{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SYKTM5IZB5H6QEGTLWAXMKL4RW","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":"905bfb57fac9a575e4a9f56ff9ee0e6c15d7527fd83dafaaaaedc50783f24eb7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-07T15:41:37Z","title_canon_sha256":"b4ecc764400af42f0d8cd7417dc54ad6239be7862c60fb9c076d6f189fe7de96"},"schema_version":"1.0","source":{"id":"1008.1351","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1351","created_at":"2026-05-18T02:05:58Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1351v1","created_at":"2026-05-18T02:05:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1351","created_at":"2026-05-18T02:05:58Z"},{"alias_kind":"pith_short_12","alias_value":"SYKTM5IZB5H6","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SYKTM5IZB5H6QEGT","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SYKTM5IZ","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:fb03a37bb1bcb09c5090de82fd2c209fa9f9ef6377eca323f066830c266ad96a","target":"graph","created_at":"2026-05-18T02:05:58Z","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":"From the realization of $q-$oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szeg\\H{o} polynomials as well as their relevant properties. We also compute the matrix elements associated to the $(p,q)-$oscillator algebra (a generalization of the $q-$one) and perform the Fourier-Gauss transform of a generalization of the deformed exponential functions.","authors_text":"E. B. Ngompe Nkouankam, M. N. Hounkonnou","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-07T15:41:37Z","title":"$(q,\\mu)$ and $(p,q,\\zeta)-$exponential functions: Rogers-Szeg\\H{o} polynomials and Fourier-Gauss transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1351","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":"sha256:6015d3f2085d23175cb19636a372e982d7828010f781e1d9b517904fa61289ab","target":"record","created_at":"2026-05-18T02:05:58Z","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":"905bfb57fac9a575e4a9f56ff9ee0e6c15d7527fd83dafaaaaedc50783f24eb7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-07T15:41:37Z","title_canon_sha256":"b4ecc764400af42f0d8cd7417dc54ad6239be7862c60fb9c076d6f189fe7de96"},"schema_version":"1.0","source":{"id":"1008.1351","kind":"arxiv","version":1}},"canonical_sha256":"96153675190f4fe810d35d8176297c8d8d351c053d2e56a8cc852f97d796b07d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96153675190f4fe810d35d8176297c8d8d351c053d2e56a8cc852f97d796b07d","first_computed_at":"2026-05-18T02:05:58.077881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:58.077881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HQh/J8GpQp7s9UyvBZK3tGGcuCzX2iBgSi4hCWin2skX28xFHv7ol5eA8hbtl4AgULUugvulFBYN5HIqSVgNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:58.078598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1351","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6015d3f2085d23175cb19636a372e982d7828010f781e1d9b517904fa61289ab","sha256:fb03a37bb1bcb09c5090de82fd2c209fa9f9ef6377eca323f066830c266ad96a"],"state_sha256":"10dc9f2e46f013c0a88c84dab9cab629da541f4de458d2d96b7dde7738c52a21"}