{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AX5B6YQ3TV4J2XCVZWZMH7JEIJ","short_pith_number":"pith:AX5B6YQ3","canonical_record":{"source":{"id":"1605.03326","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-11T08:34:38Z","cross_cats_sorted":[],"title_canon_sha256":"19239e13718930686b09938eaec0d2cefcf0c010b07babcf3e5761689109f52d","abstract_canon_sha256":"0fcaa61a06c9aff07b16894089d7af062ec2a4078715487cf20e6830b8fb2aa4"},"schema_version":"1.0"},"canonical_sha256":"05fa1f621b9d789d5c55cdb2c3fd244264a5c673c503f0195c556791befeecd2","source":{"kind":"arxiv","id":"1605.03326","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03326","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03326v5","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03326","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"AX5B6YQ3TV4J","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AX5B6YQ3TV4J2XCV","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AX5B6YQ3","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AX5B6YQ3TV4J2XCVZWZMH7JEIJ","target":"record","payload":{"canonical_record":{"source":{"id":"1605.03326","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-11T08:34:38Z","cross_cats_sorted":[],"title_canon_sha256":"19239e13718930686b09938eaec0d2cefcf0c010b07babcf3e5761689109f52d","abstract_canon_sha256":"0fcaa61a06c9aff07b16894089d7af062ec2a4078715487cf20e6830b8fb2aa4"},"schema_version":"1.0"},"canonical_sha256":"05fa1f621b9d789d5c55cdb2c3fd244264a5c673c503f0195c556791befeecd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:41.833053Z","signature_b64":"6ZVopgQWCTKiJCI/aZ2J3PHdh5lOxqdprhWDuWFWTaAzu8f2i8D+n/p4xjWCsCQYN0/JpUHIl5MLTqqzeBtUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05fa1f621b9d789d5c55cdb2c3fd244264a5c673c503f0195c556791befeecd2","last_reissued_at":"2026-05-18T01:12:41.832556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:41.832556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.03326","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bXqTzRPFm3xLIOj3p5nTs7krXhOqgL+xsEvWX6DrRoKZncfA4NjyX0M7UUX94omP8Chff2s46gZiWG53ppffDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:36:01.648372Z"},"content_sha256":"0ddd26dc4a06ebcff94910ac14198d4d95b379f4da01985b161a8f2ccc0c2bb4","schema_version":"1.0","event_id":"sha256:0ddd26dc4a06ebcff94910ac14198d4d95b379f4da01985b161a8f2ccc0c2bb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AX5B6YQ3TV4J2XCVZWZMH7JEIJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Taylor formula with integral remainder for Besov-Dunkl spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chokri Abdelkefi, Faten Rached, Safa Chabchoub","submitted_at":"2016-05-11T08:34:38Z","abstract_excerpt":"In the present paper, we propose to prove some properties and estimates of the integral remainder in the generalized Taylor formula associated to the Dunkl operator on the real line and to describe the Besov-Dunkl spaces for which the remainder has a given order."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03326","kind":"arxiv","version":5},"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":"2026-05-18T01:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GicpyTByaiHEDbs710ZkMPtvP9Hd545Xh2RbxZqGO5raQ3DcanBWPE/72ZjHlrBPHIU+4cH2CKDC0MfmfjlEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:36:01.648721Z"},"content_sha256":"9248640ab6498d4ad61a92d85a5a54ff5fd2875c9e0705b672a809dbcbb3b1bb","schema_version":"1.0","event_id":"sha256:9248640ab6498d4ad61a92d85a5a54ff5fd2875c9e0705b672a809dbcbb3b1bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AX5B6YQ3TV4J2XCVZWZMH7JEIJ/bundle.json","state_url":"https://pith.science/pith/AX5B6YQ3TV4J2XCVZWZMH7JEIJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AX5B6YQ3TV4J2XCVZWZMH7JEIJ/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":"2026-06-26T04:36:01Z","links":{"resolver":"https://pith.science/pith/AX5B6YQ3TV4J2XCVZWZMH7JEIJ","bundle":"https://pith.science/pith/AX5B6YQ3TV4J2XCVZWZMH7JEIJ/bundle.json","state":"https://pith.science/pith/AX5B6YQ3TV4J2XCVZWZMH7JEIJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AX5B6YQ3TV4J2XCVZWZMH7JEIJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AX5B6YQ3TV4J2XCVZWZMH7JEIJ","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":"0fcaa61a06c9aff07b16894089d7af062ec2a4078715487cf20e6830b8fb2aa4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-11T08:34:38Z","title_canon_sha256":"19239e13718930686b09938eaec0d2cefcf0c010b07babcf3e5761689109f52d"},"schema_version":"1.0","source":{"id":"1605.03326","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03326","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03326v5","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03326","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"AX5B6YQ3TV4J","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AX5B6YQ3TV4J2XCV","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AX5B6YQ3","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:9248640ab6498d4ad61a92d85a5a54ff5fd2875c9e0705b672a809dbcbb3b1bb","target":"graph","created_at":"2026-05-18T01:12:41Z","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 the present paper, we propose to prove some properties and estimates of the integral remainder in the generalized Taylor formula associated to the Dunkl operator on the real line and to describe the Besov-Dunkl spaces for which the remainder has a given order.","authors_text":"Chokri Abdelkefi, Faten Rached, Safa Chabchoub","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-11T08:34:38Z","title":"Generalized Taylor formula with integral remainder for Besov-Dunkl spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03326","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":"sha256:0ddd26dc4a06ebcff94910ac14198d4d95b379f4da01985b161a8f2ccc0c2bb4","target":"record","created_at":"2026-05-18T01:12:41Z","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":"0fcaa61a06c9aff07b16894089d7af062ec2a4078715487cf20e6830b8fb2aa4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-11T08:34:38Z","title_canon_sha256":"19239e13718930686b09938eaec0d2cefcf0c010b07babcf3e5761689109f52d"},"schema_version":"1.0","source":{"id":"1605.03326","kind":"arxiv","version":5}},"canonical_sha256":"05fa1f621b9d789d5c55cdb2c3fd244264a5c673c503f0195c556791befeecd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05fa1f621b9d789d5c55cdb2c3fd244264a5c673c503f0195c556791befeecd2","first_computed_at":"2026-05-18T01:12:41.832556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:41.832556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6ZVopgQWCTKiJCI/aZ2J3PHdh5lOxqdprhWDuWFWTaAzu8f2i8D+n/p4xjWCsCQYN0/JpUHIl5MLTqqzeBtUDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:41.833053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03326","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ddd26dc4a06ebcff94910ac14198d4d95b379f4da01985b161a8f2ccc0c2bb4","sha256:9248640ab6498d4ad61a92d85a5a54ff5fd2875c9e0705b672a809dbcbb3b1bb"],"state_sha256":"6558c79e282c9fc1d287f521017187cc880b41b11bedee5d011ca85fff027b82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bY+pM+Vk9QYA9tf31ktdAw7kVxxUtVGSCT4V9KfOLZOgF0j5ICu0WAw2pYYXOzxMO0b0ZIeH8RLnODtFrUl9DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T04:36:01.650701Z","bundle_sha256":"e0b137d2270227a9486da818c549bcf0a7b4719cf779b596fa85f88ec12a6408"}}