{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TBYJUFJ7PWNB5SNTON5UX7WFJO","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":"db962218f8216490b645ece61cf94d07e6ffe38a14d5fe8f333d658cc4544491","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-06T06:33:00Z","title_canon_sha256":"a10b8b8738ff9a7237bb9d5539332166362f3caf1a7253819846e47afd2e35fe"},"schema_version":"1.0","source":{"id":"1905.01835","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01835","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01835v2","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01835","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"TBYJUFJ7PWNB","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"TBYJUFJ7PWNB5SNT","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"TBYJUFJ7","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:d0f8757f73e5b09e713b40a2b650a9f0ecd21d83fbd8c091e16851b859e5e251","target":"graph","created_at":"2026-05-17T23:40:17Z","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":"In this paper, some important properties of the windowed offset linear canonical transform (WOLCT) such as shift, modulation and orthogonality relation are introduced. Based on these properties we derive the convolution and correlation theorems for the WOLCT.","authors_text":"Bing-Zhao Li, Wen-Biao Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-06T06:33:00Z","title":"Convolution and correlation theorems for the windowed offset linear canonical transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01835","kind":"arxiv","version":2},"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":"sha256:618618dae6d5bab21a88aab99b8bc05d2e7f15414eaebf89c26863a95e1cb89d","target":"record","created_at":"2026-05-17T23:40:17Z","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":"db962218f8216490b645ece61cf94d07e6ffe38a14d5fe8f333d658cc4544491","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-06T06:33:00Z","title_canon_sha256":"a10b8b8738ff9a7237bb9d5539332166362f3caf1a7253819846e47afd2e35fe"},"schema_version":"1.0","source":{"id":"1905.01835","kind":"arxiv","version":2}},"canonical_sha256":"98709a153f7d9a1ec9b3737b4bfec54b852e6920ccbfc1b406087bcdd952d032","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98709a153f7d9a1ec9b3737b4bfec54b852e6920ccbfc1b406087bcdd952d032","first_computed_at":"2026-05-17T23:40:17.166482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:17.166482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cWJtG5tWJJMLYJihV6kIvwlYj08O0XAu0/6SILpYwf67h8rDCp4Hh9qZbBl5uhth8MhHHnlxMkp/gxmUhshJCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:17.167109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01835","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:618618dae6d5bab21a88aab99b8bc05d2e7f15414eaebf89c26863a95e1cb89d","sha256:d0f8757f73e5b09e713b40a2b650a9f0ecd21d83fbd8c091e16851b859e5e251"],"state_sha256":"e993c8bc465d10fc65d41d4ebf77d731564d9bbdeb920f0158661551438fb61f"}