{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TCRY664KRKGEBRUMUQAURPN22N","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":"f9d251b991740917060b65181d18a7dec1cde336baac69c93d7ab5597d0a6551","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-08-11T17:01:23Z","title_canon_sha256":"440c199bf92ee90759e5acda34c2bac227776a1a2c99221b9dd9d788bac5ba53"},"schema_version":"1.0","source":{"id":"1108.2463","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2463","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2463v5","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2463","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"TCRY664KRKGE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TCRY664KRKGEBRUM","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TCRY664K","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:e43286522b583d890f644640aa55de58fd68e63765155eeb7e41a53ea1de5d28","target":"graph","created_at":"2026-05-18T03:21:32Z","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 prove a version of the Titchmarsh convolution theorem for distributions on the circle. We show that the \"naive form\" of the Titchmarsh theorem could be violated, but that such a violation is only possible for the convolution of distributions which both possess certain symmetry properties.","authors_text":"Alexander Komech, Andrew Comech","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-08-11T17:01:23Z","title":"On the Titchmarsh convolution theorem for distributions on the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2463","kind":"arxiv","version":5},"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":"sha256:10ac2e1cdd016df6b5099b49f68f5caa31c11a5899a497e6e099dec2cf299f8a","target":"record","created_at":"2026-05-18T03:21:32Z","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":"f9d251b991740917060b65181d18a7dec1cde336baac69c93d7ab5597d0a6551","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-08-11T17:01:23Z","title_canon_sha256":"440c199bf92ee90759e5acda34c2bac227776a1a2c99221b9dd9d788bac5ba53"},"schema_version":"1.0","source":{"id":"1108.2463","kind":"arxiv","version":5}},"canonical_sha256":"98a38f7b8a8a8c40c68ca40148bdbad362602cf097990282fba349e6c8ad2882","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98a38f7b8a8a8c40c68ca40148bdbad362602cf097990282fba349e6c8ad2882","first_computed_at":"2026-05-18T03:21:32.025389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:32.025389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D2PGT3zqpk7bKL9MFVdy1xl6Vpyf++K4uyru8/3+o7ItaoSKmoAvGgOD8pPq/zRoJ7DMjlrzRXTM07tZT0JZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:32.025793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2463","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10ac2e1cdd016df6b5099b49f68f5caa31c11a5899a497e6e099dec2cf299f8a","sha256:e43286522b583d890f644640aa55de58fd68e63765155eeb7e41a53ea1de5d28"],"state_sha256":"5b91f13b431ab29b1f4015ab77014842f4ad41d5544d1e2d10974edad56bc38f"}