{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EHAWRFBRVZVPUT2KCQQSFFLT2E","short_pith_number":"pith:EHAWRFBR","canonical_record":{"source":{"id":"1312.0929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-03T20:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"bfa2de17c260db3c3c794bb32677c7cc9f61e6da230686d8ceae8700df1441cc","abstract_canon_sha256":"9f5a86606aeba4eccbe2350869bc2c87290d176a1cca259ff8a2a318dd4085a3"},"schema_version":"1.0"},"canonical_sha256":"21c1689431ae6afa4f4a1421229573d12b9d16381373edb70b33892ac5db8ca2","source":{"kind":"arxiv","id":"1312.0929","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0929","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0929v1","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0929","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"EHAWRFBRVZVP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EHAWRFBRVZVPUT2K","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EHAWRFBR","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EHAWRFBRVZVPUT2KCQQSFFLT2E","target":"record","payload":{"canonical_record":{"source":{"id":"1312.0929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-03T20:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"bfa2de17c260db3c3c794bb32677c7cc9f61e6da230686d8ceae8700df1441cc","abstract_canon_sha256":"9f5a86606aeba4eccbe2350869bc2c87290d176a1cca259ff8a2a318dd4085a3"},"schema_version":"1.0"},"canonical_sha256":"21c1689431ae6afa4f4a1421229573d12b9d16381373edb70b33892ac5db8ca2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:36.377211Z","signature_b64":"WZeHmZZLv37dJqOzLOKBJL34/cz8Iyl/8/ijk0tlfyEcbnCp1mAAY20tP43601T1oAhgsKZCwjGo+GZp3VnrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21c1689431ae6afa4f4a1421229573d12b9d16381373edb70b33892ac5db8ca2","last_reissued_at":"2026-05-18T03:05:36.376792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:36.376792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.0929","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":"2026-05-18T03:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"70coiGFQv23KbhCm5ntQ22wCH74U2cLpvaeUoj6B1iUJWK6pwiEONO5QTIIFMCvh4aTxVQxXuwwNs2KIZWAvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:02:38.083005Z"},"content_sha256":"275f47a6f27e8060b1eadca44781799af33ca7a7b544b82509a87ce189ece12f","schema_version":"1.0","event_id":"sha256:275f47a6f27e8060b1eadca44781799af33ca7a7b544b82509a87ce189ece12f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EHAWRFBRVZVPUT2KCQQSFFLT2E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time analyticity with higher norm estimates for the 2D Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bingsheng Zhang, Ciprian Foias, Michael S. Jolly, Rishika Rupam, Ruomeng Lan, Yong Yang","submitted_at":"2013-12-03T20:49:10Z","abstract_excerpt":"This paper establishes bounds on norms of all orders for solutions on the global attractor of the 2D Navier-Stokes equations, complexified in time. Specifically, for periodic boundary conditions on $[0,L]^2$, and a force $g\\in\\calD(A^{\\frac{\\alpha-1}{2}})$, we show there is a fixed strip about the real time axis on which a uniform bound $|A^{\\alpha}u|< m_\\alpha\\nu\\kappa_0^\\alpha$ holds for each $\\alpha \\in \\bN$. Here $\\nu$ is viscosity, $\\k0=2\\pi/L$, and $m_\\alpha$ is explicitly given in terms of $g$ and $\\alpha$. We show that if any element in $\\calA$ is in $\\D(A^\\alpha)$, then all of $\\calA$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0929","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":"2026-05-18T03:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZB9dc8/0e53czTCnReENRsOz/i/QuIiGnUoCxT8DtIA7mKQ7Mty4J0Ua5V5Xu+gj6SVec0TlYus42V410P1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:02:38.083369Z"},"content_sha256":"1f170e84a7bac3fa12bba4a238ce1fa2b083f5514387bde2f66ce7920352a6f7","schema_version":"1.0","event_id":"sha256:1f170e84a7bac3fa12bba4a238ce1fa2b083f5514387bde2f66ce7920352a6f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHAWRFBRVZVPUT2KCQQSFFLT2E/bundle.json","state_url":"https://pith.science/pith