{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WLJ2MNIMHSKAMQQKFUCECY53ZC","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":"e35ba8ea3ecc84409f26330d1e5a7f075adbc782204a4d868186f4f3cff9f617","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-25T13:37:11Z","title_canon_sha256":"e6ce1746d4e57f61db9caaf738382624084c36163b2548a43850cff37bcaa324"},"schema_version":"1.0","source":{"id":"1904.11328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11328","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11328v1","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11328","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"pith_short_12","alias_value":"WLJ2MNIMHSKA","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WLJ2MNIMHSKAMQQK","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WLJ2MNIM","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:9273e5b455f872d8d3724e2a2e5e8cdd028e463d8a4440bdad7fd5a904503a60","target":"graph","created_at":"2026-05-17T23:47:45Z","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 the uncertainty principles related to the generalized Logan problem in $\\mathbb{R}^{d}$. Our main result provides the complete solution of the following problem: for a fixed $m\\in \\mathbb{Z}_{+}$, find \\[ \\sup\\{|x|\\colon (-1)^{m}f(x)>0\\}\\cdot \\sup \\{|x|\\colon x\\in \\mathrm{supp}\\,\\widehat{f}\\,\\}\\to \\inf, \\] where the infimum is taken over all nontrivial positive definite bandlimited functions such that $\\int_{\\mathbb{R}^d}|x|^{2k}f(x)\\,dx=0$ for $k=0,\\dots,m-1$ if $m\\ge 1$.\n  We also obtain the uncertainty principle for bandlimited functions related to the recent result by Bourgain, Cl","authors_text":"D.V. Gorbachev, S.Yu. Tikhonov, V.I. Ivanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-25T13:37:11Z","title":"Uncertainty principles for eventually constant sign bandlimited functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11328","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:cc1c65fbdcaa4aa492644f355e72b68db56b39ab2c74452f4516acc2e47da181","target":"record","created_at":"2026-05-17T23:47:45Z","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":"e35ba8ea3ecc84409f26330d1e5a7f075adbc782204a4d868186f4f3cff9f617","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-25T13:37:11Z","title_canon_sha256":"e6ce1746d4e57f61db9caaf738382624084c36163b2548a43850cff37bcaa324"},"schema_version":"1.0","source":{"id":"1904.11328","kind":"arxiv","version":1}},"canonical_sha256":"b2d3a6350c3c9406420a2d044163bbc8a3ec5c10de4e1de90ce9a4e2f9884212","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2d3a6350c3c9406420a2d044163bbc8a3ec5c10de4e1de90ce9a4e2f9884212","first_computed_at":"2026-05-17T23:47:45.184175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:45.184175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cqYBQFskbpzXhujvseuTU73DsTqSLQiI4tzg1HFN7pbIzL826Qh+Heix6hGjhKKyUt54ch5wzQDcyHLujmtzBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:45.184949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.11328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc1c65fbdcaa4aa492644f355e72b68db56b39ab2c74452f4516acc2e47da181","sha256:9273e5b455f872d8d3724e2a2e5e8cdd028e463d8a4440bdad7fd5a904503a60"],"state_sha256":"966d18abb91e0b44fbfa853220dab14f0144db6eaec06981f173bb6d6da8bbb8"}