{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L5T7DP2ZP33Q6K53JVWUCYAXDX","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":"70d532fd72e77ed7732ead826d6892af9c005b5940086daf4debd4ad828a5e60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-12T06:28:03Z","title_canon_sha256":"f7fdb056cfb999cf6359830e4408674cb31ccdc3b4207da555638c360d6804dd"},"schema_version":"1.0","source":{"id":"1807.04436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04436","created_at":"2026-05-18T00:10:53Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04436v1","created_at":"2026-05-18T00:10:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04436","created_at":"2026-05-18T00:10:53Z"},{"alias_kind":"pith_short_12","alias_value":"L5T7DP2ZP33Q","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L5T7DP2ZP33Q6K53","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L5T7DP2Z","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:1f1f9b259f167440535b73dbaae0e9274157d21b2f016a6de3235a63cd8cf65b","target":"graph","created_at":"2026-05-18T00:10:53Z","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 study Liouville theorems for the non-stationary Stokes equations in exterior domains in $ \\mathbb{R}^{n}$ under decay conditions for spatial variables. As applications, we prove that the Stokes semigroup is a bounded analytic semigroup on $L^{ \\infty}_{ \\sigma}$ of angle $ \\pi/2$ for $n \\geq 3$. We also prove large time estimates for $n=2$ with zero net force.","authors_text":"Ken Abe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-12T06:28:03Z","title":"Liouville theorems for the Stokes equations with applications to large time estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04436","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":"sha256:8a772318c0a675234c59472d00377b52d9fe33e76b866a1fd1a53c5df06b4b60","target":"record","created_at":"2026-05-18T00:10:53Z","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":"70d532fd72e77ed7732ead826d6892af9c005b5940086daf4debd4ad828a5e60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-12T06:28:03Z","title_canon_sha256":"f7fdb056cfb999cf6359830e4408674cb31ccdc3b4207da555638c360d6804dd"},"schema_version":"1.0","source":{"id":"1807.04436","kind":"arxiv","version":1}},"canonical_sha256":"5f67f1bf597ef70f2bbb4d6d4160171de63316d983a1229c546d3ba3762e0a7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f67f1bf597ef70f2bbb4d6d4160171de63316d983a1229c546d3ba3762e0a7b","first_computed_at":"2026-05-18T00:10:53.529082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:53.529082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q8slbWwkqONp+x+8LdBuxulicy9f1KJYc5t70FTZGHJdrGQjYDu6NhzHDDAFwSA3SQ2ZxWohGESloG4dyLqPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:53.529676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.04436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a772318c0a675234c59472d00377b52d9fe33e76b866a1fd1a53c5df06b4b60","sha256:1f1f9b259f167440535b73dbaae0e9274157d21b2f016a6de3235a63cd8cf65b"],"state_sha256":"a8831e003aac97ad039fd22a479e65b8b53b6cb6e8e2f10d55312b2ce6f17aa1"}