{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YZDCIAJWP5AQNZMU7H2CR5VDX6","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":"ce8e91e27746c02563a45016fbf00c76fcda9ab05a18ebef8b47ffb54692d510","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-02T06:00:32Z","title_canon_sha256":"808fb2d0b678b6dffec62e6d8d839ab964bcb7f18a8e009ae522efb598bdc8a0"},"schema_version":"1.0","source":{"id":"1605.00359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00359","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00359v1","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00359","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"YZDCIAJWP5AQ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YZDCIAJWP5AQNZMU","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YZDCIAJW","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:9e16fb4683f23751025f8be2283fcd1b9a7bd248784d1f05155c2cc511cbc05e","target":"graph","created_at":"2026-05-18T01:15:56Z","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 we introduce the notions of $q$-Duhamel product and $q$-integration operator. We prove that the classical Wiener algebra $W(\\mathbb{D})$ of all analytic functions on the unit disc $\\mathbb{D}$ of the complex plane $\\mathbb{C}$ with absolutely convergent Taylor series is a Banach algebra with respect to $q$-Duhamel product. We also describe the cyclic vectors of the $q$-integration operator on $W(\\mathbb{D})$ and characterize its commutant in terms of the $q$-Duhamel product operators.","authors_text":"F. Bouzeffour, M. T. Garayev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-02T06:00:32Z","title":"Duhamel convolution product in the setting of Quantum calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00359","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:fc82fdb661f505349296714cfa2a83c19155d279ecd6531141caffd844ac0727","target":"record","created_at":"2026-05-18T01:15:56Z","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":"ce8e91e27746c02563a45016fbf00c76fcda9ab05a18ebef8b47ffb54692d510","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-02T06:00:32Z","title_canon_sha256":"808fb2d0b678b6dffec62e6d8d839ab964bcb7f18a8e009ae522efb598bdc8a0"},"schema_version":"1.0","source":{"id":"1605.00359","kind":"arxiv","version":1}},"canonical_sha256":"c6462401367f4106e594f9f428f6a3bf9bbcff3ab45f5c0e04d137949a8cb379","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6462401367f4106e594f9f428f6a3bf9bbcff3ab45f5c0e04d137949a8cb379","first_computed_at":"2026-05-18T01:15:56.051685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:56.051685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NtdtORL+e79u57cjRMugqMJeUb1V7NwP+PNHvMoTAKYy6pU3uL9eKlZlqBT5aNJTDvEFZarSzpbkyiC16nW1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:56.052327Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc82fdb661f505349296714cfa2a83c19155d279ecd6531141caffd844ac0727","sha256:9e16fb4683f23751025f8be2283fcd1b9a7bd248784d1f05155c2cc511cbc05e"],"state_sha256":"b9934283e005b7c14e09dd41cc45afb2ae43bb3c8e46369d79de2881e561cb81"}