{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6UZH3JRFRP4F2ZC2E5RPLFDBFP","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":"af2296efc60847e3b10e3e49e4c7066f90d0ad9d51ca0622098bcbdd8467d308","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-03T17:13:04Z","title_canon_sha256":"b76380a8257698d53e90e3aa382ca1bad964d094085d8714760fad97426fc00f"},"schema_version":"1.0","source":{"id":"1512.01160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01160","created_at":"2026-05-18T00:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01160v1","created_at":"2026-05-18T00:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01160","created_at":"2026-05-18T00:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"6UZH3JRFRP4F","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6UZH3JRFRP4F2ZC2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6UZH3JRF","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:dedeea62b2b6629ce1df7ef5442e9ccdf0ee4db51761e220a665f57986015754","target":"graph","created_at":"2026-05-18T00:53:34Z","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 Lieb-Thirring inequalities on the d-dimensional torus with arbitrary periods. In the space of functions with zero average with respect to the shortest coordinate we prove the Lieb-Thirring inequalities for the $\\gamma$-moments of the negative eigenvalues with constants independent of ratio of the periods. Applications to the attractors of the damped Navier-Stokes system are given.","authors_text":"Alexei Ilyin, Ari Laptev","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-03T17:13:04Z","title":"Lieb-Thirring inequalities on the torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01160","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:f3b03088fa1e655b579e2481ba0ef51af8bfb5dfd4236bcd2289629f1a02a2dc","target":"record","created_at":"2026-05-18T00:53:34Z","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":"af2296efc60847e3b10e3e49e4c7066f90d0ad9d51ca0622098bcbdd8467d308","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-03T17:13:04Z","title_canon_sha256":"b76380a8257698d53e90e3aa382ca1bad964d094085d8714760fad97426fc00f"},"schema_version":"1.0","source":{"id":"1512.01160","kind":"arxiv","version":1}},"canonical_sha256":"f5327da6258bf85d645a2762f594612bc343ec6aad76c5597ec6b336157285ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5327da6258bf85d645a2762f594612bc343ec6aad76c5597ec6b336157285ea","first_computed_at":"2026-05-18T00:53:34.817773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:34.817773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n8rAZWQqZ/Cm/+V7APwa+QK1bObBHXpIcjq6u6Tb0sPqGrU76Dk7Ys38hO5qyaqR78/LsvS6G7eC1Rio9/6TAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:34.818213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3b03088fa1e655b579e2481ba0ef51af8bfb5dfd4236bcd2289629f1a02a2dc","sha256:dedeea62b2b6629ce1df7ef5442e9ccdf0ee4db51761e220a665f57986015754"],"state_sha256":"a4dc01fdb2b4fe7b1130f34af041acb33fdd9b6e60d801cd17d17504c444e634"}