{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:B6FSU7MGL4CKVIYKTFGDXUIXRE","short_pith_number":"pith:B6FSU7MG","canonical_record":{"source":{"id":"2101.00375","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-01-02T05:26:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bdf32b23cf6d6dafc287c55fefc7fdf4941648dedf68e7b970364ce868d1b7e9","abstract_canon_sha256":"f2475a263acb96e2efb4d7fc873b6a3167980c58fd1e4cbc12f6b53fab0069fd"},"schema_version":"1.0"},"canonical_sha256":"0f8b2a7d865f04aaa30a994c3bd117892fa7bff772e850d59491a409bf0e575d","source":{"kind":"arxiv","id":"2101.00375","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.00375","created_at":"2026-07-05T02:10:28Z"},{"alias_kind":"arxiv_version","alias_value":"2101.00375v2","created_at":"2026-07-05T02:10:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.00375","created_at":"2026-07-05T02:10:28Z"},{"alias_kind":"pith_short_12","alias_value":"B6FSU7MGL4CK","created_at":"2026-07-05T02:10:28Z"},{"alias_kind":"pith_short_16","alias_value":"B6FSU7MGL4CKVIYK","created_at":"2026-07-05T02:10:28Z"},{"alias_kind":"pith_short_8","alias_value":"B6FSU7MG","created_at":"2026-07-05T02:10:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:B6FSU7MGL4CKVIYKTFGDXUIXRE","target":"record","payload":{"canonical_record":{"source":{"id":"2101.00375","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-01-02T05:26:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bdf32b23cf6d6dafc287c55fefc7fdf4941648dedf68e7b970364ce868d1b7e9","abstract_canon_sha256":"f2475a263acb96e2efb4d7fc873b6a3167980c58fd1e4cbc12f6b53fab0069fd"},"schema_version":"1.0"},"canonical_sha256":"0f8b2a7d865f04aaa30a994c3bd117892fa7bff772e850d59491a409bf0e575d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:10:28.191983Z","signature_b64":"28F0SyRZdaQ6uiXxBhKR7EWqzsjyjuffEVf1fM+NrAhkjFaqHdRJy3Clx4XDHs1cUAbkh8pjSs4tYqREFGeaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f8b2a7d865f04aaa30a994c3bd117892fa7bff772e850d59491a409bf0e575d","last_reissued_at":"2026-07-05T02:10:28.191621Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:10:28.191621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2101.00375","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":"2026-07-05T02:10:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jr6p79KVeBmARFnl07ePDl8JAyTQQ/tiPP790tiKpHWnVJMifnWaUchMfVxQXihHqigzXWAsibK4T1SYeLeeBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T23:56:13.160733Z"},"content_sha256":"cd8fab4647100b8fdd6a3d5be1f972fdb3c7319f33f6782f6be5ee992b890abe","schema_version":"1.0","event_id":"sha256:cd8fab4647100b8fdd6a3d5be1f972fdb3c7319f33f6782f6be5ee992b890abe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:B6FSU7MGL4CKVIYKTFGDXUIXRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The vortex dynamics in incompressible viscous turbulent flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Jiawei Li, Zhongmin Qian","submitted_at":"2021-01-02T05:26:12Z","abstract_excerpt":"In this paper, we consider turbulence from a geometric perspective based on the vorticity equations for incompressible viscous fluid flows. We derive several quantitative statements about the statistics of turbulent flows. In particular we establish an entropy decay inequality which involves the turbulent kinetic energy and $L^{1}$-enstrophy, and we identify the small time scale of the vorticity broken down and the vorticity creation under the universality assumption of small time scales of turbulence flows."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.00375","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.00375/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:10:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XAZX6HkaqGxs7N465xrAZuD7h56ZY+9g+FVFpXyDNmpn487Q/Ho+cQz7k787e5GTCZYNO8eNxtG537FMwu7dBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T23:56:13.161106Z"},"content_sha256":"1645169368ba48bfb80a975215ff60f29e1e02ca1f53ea946728c4583d982446","schema_version":"1.0","event_id":"sha256:1645169368ba48bfb80a975215ff60f29e1e02ca1f53ea946728c4583d982446"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6FSU7MGL4CKVIYKTFGDXUIXRE/bundle.json","state_url":