{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZTR5INCYUCCQ2BQYGNTYT2A64Q","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":"5f9aab424b41963b239e6d35d5e1b6dca52d02aa1c6c2ff74cb80f242c5b5205","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-25T00:44:34Z","title_canon_sha256":"5e78546d44d25a518a14b81ab2cb6c3e4251ea9038878e13094d360a7053469d"},"schema_version":"1.0","source":{"id":"1403.6200","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6200","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6200v3","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6200","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZTR5INCYUCCQ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZTR5INCYUCCQ2BQY","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZTR5INCY","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:c356a1b9de38c6e051eecccbcc25ece0c4800f12edc41a016f2419c826e3396a","target":"graph","created_at":"2026-05-18T01:31:46Z","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":"As in our previous paper, the 3D Navier-Stokes equations with a translationally bounded force contain pullback attractors in a weak sense. Moreover, those attractors consist of complete bounded trajectories. In this paper, we present a sufficient condition under which the pullback attractors are degenerate. That is, if the Grashof constant is small enough, the pullback attractor will be a single point on a unique, complete, bounded, strong solution. We then apply our results to provide a new proof of the existence of a unique, strong, periodic solution to the 3D Navier-Stokes with a small, per","authors_text":"Alexey Cheskidov, Landon Kavlie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-25T00:44:34Z","title":"Degenerate pullback attractors for the 3D Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6200","kind":"arxiv","version":3},"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":"sha256:0bc171f706f7109b7f2eefa220f602f95d93102d2c3be5da068eda4fff111b01","target":"record","created_at":"2026-05-18T01:31:46Z","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":"5f9aab424b41963b239e6d35d5e1b6dca52d02aa1c6c2ff74cb80f242c5b5205","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-25T00:44:34Z","title_canon_sha256":"5e78546d44d25a518a14b81ab2cb6c3e4251ea9038878e13094d360a7053469d"},"schema_version":"1.0","source":{"id":"1403.6200","kind":"arxiv","version":3}},"canonical_sha256":"cce3d43458a0850d0618336789e81ee42f9a6d85b6e89b068f0892832d5cc4a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cce3d43458a0850d0618336789e81ee42f9a6d85b6e89b068f0892832d5cc4a1","first_computed_at":"2026-05-18T01:31:46.701012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:46.701012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ridAdKLF/FtwdvAfUd2ahTQO0omek5ojgtUJeOqm1vy3FIKL0lp6Ga5Psa+3u2pwe2P7auOYRK3Mis76ckMYAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:46.701354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6200","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bc171f706f7109b7f2eefa220f602f95d93102d2c3be5da068eda4fff111b01","sha256:c356a1b9de38c6e051eecccbcc25ece0c4800f12edc41a016f2419c826e3396a"],"state_sha256":"346a38072519279f52d293f185c154dff08101c2436854c391dc9a5d03861711"}