{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:L4LKFMGEUY3HBBOLOWZUVX7CBB","short_pith_number":"pith:L4LKFMGE","canonical_record":{"source":{"id":"1811.09816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-24T11:43:19Z","cross_cats_sorted":[],"title_canon_sha256":"bdad017148dedbf6b1e71e7abc4bc979f76fb4292a2621626b4979ee8676c1fe","abstract_canon_sha256":"0eb09734f2467382b5bd7d6c836019d6c02a4f43173bbb9dd395e17743841f67"},"schema_version":"1.0"},"canonical_sha256":"5f16a2b0c4a6367085cb75b34adfe208626c2f2526c6a258f44fa1e1d98fb801","source":{"kind":"arxiv","id":"1811.09816","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09816","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09816v1","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09816","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"pith_short_12","alias_value":"L4LKFMGEUY3H","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L4LKFMGEUY3HBBOL","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L4LKFMGE","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:L4LKFMGEUY3HBBOLOWZUVX7CBB","target":"record","payload":{"canonical_record":{"source":{"id":"1811.09816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-24T11:43:19Z","cross_cats_sorted":[],"title_canon_sha256":"bdad017148dedbf6b1e71e7abc4bc979f76fb4292a2621626b4979ee8676c1fe","abstract_canon_sha256":"0eb09734f2467382b5bd7d6c836019d6c02a4f43173bbb9dd395e17743841f67"},"schema_version":"1.0"},"canonical_sha256":"5f16a2b0c4a6367085cb75b34adfe208626c2f2526c6a258f44fa1e1d98fb801","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:01.139433Z","signature_b64":"BJ9wht3xql1kLeG/7WpneoKBw9VadJkzmnvoxhZHX0otdITJdeUkIlpTcx1U8e5WzwxKDrF0Kou7+tprSurlDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f16a2b0c4a6367085cb75b34adfe208626c2f2526c6a258f44fa1e1d98fb801","last_reissued_at":"2026-05-18T00:00:01.138880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:01.138880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.09816","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cuQtkPTOCDAkbz8jxH3LEB3iY0cd1GSiimHB8QS7kkmU3D1zAUzNZ+lqOajCsFyw853pALL2Qx7fgyfI1YAVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:01:52.821982Z"},"content_sha256":"85c17ac193a7c0ea4167929d0281e01eba73e276256d2bb66e2b7d97f6a95d72","schema_version":"1.0","event_id":"sha256:85c17ac193a7c0ea4167929d0281e01eba73e276256d2bb66e2b7d97f6a95d72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:L4LKFMGEUY3HBBOLOWZUVX7CBB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Navier--Stokes equations in a curved thin domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tatsu-Hiko Miura","submitted_at":"2018-11-24T11:43:19Z","abstract_excerpt":"We consider the three-dimensional incompressible Navier--Stokes equations in a curved thin domain with Navier's slip boundary conditions. The curved thin domain is defined as a region between two closed surfaces which are very close to each other and degenerates into a given closed surface as its width tends to zero. We establish the global-in-time existence and uniform estimates of a strong solution for large data when the width of the thin domain is very small. Moreover, we study a singular limit problem as the thickness of the thin domain tends to zero and rigorously derive limit equations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09816","kind":"arxiv","version":1},"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":"2026-05-18T00:00:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7QGBJ7Q3HwpBz11T2YcOc3odjucfn9UjUuTmqACDovJLlYaMo1BzRdJAau65scwTZpWnleYP/+PF3aFePsszDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:01:52.822343Z"},"content_sha256":"c030890b151d31857773282d61ca15e357b15b447508aaac0a5c7d323817f4c2","schema_version":"1.0","event_id":"sha256:c030890b151d31857773282d61ca15e357b15b447508aaac0a5c7d323817f4c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L4LKFMGEUY3HBBOLOWZUVX7CBB/bundle.json","state_url":"https://pith.science/pith/L4LKFMGEUY3HBBOLOWZUVX7CBB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L4LKFMGEUY3HBBOLOWZUVX7CBB/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":"2026-07-02T21:01:52Z","links":{"resolver":"https://pith.science/pith/L4LKFMGEUY3HBBOLOWZUVX7CBB","bundle":"https://pith.science/pith/L4LKFMGEUY3HBBOLOWZUVX7CBB/bundle.json","state":"https://pith.science/pith/L4LKFMGEUY3HBBOLOWZUVX7CBB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L4LKFMGEUY3HBBOLOWZUVX7CBB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L4LKFMGEUY3HBBOLOWZUVX7CBB","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":"0eb09734f2467382b5bd7d6c836019d6c02a4f43173bbb9dd395e17743841f67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-24T11:43:19Z","title_canon_sha256":"bdad017148dedbf6b1e71e7abc4bc979f76fb4292a2621626b4979ee8676c1fe"},"schema_version":"1.0","source":{"id":"1811.09816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09816","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09816v1","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09816","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"pith_short_12","alias_value":"L4LKFMGEUY3H","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L4LKFMGEUY3HBBOL","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L4LKFMGE","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:c030890b151d31857773282d61ca15e357b15b447508aaac0a5c7d323817f4c2","target":"graph","created_at":"2026-05-18T00:00:01Z","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 consider the three-dimensional incompressible Navier--Stokes equations in a curved thin domain with Navier's slip boundary conditions. The curved thin domain is defined as a region between two closed surfaces which are very close to each other and degenerates into a given closed surface as its width tends to zero. We establish the global-in-time existence and uniform estimates of a strong solution for large data when the width of the thin domain is very small. Moreover, we study a singular limit problem as the thickness of the thin domain tends to zero and rigorously derive limit equations ","authors_text":"Tatsu-Hiko Miura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-24T11:43:19Z","title":"Navier--Stokes equations in a curved thin domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09816","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":"sha256:85c17ac193a7c0ea4167929d0281e01eba73e276256d2bb66e2b7d97f6a95d72","target":"record","created_at":"2026-05-18T00:00:01Z","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":"0eb09734f2467382b5bd7d6c836019d6c02a4f43173bbb9dd395e17743841f67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-24T11:43:19Z","title_canon_sha256":"bdad017148dedbf6b1e71e7abc4bc979f76fb4292a2621626b4979ee8676c1fe"},"schema_version":"1.0","source":{"id":"1811.09816","kind":"arxiv","version":1}},"canonical_sha256":"5f16a2b0c4a6367085cb75b34adfe208626c2f2526c6a258f44fa1e1d98fb801","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f16a2b0c4a6367085cb75b34adfe208626c2f2526c6a258f44fa1e1d98fb801","first_computed_at":"2026-05-18T00:00:01.138880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:01.138880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BJ9wht3xql1kLeG/7WpneoKBw9VadJkzmnvoxhZHX0otdITJdeUkIlpTcx1U8e5WzwxKDrF0Kou7+tprSurlDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:01.139433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85c17ac193a7c0ea4167929d0281e01eba73e276256d2bb66e2b7d97f6a95d72","sha256:c030890b151d31857773282d61ca15e357b15b447508aaac0a5c7d323817f4c2"],"state_sha256":"6c9f2a187583fe2b8c824b8e13267e523e3d860d834f174ec5884916029718ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PBUw76GfYgS/awF3YUbN6NGgquwREOH7WMws63/PZtwMcqjRtRFOK12ui1o/evUF8aiDf28VIvp9FdhrH3hLDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T21:01:52.824264Z","bundle_sha256":"36b07db85fd13ba06e41c64795739b02a25086366abd17a1ddced4189909141b"}}