"https://pith.science/pith/B6FSU7MGL4CKVIYKTFGDXUIXRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6FSU7MGL4CKVIYKTFGDXUIXRE/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":"2026-07-08T23:56:13Z","links":{"resolver":"https://pith.science/pith/B6FSU7MGL4CKVIYKTFGDXUIXRE","bundle":"https://pith.science/pith/B6FSU7MGL4CKVIYKTFGDXUIXRE/bundle.json","state":"https://pith.science/pith/B6FSU7MGL4CKVIYKTFGDXUIXRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6FSU7MGL4CKVIYKTFGDXUIXRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:B6FSU7MGL4CKVIYKTFGDXUIXRE","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":"f2475a263acb96e2efb4d7fc873b6a3167980c58fd1e4cbc12f6b53fab0069fd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-01-02T05:26:12Z","title_canon_sha256":"bdf32b23cf6d6dafc287c55fefc7fdf4941648dedf68e7b970364ce868d1b7e9"},"schema_version":"1.0","source":{"id":"2101.00375","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.00375","created_at":"2026-07-05T02:10:28Z"},{"alias_kind":"arxiv_version","alias_value":"2101.00375v2","created_at":"2026-07-05T02:10:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.00375","created_at":"2026-07-05T02:10:28Z"},{"alias_kind":"pith_short_12","alias_value":"B6FSU7MGL4CK","created_at":"2026-07-05T02:10:28Z"},{"alias_kind":"pith_short_16","alias_value":"B6FSU7MGL4CKVIYK","created_at":"2026-07-05T02:10:28Z"},{"alias_kind":"pith_short_8","alias_value":"B6FSU7MG","created_at":"2026-07-05T02:10:28Z"}],"graph_snapshots":[{"event_id":"sha256:1645169368ba48bfb80a975215ff60f29e1e02ca1f53ea946728c4583d982446","target":"graph","created_at":"2026-07-05T02:10:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2101.00375/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider turbulence from a geometric perspective based on the vorticity equations for incompressible viscous fluid flows. We derive several quantitative statements about the statistics of turbulent flows. In particular we establish an entropy decay inequality which involves the turbulent kinetic energy and $L^{1}$-enstrophy, and we identify the small time scale of the vorticity broken down and the vorticity creation under the universality assumption of small time scales of turbulence flows.","authors_text":"Jiawei Li, Zhongmin Qian","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-01-02T05:26:12Z","title":"The vortex dynamics in incompressible viscous turbulent flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.00375","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:cd8fab4647100b8fdd6a3d5be1f972fdb3c7319f33f6782f6be5ee992b890abe","target":"record","created_at":"2026-07-05T02:10:28Z","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":"f2475a263acb96e2efb4d7fc873b6a3167980c58fd1e4cbc12f6b53fab0069fd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-01-02T05:26:12Z","title_canon_sha256":"bdf32b23cf6d6dafc287c55fefc7fdf4941648dedf68e7b970364ce868d1b7e9"},"schema_version":"1.0","source":{"id":"2101.00375","kind":"arxiv","version":2}},"canonical_sha256":"0f8b2a7d865f04aaa30a994c3bd117892fa7bff772e850d59491a409bf0e575d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f8b2a7d865f04aaa30a994c3bd117892fa7bff772e850d59491a409bf0e575d","first_computed_at":"2026-07-05T02:10:28.191621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:10:28.191621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"28F0SyRZdaQ6uiXxBhKR7EWqzsjyjuffEVf1fM+NrAhkjFaqHdRJy3Clx4XDHs1cUAbkh8pjSs4tYqREFGeaDg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:10:28.191983Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.00375","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd8fab4647100b8fdd6a3d5be1f972fdb3c7319f33f6782f6be5ee992b890abe","sha256:1645169368ba48bfb80a975215ff60f29e1e02ca1f53ea946728c4583d982446"],"state_sha256":"3f78b6aceb6a2f84c5472463e2e6aaba7e06b12104c97aa25d9df435be81dea9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AaRzKlUVk5QWtADV8jpdF5kvi70lCjJnOClaQKsfMVcls6R74NSHKsTh5UHQWrpbjjNV0ZDEyzabiVzuTYNMBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T23:56:13.163275Z","bundle_sha256":"201124a960996e9e9fde88454af6257bbf83b62c0549849c6f2bfd92b44d5772"}}