{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IKRDG54WT6MYA34B4DIFDX4C4I","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":"6413077a9a0e441024ac5b230a7ac965652b019be31a18743565fb68ea13dd1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-05T15:12:21Z","title_canon_sha256":"958d003d7b10f2c18f4b1ba7174068140dcf6644c69eba298924f45b30c17196"},"schema_version":"1.0","source":{"id":"1806.01740","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01740","created_at":"2026-05-18T00:14:11Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01740v1","created_at":"2026-05-18T00:14:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01740","created_at":"2026-05-18T00:14:11Z"},{"alias_kind":"pith_short_12","alias_value":"IKRDG54WT6MY","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IKRDG54WT6MYA34B","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IKRDG54W","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:cc6294ad4e255860f6747356f3becebee8870f7a1780dd110e9a47dd15bfda91","target":"graph","created_at":"2026-05-18T00:14:11Z","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":"A directional time-frequency localization measure for functions defined on the $d$-dimensional Euclidean space is introduced. A connection between this measure and its periodic counterpart is established. For a class of functions, an optimization problem for finding the optimal direction, along which a function is best or worst localized, is solved.","authors_text":"A. Krivoshein, E. Lebedeva, E. Neiman, J. Prestin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-05T15:12:21Z","title":"Directional Heisenberg uncertainty product"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01740","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:baa9734b03522946a6c3204a96e412227729890749384a09dcbe313b7fdd6fa7","target":"record","created_at":"2026-05-18T00:14:11Z","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":"6413077a9a0e441024ac5b230a7ac965652b019be31a18743565fb68ea13dd1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-05T15:12:21Z","title_canon_sha256":"958d003d7b10f2c18f4b1ba7174068140dcf6644c69eba298924f45b30c17196"},"schema_version":"1.0","source":{"id":"1806.01740","kind":"arxiv","version":1}},"canonical_sha256":"42a23377969f99806f81e0d051df82e218a39d6151e3933eb0567a41c2c183de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42a23377969f99806f81e0d051df82e218a39d6151e3933eb0567a41c2c183de","first_computed_at":"2026-05-18T00:14:11.923046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:11.923046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"86P87/FvHgJfC1QVnoCQVo2o0GK8mh+Nh8l3+YQ/CwiLPucTSdDncmo4/P3E7rC2QmHfaRt7OnEiS+QrNi7cCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:11.923505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.01740","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baa9734b03522946a6c3204a96e412227729890749384a09dcbe313b7fdd6fa7","sha256:cc6294ad4e255860f6747356f3becebee8870f7a1780dd110e9a47dd15bfda91"],"state_sha256":"e9b8fcdff641f1aa04ed924ba99f080f6e35260983cf8cc3b58d437d5975529e"}