{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:JFKPX2VOXM3SLIAUTC3XNO7B56","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":"611c55392baf633cd8a915ca05724ebd58610cbe0d8e3a2aa685c112d015d076","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-09-15T17:50:33Z","title_canon_sha256":"a214f940a96bfbdd2f4438da33e7a1d16baf422e2d24ca45e4e75a124fe63421"},"schema_version":"1.0","source":{"id":"2009.07259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.07259","created_at":"2026-07-05T08:19:06Z"},{"alias_kind":"arxiv_version","alias_value":"2009.07259v1","created_at":"2026-07-05T08:19:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07259","created_at":"2026-07-05T08:19:06Z"},{"alias_kind":"pith_short_12","alias_value":"JFKPX2VOXM3S","created_at":"2026-07-05T08:19:06Z"},{"alias_kind":"pith_short_16","alias_value":"JFKPX2VOXM3SLIAU","created_at":"2026-07-05T08:19:06Z"},{"alias_kind":"pith_short_8","alias_value":"JFKPX2VO","created_at":"2026-07-05T08:19:06Z"}],"graph_snapshots":[{"event_id":"sha256:ac5e69bf2c91e589aa639d9d87a125eca8d5bd2e6978529b3c6030e705ff1cd5","target":"graph","created_at":"2026-07-05T08:19:06Z","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/2009.07259/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we use frequency decomposition techniques to give a direct proof of global existence and regularity for the Navier-Stokes equations on two-dimensional Riemannian manifolds without boundary. Our techniques are inspired by an approach of Mattingly and Sinai [15] which was developed in the context of periodic boundary conditions on a flat background, and which is based on a maximum principle for Fourier coefficients.\n  The extension to general manifolds requires several new ideas, connected to the less favorable spectral localization properties in our setting. Our arguments make us","authors_text":"Aynur Bulut, Khang Manh Huynh","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-09-15T17:50:33Z","title":"A geometric trapping approach to global regularity for 2D Navier-Stokes on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07259","kind":"arxiv","version":1},"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:ec52fa4041ec84606e39e8433cfaa5d6e9d09e4a9e8b751a4973c96ff0812064","target":"record","created_at":"2026-07-05T08:19:06Z","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":"611c55392baf633cd8a915ca05724ebd58610cbe0d8e3a2aa685c112d015d076","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-09-15T17:50:33Z","title_canon_sha256":"a214f940a96bfbdd2f4438da33e7a1d16baf422e2d24ca45e4e75a124fe63421"},"schema_version":"1.0","source":{"id":"2009.07259","kind":"arxiv","version":1}},"canonical_sha256":"4954fbeaaebb3725a01498b776bbe1ef9823b3146cb1637735c3a037d5c1d769","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4954fbeaaebb3725a01498b776bbe1ef9823b3146cb1637735c3a037d5c1d769","first_computed_at":"2026-07-05T08:19:06.328698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:19:06.328698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tGggCfU3ru53qAPcqY+tVMIHJom+mhNjCRGi1luYqc8OpMXMM597TxcvyNf/JHQZlS4NbZM03jxne9DT690IDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:19:06.329238Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.07259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec52fa4041ec84606e39e8433cfaa5d6e9d09e4a9e8b751a4973c96ff0812064","sha256:ac5e69bf2c91e589aa639d9d87a125eca8d5bd2e6978529b3c6030e705ff1cd5"],"state_sha256":"e181a6d8f93d15947e4722d7149f25b9cfbd9170a03bb02ca6374242d6f873cb"}