{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MR6A5YHTG22DMOCMIWU3Z2E43M","short_pith_number":"pith:MR6A5YHT","canonical_record":{"source":{"id":"1802.03785","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2018-02-11T18:24:07Z","cross_cats_sorted":[],"title_canon_sha256":"3e8a8a4260814208d69637d37ca04d20dcb20c6040aa12500289f4c343102194","abstract_canon_sha256":"f3ef6a9490504a1ba19b828dc0dd9b90a7bf630acc153842da3a046dc03aaa74"},"schema_version":"1.0"},"canonical_sha256":"647c0ee0f336b436384c45a9bce89cdb29b74cae916ad5b7c161e0a599e87378","source":{"kind":"arxiv","id":"1802.03785","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03785","created_at":"2026-05-18T00:14:00Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03785v2","created_at":"2026-05-18T00:14:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03785","created_at":"2026-05-18T00:14:00Z"},{"alias_kind":"pith_short_12","alias_value":"MR6A5YHTG22D","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MR6A5YHTG22DMOCM","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MR6A5YHT","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MR6A5YHTG22DMOCMIWU3Z2E43M","target":"record","payload":{"canonical_record":{"source":{"id":"1802.03785","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2018-02-11T18:24:07Z","cross_cats_sorted":[],"title_canon_sha256":"3e8a8a4260814208d69637d37ca04d20dcb20c6040aa12500289f4c343102194","abstract_canon_sha256":"f3ef6a9490504a1ba19b828dc0dd9b90a7bf630acc153842da3a046dc03aaa74"},"schema_version":"1.0"},"canonical_sha256":"647c0ee0f336b436384c45a9bce89cdb29b74cae916ad5b7c161e0a599e87378","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:00.313754Z","signature_b64":"FHbTIYN9oK9BbX2hOTeQvSANUsKRuDtwykc+vqWZk+DNMJzM37+T3luOrv+h/PdHa+A9DmJTtY9K6QIY8zZ2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"647c0ee0f336b436384c45a9bce89cdb29b74cae916ad5b7c161e0a599e87378","last_reissued_at":"2026-05-18T00:14:00.313070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:00.313070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.03785","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+2nNemqtT4H4x7wXuO6VPBgXMOTwJnCe/erHm7XQRJJdr3RVGM/e+Na6NzzxttP1MFNcQ5gou9TLbRKuZCXzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:10:50.427715Z"},"content_sha256":"e11a51cfa6ce92cf82568039c4f76c04588a17f5c913f773d2b8d7ed5b00e119","schema_version":"1.0","event_id":"sha256:e11a51cfa6ce92cf82568039c4f76c04588a17f5c913f773d2b8d7ed5b00e119"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MR6A5YHTG22DMOCMIWU3Z2E43M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uncertainty Principles for the Offset Linear Canonical Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Haiye Huo","submitted_at":"2018-02-11T18:24:07Z","abstract_excerpt":"The offset linear canonical transform (OLCT) provides a more general framework for a number of well known linear integral transforms in signal processing and optics, such as Fourier transform, fractional Fourier transform, linear canonical transform. In this paper, to characterize simultaneous localization of a signal and its OLCT, we extend some different uncertainty principles (UPs), including Nazarov's UP, Hardy's UP, Beurling's UP, logarithmic UP and entropic UP, which have already been well studied in the Fourier transform domain over the last few decades, to the OLCT domain in a broader "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03785","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9oqHDw2z0Ooe9BJcDuomFSxNF2NDmJ6D2keoYUdE5ps5Gl1RbSdFKgdMnLyc+x9gYyMlBBlln50POmbnHZmyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:10:50.428041Z"},"content_sha256":"f9979bf375ff2350240700ede8202f07763c549ca9b64aff212f3cba5b09e920","schema_version":"1.0","event_id":"sha256:f9979bf375ff2350240700ede8202f07763c549ca9b64aff212f3cba5b09e920"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MR6A5YHTG22DMOCMIWU3Z2E43M/bundle.json","state_url":"https://pith.science/pith/MR6A5YHTG22DMOCMIWU3Z2E43M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