1.0","source":{"id":"1007.2587","kind":"arxiv","version":3}},"canonical_sha256":"a7b28bbdfc6eb5cab03bfd69e54fcc45fec01f6c7ed059dfbc0222b1b8634357","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7b28bbdfc6eb5cab03bfd69e54fcc45fec01f6c7ed059dfbc0222b1b8634357","first_computed_at":"2026-05-18T04:18:45.042038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:45.042038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dAsNh5+f17158LNoRxYgte53En5ZkGkUZzjz5UpsiMEcasKkh1rfmoxf7IulLKH85P4RkyXL9ArIzFj+SwsJAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:45.042769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.2587","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9101dfe500c8ca16b6df0a2b4f81ae38e18c3bf1435590be3dc5f5eb8e28d8ac","sha256:c52861d2d0f3c079bccae5c6b581465a97d5585876a51d9313b35dab61d45107"],"state_sha256":"d8206056e3f4fba3811eea7e32287bdda6a34375a4c28f6296095ce353d4f515"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pbqUQfUfDd8OvQGWk9WI0RnwWQ9crEIM6XIq/mHhkwcMsQpX1LmDY71yGRbyGKeRcYRSJ7DGPhIZwtQU2MILCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T11:37:16.231963Z","bundle_sha256":"9acc6a780f77ff772e1aa9577adc78906fb1dbc430c9c95144ed211774570c36"}}