{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZYX3BE6MNO6455DIRKPSBSIJZD","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":"0c55a12af3e928f7f30df62e496549bd30063b21951ad61515cb7ab0b05a6990","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-03-23T16:23:36Z","title_canon_sha256":"e2d2cf005a2cb9d7b1d1ff7aafc07fc9f234c7d0b0ed6056fee2153240a0d3d2"},"schema_version":"1.0","source":{"id":"2503.18131","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.18131","created_at":"2026-07-07T02:17:06Z"},{"alias_kind":"arxiv_version","alias_value":"2503.18131v3","created_at":"2026-07-07T02:17:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.18131","created_at":"2026-07-07T02:17:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZYX3BE6MNO64","created_at":"2026-07-07T02:17:06Z"},{"alias_kind":"pith_short_16","alias_value":"ZYX3BE6MNO6455DI","created_at":"2026-07-07T02:17:06Z"},{"alias_kind":"pith_short_8","alias_value":"ZYX3BE6M","created_at":"2026-07-07T02:17:06Z"}],"graph_snapshots":[{"event_id":"sha256:e52b8682d3bb037b4b977493163363039f54d2299f8caf50167a6d468bd419e1","target":"graph","created_at":"2026-07-07T02:17:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.18131/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that for any weight $w$, which has at most polynomial decay at the endpoints of the interval, there exists a complete and minimal system $\\{e^{i\\lambda_n t}\\}_{n\\in \\mathbb{N}}$ of exponentials in the weighted space $L^2(w)$ which is not hereditarily complete.","authors_text":"Andrei V. Semenov","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-03-23T16:23:36Z","title":"Hereditary completeness for systems of exponentials in weighted $L^2$-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.18131","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":"sha256:5e0574a5499f7a46c6f8ea066f85f911f3c41a946976a9547f7d38156d3879cb","target":"record","created_at":"2026-07-07T02:17:06Z","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":"0c55a12af3e928f7f30df62e496549bd30063b21951ad61515cb7ab0b05a6990","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-03-23T16:23:36Z","title_canon_sha256":"e2d2cf005a2cb9d7b1d1ff7aafc07fc9f234c7d0b0ed6056fee2153240a0d3d2"},"schema_version":"1.0","source":{"id":"2503.18131","kind":"arxiv","version":3}},"canonical_sha256":"ce2fb093cc6bbdcef4688a9f20c909c8e5153b26afc81a32a97fa88233414997","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce2fb093cc6bbdcef4688a9f20c909c8e5153b26afc81a32a97fa88233414997","first_computed_at":"2026-07-07T02:17:06.477865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:17:06.477865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A1bmlOZDHSs2p0m8L/0ZvZ1TrvVBG7bnO4JXt9NF2AmNHb+K/u53IBOA/Uz8zlGV1rxT4Cps1qob+GU5JTSwCA==","signature_status":"signed_v1","signed_at":"2026-07-07T02:17:06.478987Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.18131","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e0574a5499f7a46c6f8ea066f85f911f3c41a946976a9547f7d38156d3879cb","sha256:e52b8682d3bb037b4b977493163363039f54d2299f8caf50167a6d468bd419e1"],"state_sha256":"8c0508acf230a42f2702c7a76c6ceee8cd547a55be79f37e992b748e7f16162a"}