{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:4EVKEKSC2EMZYGNOEDSZSYMZQV","short_pith_number":"pith:4EVKEKSC","canonical_record":{"source":{"id":"1904.09440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-20T12:41:06Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"44acf206e8021f79b5c66040373bc769e9c2e4e61ec94f05c1d3aac06ea91115","abstract_canon_sha256":"24d46b2c3ef926aca29f01829a782132cc19b5538a8594d96a8a8bb6f2458ac0"},"schema_version":"1.0"},"canonical_sha256":"e12aa22a42d1199c19ae20e599619985606282dc5fd4689ae780b09774b43f2c","source":{"kind":"arxiv","id":"1904.09440","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09440","created_at":"2026-05-17T23:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09440v1","created_at":"2026-05-17T23:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09440","created_at":"2026-05-17T23:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"4EVKEKSC2EMZ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4EVKEKSC2EMZYGNO","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4EVKEKSC","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:4EVKEKSC2EMZYGNOEDSZSYMZQV","target":"record","payload":{"canonical_record":{"source":{"id":"1904.09440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-20T12:41:06Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"44acf206e8021f79b5c66040373bc769e9c2e4e61ec94f05c1d3aac06ea91115","abstract_canon_sha256":"24d46b2c3ef926aca29f01829a782132cc19b5538a8594d96a8a8bb6f2458ac0"},"schema_version":"1.0"},"canonical_sha256":"e12aa22a42d1199c19ae20e599619985606282dc5fd4689ae780b09774b43f2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:04.181917Z","signature_b64":"aKrNm3hFZCKjmhjVYD1UBYQQLHa7XEOMYaE52Rb4c9yU0AuS7pGXoGp9UY1cO2jm1xtV/lka4A0KsFBAya/5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e12aa22a42d1199c19ae20e599619985606282dc5fd4689ae780b09774b43f2c","last_reissued_at":"2026-05-17T23:48:04.181478Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:04.181478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.09440","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e3WG3PENXj24Sa+qiGsPgD2vWa9S3RmUOte381L5cGlKLYA9Fw0g17ts4KFVfZrdiapOT/g255axxlIZTDe3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:27:14.722606Z"},"content_sha256":"19c8900b01d9d0dda5115e2eba843b41a81103a030bb6700b7c77b4da0117840","schema_version":"1.0","event_id":"sha256:19c8900b01d9d0dda5115e2eba843b41a81103a030bb6700b7c77b4da0117840"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:4EVKEKSC2EMZYGNOEDSZSYMZQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On bicomplex Fourier--Wigner transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Aiad El Gourari, Allal Ghanmi, Khalil Zine","submitted_at":"2019-04-20T12:41:06Z","abstract_excerpt":"We consider the $1$- and $2$-d bicomplex analogs of the classical Fourier--Wigner transform. Their basic properties, including Moyal's identity and characterization of their ranges giving rise to new bicomplex--polyanalytic functional spaces are discussed. Particular case of special window is also considered. An orthogonal basis for the space of bicomplex--valued square integrable functions on the bicomplex numbers is constructed by means of the polyanalytic complex Hermite functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09440","kind":"arxiv","version":1},"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":"2026-05-17T23:48:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYavYJ7RfvVe23PThAMPQasRrzkIJYN67yCcBRYHw2LGpfWubUDvqvztr+l+CfQjUZwDcti5hemyydJ0ssUABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:27:14.722940Z"},"content_sha256":"313f0d4fee2bd23320f5493a0734a0bdf3cbb7726a120526cc2c83df6fdb355f","schema_version":"1.0","event_id":"sha256:313f0d4fee2bd23320f5493a0734a0bdf3cbb7726a120526cc2c83df6fdb355f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4EVKEKSC2EMZYGNOEDSZSYMZQV/bundle.json","state_url":"https://pith.science/pith/4EVKEKSC2EMZYGNOEDSZSYMZQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4EVKEKSC2EMZYGNOEDSZSYMZQV/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":"2026-06-01T11:27:14Z","links":{"resolver":"https://pith.science/pith/4EVKEKSC2EMZYGNOEDSZSYMZQV","bundle":"https://pith.science/pith/4EVKEKSC2EMZYGNOEDSZSYMZQV/bundle.json","state":"https://pith.science/pith/4EVKEKSC2EMZYGNOEDSZSYMZQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4EVKEKSC2EMZYGNOEDSZSYMZQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4EVKEKSC2EMZYGNOEDSZSYMZQV","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":"24d46b2c3ef926aca29f01829a782132cc19b5538a8594d96a8a8bb6f2458ac0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-20T12:41:06Z","title_canon_sha256":"44acf206e8021f79b5c66040373bc769e9c2e4e61ec94f05c1d3aac06ea91115"},"schema_version":"1.0","source":{"id":"1904.09440","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09440","created_at":"2026-05-17T23:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09440v1","created_at":"2026-05-17T23:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09440","created_at":"2026-05-17T23:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"4EVKEKSC2EMZ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4EVKEKSC2EMZYGNO","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4EVKEKSC","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:313f0d4fee2bd23320f5493a0734a0bdf3cbb7726a120526cc2c83df6fdb355f","target":"graph","created_at":"2026-05-17T23:48:04Z","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 consider the $1$- and $2$-d bicomplex analogs of the classical Fourier--Wigner transform. Their basic properties, including Moyal's identity and characterization of their ranges giving rise to new bicomplex--polyanalytic functional spaces are discussed. Particular case of special window is also considered. An orthogonal basis for the space of bicomplex--valued square integrable functions on the bicomplex numbers is constructed by means of the polyanalytic complex Hermite functions.","authors_text":"Aiad El Gourari, Allal Ghanmi, Khalil Zine","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-20T12:41:06Z","title":"On bicomplex Fourier--Wigner transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09440","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":"sha256:19c8900b01d9d0dda5115e2eba843b41a81103a030bb6700b7c77b4da0117840","target":"record","created_at":"2026-05-17T23:48:04Z","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":"24d46b2c3ef926aca29f01829a782132cc19b5538a8594d96a8a8bb6f2458ac0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-20T12:41:06Z","title_canon_sha256":"44acf206e8021f79b5c66040373bc769e9c2e4e61ec94f05c1d3aac06ea91115"},"schema_version":"1.0","source":{"id":"1904.09440","kind":"arxiv","version":1}},"canonical_sha256":"e12aa22a42d1199c19ae20e599619985606282dc5fd4689ae780b09774b43f2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e12aa22a42d1199c19ae20e599619985606282dc5fd4689ae780b09774b43f2c","first_computed_at":"2026-05-17T23:48:04.181478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:04.181478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aKrNm3hFZCKjmhjVYD1UBYQQLHa7XEOMYaE52Rb4c9yU0AuS7pGXoGp9UY1cO2jm1xtV/lka4A0KsFBAya/5Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:04.181917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.09440","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19c8900b01d9d0dda5115e2eba843b41a81103a030bb6700b7c77b4da0117840","sha256:313f0d4fee2bd23320f5493a0734a0bdf3cbb7726a120526cc2c83df6fdb355f"],"state_sha256":"0cf1974ca9c8ba5cc182c7ef6d678df9d967796510bebbff298a33d2dc0b5eb0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+0r8ASf5Us8U2lU87jk13loze9ruCLCbSbhGnfRO/98Iovu3vBbj+mxygxcLivI4NY+IR+d8Ogk4+eGkusETAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:27:14.724827Z","bundle_sha256":"b5c64803ace928a5f1fd78fcc2e709275a1fbf8f1546ff54eb5c7c82ba416304"}}