/EHAWRFBRVZVPUT2KCQQSFFLT2E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHAWRFBRVZVPUT2KCQQSFFLT2E/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":"2026-06-20T02:02:38Z","links":{"resolver":"https://pith.science/pith/EHAWRFBRVZVPUT2KCQQSFFLT2E","bundle":"https://pith.science/pith/EHAWRFBRVZVPUT2KCQQSFFLT2E/bundle.json","state":"https://pith.science/pith/EHAWRFBRVZVPUT2KCQQSFFLT2E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHAWRFBRVZVPUT2KCQQSFFLT2E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EHAWRFBRVZVPUT2KCQQSFFLT2E","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":"9f5a86606aeba4eccbe2350869bc2c87290d176a1cca259ff8a2a318dd4085a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-03T20:49:10Z","title_canon_sha256":"bfa2de17c260db3c3c794bb32677c7cc9f61e6da230686d8ceae8700df1441cc"},"schema_version":"1.0","source":{"id":"1312.0929","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0929","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0929v1","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0929","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"EHAWRFBRVZVP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EHAWRFBRVZVPUT2K","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EHAWRFBR","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:1f170e84a7bac3fa12bba4a238ce1fa2b083f5514387bde2f66ce7920352a6f7","target":"graph","created_at":"2026-05-18T03:05:36Z","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":"This paper establishes bounds on norms of all orders for solutions on the global attractor of the 2D Navier-Stokes equations, complexified in time. Specifically, for periodic boundary conditions on $[0,L]^2$, and a force $g\\in\\calD(A^{\\frac{\\alpha-1}{2}})$, we show there is a fixed strip about the real time axis on which a uniform bound $|A^{\\alpha}u|< m_\\alpha\\nu\\kappa_0^\\alpha$ holds for each $\\alpha \\in \\bN$. Here $\\nu$ is viscosity, $\\k0=2\\pi/L$, and $m_\\alpha$ is explicitly given in terms of $g$ and $\\alpha$. We show that if any element in $\\calA$ is in $\\D(A^\\alpha)$, then all of $\\calA$","authors_text":"Bingsheng Zhang, Ciprian Foias, Michael S. Jolly, Rishika Rupam, Ruomeng Lan, Yong Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-03T20:49:10Z","title":"Time analyticity with higher norm estimates for the 2D Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0929","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":"sha256:275f47a6f27e8060b1eadca44781799af33ca7a7b544b82509a87ce189ece12f","target":"record","created_at":"2026-05-18T03:05:36Z","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":"9f5a86606aeba4eccbe2350869bc2c87290d176a1cca259ff8a2a318dd4085a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-03T20:49:10Z","title_canon_sha256":"bfa2de17c260db3c3c794bb32677c7cc9f61e6da230686d8ceae8700df1441cc"},"schema_version":"1.0","source":{"id":"1312.0929","kind":"arxiv","version":1}},"canonical_sha256":"21c1689431ae6afa4f4a1421229573d12b9d16381373edb70b33892ac5db8ca2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21c1689431ae6afa4f4a1421229573d12b9d16381373edb70b33892ac5db8ca2","first_computed_at":"2026-05-18T03:05:36.376792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:36.376792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WZeHmZZLv37dJqOzLOKBJL34/cz8Iyl/8/ijk0tlfyEcbnCp1mAAY20tP43601T1oAhgsKZCwjGo+GZp3VnrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:36.377211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0929","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:275f47a6f27e8060b1eadca44781799af33ca7a7b544b82509a87ce189ece12f","sha256:1f170e84a7bac3fa12bba4a238ce1fa2b083f5514387bde2f66ce7920352a6f7"],"state_sha256":"61c61015e628f85b7d9fb76741dc6f5e39d7b272128abb42365ccd3d3af16862"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iapdN5SKK7gn5wymWzPc6XP315NqiJ67509UNK7VS7PV4V8y2f/bZo1clbYhWeXTVazQZKMrg+DtMd8d8OwFBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T02:02:38.085390Z","bundle_sha256":"ed13ce6e84b9419be3bf9f9f4a04da1bf2b39e361758f747d8a9ecb42c125263"}}