MR6A5YHTG22DMOCMIWU3Z2E43M/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T08:10:50Z","links":{"resolver":"https://pith.science/pith/MR6A5YHTG22DMOCMIWU3Z2E43M","bundle":"https://pith.science/pith/MR6A5YHTG22DMOCMIWU3Z2E43M/bundle.json","state":"https://pith.science/pith/MR6A5YHTG22DMOCMIWU3Z2E43M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MR6A5YHTG22DMOCMIWU3Z2E43M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MR6A5YHTG22DMOCMIWU3Z2E43M","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":"f3ef6a9490504a1ba19b828dc0dd9b90a7bf630acc153842da3a046dc03aaa74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2018-02-11T18:24:07Z","title_canon_sha256":"3e8a8a4260814208d69637d37ca04d20dcb20c6040aa12500289f4c343102194"},"schema_version":"1.0","source":{"id":"1802.03785","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03785","created_at":"2026-05-18T00:14:00Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03785v2","created_at":"2026-05-18T00:14:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03785","created_at":"2026-05-18T00:14:00Z"},{"alias_kind":"pith_short_12","alias_value":"MR6A5YHTG22D","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MR6A5YHTG22DMOCM","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MR6A5YHT","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:f9979bf375ff2350240700ede8202f07763c549ca9b64aff212f3cba5b09e920","target":"graph","created_at":"2026-05-18T00:14:00Z","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":"The offset linear canonical transform (OLCT) provides a more general framework for a number of well known linear integral transforms in signal processing and optics, such as Fourier transform, fractional Fourier transform, linear canonical transform. In this paper, to characterize simultaneous localization of a signal and its OLCT, we extend some different uncertainty principles (UPs), including Nazarov's UP, Hardy's UP, Beurling's UP, logarithmic UP and entropic UP, which have already been well studied in the Fourier transform domain over the last few decades, to the OLCT domain in a broader ","authors_text":"Haiye Huo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2018-02-11T18:24:07Z","title":"Uncertainty Principles for the Offset Linear Canonical Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03785","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:e11a51cfa6ce92cf82568039c4f76c04588a17f5c913f773d2b8d7ed5b00e119","target":"record","created_at":"2026-05-18T00:14:00Z","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":"f3ef6a9490504a1ba19b828dc0dd9b90a7bf630acc153842da3a046dc03aaa74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2018-02-11T18:24:07Z","title_canon_sha256":"3e8a8a4260814208d69637d37ca04d20dcb20c6040aa12500289f4c343102194"},"schema_version":"1.0","source":{"id":"1802.03785","kind":"arxiv","version":2}},"canonical_sha256":"647c0ee0f336b436384c45a9bce89cdb29b74cae916ad5b7c161e0a599e87378","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"647c0ee0f336b436384c45a9bce89cdb29b74cae916ad5b7c161e0a599e87378","first_computed_at":"2026-05-18T00:14:00.313070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:00.313070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FHbTIYN9oK9BbX2hOTeQvSANUsKRuDtwykc+vqWZk+DNMJzM37+T3luOrv+h/PdHa+A9DmJTtY9K6QIY8zZ2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:00.313754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03785","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e11a51cfa6ce92cf82568039c4f76c04588a17f5c913f773d2b8d7ed5b00e119","sha256:f9979bf375ff2350240700ede8202f07763c549ca9b64aff212f3cba5b09e920"],"state_sha256":"8782c0dcc7ff785278ab771050a37b6bf0ac2c01a935271fca4c053e1e32dfbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZmTMiwoZA+C1STRnNC+TWETvGQumtloQek/2vumx9RrVy76OAS1fRb8WAwt6uOsEEenr+3TF1rXh3C/VxLn2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:10:50.429833Z","bundle_sha256":"dc93f335982d3eccef4b5f445665cb673c999a47acc905e9f31e15eaaa8dc4c1"}}