{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CKJOLGOSVMP2G4QRRTVHUQIQOA","short_pith_number":"pith:CKJOLGOS","canonical_record":{"source":{"id":"1410.3415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-13T18:05:09Z","cross_cats_sorted":[],"title_canon_sha256":"d305ab6199d448b8ff43aac851de96becf55ea13cdcb44443b29074e0199622e","abstract_canon_sha256":"877b0c3d3b92c676827659cfe23afe82f73a3b883094207d8e9cd0db9c3b6795"},"schema_version":"1.0"},"canonical_sha256":"1292e599d2ab1fa372118cea7a411070293939372d9eb3a8a5a9eb3278f10f3e","source":{"kind":"arxiv","id":"1410.3415","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3415","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3415v1","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3415","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"CKJOLGOSVMP2","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CKJOLGOSVMP2G4QR","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CKJOLGOS","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CKJOLGOSVMP2G4QRRTVHUQIQOA","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-13T18:05:09Z","cross_cats_sorted":[],"title_canon_sha256":"d305ab6199d448b8ff43aac851de96becf55ea13cdcb44443b29074e0199622e","abstract_canon_sha256":"877b0c3d3b92c676827659cfe23afe82f73a3b883094207d8e9cd0db9c3b6795"},"schema_version":"1.0"},"canonical_sha256":"1292e599d2ab1fa372118cea7a411070293939372d9eb3a8a5a9eb3278f10f3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:11.390885Z","signature_b64":"YOOWriUGo1cHnfLpZqZRx3LQYHHcF4w2ucSPcowtNHawg3/fEvGbbKSBaCt34E0fdG2FZzkz50ELLKd7PndFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1292e599d2ab1fa372118cea7a411070293939372d9eb3a8a5a9eb3278f10f3e","last_reissued_at":"2026-05-18T02:40:11.390295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:11.390295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3415","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":"2026-05-18T02:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6gkb3jf7McKzh7A+WbeslFG4/W4VYAmj/ig2Btv/Cfu/wRIkWNbhbcgsQJmvleH8nlX4wNe4QeRXFLBhQAwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:21:40.760624Z"},"content_sha256":"5ee02bd930ab1132ce86c73040cd8f3855bf5fc86d0869cac4ac12e345e76822","schema_version":"1.0","event_id":"sha256:5ee02bd930ab1132ce86c73040cd8f3855bf5fc86d0869cac4ac12e345e76822"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CKJOLGOSVMP2G4QRRTVHUQIQOA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Timestepping schemes for the 3d Navier-Stokes equations: small solutions and short times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Djoko Wirosoetisno, Youngjoon Hong","submitted_at":"2014-10-13T18:05:09Z","abstract_excerpt":"It is well known that the solution of the 3d Navier--Stokes equations remains bounded if the initial data and the forcing are sufficiently small relative to the viscosity, and for a finite time given any bounded initial data. In this article, we consider two temporal discretisations (semi-implicit and fully implicit) of the 3d Navier--Stokes equations in a periodic domain and prove that their solutions remain bounded in $H^1$ subject to essentially the same smallness conditions (on initial data, forcing or time) as the continuous system and to suitable timestep restrictions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3415","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":"2026-05-18T02:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iPhaHA8W/ZacCkrMD7bYbsg1qF8gZ9Z+nkI6xDWUSSJtjwonnLmzLTauHQHNqOTj1jOqGMcbfmvIFT2UNjJWBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:21:40.761021Z"},"content_sha256":"b303070b7f07956422476c5a92662faaa48cbf8216379bdcb800e89df1bc7fb1","schema_version":"1.0","event_id":"sha256:b303070b7f07956422476c5a92662faaa48cbf8216379bdcb800e89df1bc7fb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKJOLGOSVMP2G4QRRTVHUQIQOA/bundle.json","state_url":"https://pith.science/pith/CKJOLGOSVMP2G4QRRTVHUQIQOA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKJOLGOSVMP2G4QRRTVHUQIQOA/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":"2026-06-01T08:21:40Z","links":{"resolver":"https://pith.science/pith/CKJOLGOSVMP2G4QRRTVHUQIQOA","bundle":"https://pith.science/pith/CKJOLGOSVMP2G4QRRTVHUQIQOA/bundle.json","state":"https://pith.science/pith/CKJOLGOSVMP2G4QRRTVHUQIQOA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKJOLGOSVMP2G4QRRTVHUQIQOA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CKJOLGOSVMP2G4QRRTVHUQIQOA","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":"877b0c3d3b92c676827659cfe23afe82f73a3b883094207d8e9cd0db9c3b6795","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-13T18:05:09Z","title_canon_sha256":"d305ab6199d448b8ff43aac851de96becf55ea13cdcb44443b29074e0199622e"},"schema_version":"1.0","source":{"id":"1410.3415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3415","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3415v1","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3415","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"CKJOLGOSVMP2","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CKJOLGOSVMP2G4QR","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CKJOLGOS","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:b303070b7f07956422476c5a92662faaa48cbf8216379bdcb800e89df1bc7fb1","target":"graph","created_at":"2026-05-18T02:40:11Z","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":"It is well known that the solution of the 3d Navier--Stokes equations remains bounded if the initial data and the forcing are sufficiently small relative to the viscosity, and for a finite time given any bounded initial data. In this article, we consider two temporal discretisations (semi-implicit and fully implicit) of the 3d Navier--Stokes equations in a periodic domain and prove that their solutions remain bounded in $H^1$ subject to essentially the same smallness conditions (on initial data, forcing or time) as the continuous system and to suitable timestep restrictions.","authors_text":"Djoko Wirosoetisno, Youngjoon Hong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-13T18:05:09Z","title":"Timestepping schemes for the 3d Navier-Stokes equations: small solutions and short times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3415","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":"sha256:5ee02bd930ab1132ce86c73040cd8f3855bf5fc86d0869cac4ac12e345e76822","target":"record","created_at":"2026-05-18T02:40:11Z","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":"877b0c3d3b92c676827659cfe23afe82f73a3b883094207d8e9cd0db9c3b6795","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-13T18:05:09Z","title_canon_sha256":"d305ab6199d448b8ff43aac851de96becf55ea13cdcb44443b29074e0199622e"},"schema_version":"1.0","source":{"id":"1410.3415","kind":"arxiv","version":1}},"canonical_sha256":"1292e599d2ab1fa372118cea7a411070293939372d9eb3a8a5a9eb3278f10f3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1292e599d2ab1fa372118cea7a411070293939372d9eb3a8a5a9eb3278f10f3e","first_computed_at":"2026-05-18T02:40:11.390295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:11.390295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YOOWriUGo1cHnfLpZqZRx3LQYHHcF4w2ucSPcowtNHawg3/fEvGbbKSBaCt34E0fdG2FZzkz50ELLKd7PndFBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:11.390885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ee02bd930ab1132ce86c73040cd8f3855bf5fc86d0869cac4ac12e345e76822","sha256:b303070b7f07956422476c5a92662faaa48cbf8216379bdcb800e89df1bc7fb1"],"state_sha256":"9cc0f1582122876a6c48fc3ca8e0c4850c36ff2fdd7d3f1bdc3fb8dfc06e6501"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iz/fsXIXbkBBtMkGr9FweyZ5a3DOVVzbrK+JWYKHNrHFKf3yHXEkS8lvJP1cErxKpTu6+BN5vnFVzZ9jSQDMDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:21:40.763291Z","bundle_sha256":"6302257005e8b2746e560e541382a2d6792f5d59b9d8eb3aa00b1622ba7ac182"}}