{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:K2K52ZHQVPRP25SZC3TPTIMBMN","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":"aa74ac7733746ffa754a7cbe2b56a53f0d07a41c6b46e9e56eb60c2e5c8fe883","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-13T07:06:14Z","title_canon_sha256":"bbe8367481e44e3cfa03100b9c93674967d490101adaff4eddcd071ea86f4d04"},"schema_version":"1.0","source":{"id":"1202.2643","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2643","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2643v1","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2643","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"K2K52ZHQVPRP","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K2K52ZHQVPRP25SZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K2K52ZHQ","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:e6c322d5b098edf86d3fedcdcc8722f9129280617f072ee868c7df2311de78e4","target":"graph","created_at":"2026-05-18T03:16:59Z","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, the authors deal with the $q$-Genocchi numbers and polynomials with weight zero. They discover some interesting relations via the $p$-adic $q$-integral on $\\mathbb{Z}_{p}$ and familiar basis Bernstein polynomials. Finally, the authors show that the $p$-adic $\\log$ gamma functions are associated with the $q$-Genocchi numbers and polynomials with weight zero.","authors_text":"Feng Qi, Mehmet Acikgoz, Serkan Araci","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-13T07:06:14Z","title":"On the $q$-Genocchi numbers and polynomials with weight zero and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2643","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:f8146cdc030e949456ccd928b4da61198527a7830219c75e6e9b0949e5e730c2","target":"record","created_at":"2026-05-18T03:16:59Z","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":"aa74ac7733746ffa754a7cbe2b56a53f0d07a41c6b46e9e56eb60c2e5c8fe883","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-13T07:06:14Z","title_canon_sha256":"bbe8367481e44e3cfa03100b9c93674967d490101adaff4eddcd071ea86f4d04"},"schema_version":"1.0","source":{"id":"1202.2643","kind":"arxiv","version":1}},"canonical_sha256":"5695dd64f0abe2fd765916e6f9a181634ddc46283c795ed747cf62d5c50ec833","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5695dd64f0abe2fd765916e6f9a181634ddc46283c795ed747cf62d5c50ec833","first_computed_at":"2026-05-18T03:16:59.094629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:59.094629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vLGzl0quwVbXe5ezJjW0G8I7nFOn5tmCp/L89Qqti30l/Lc06ubO7wmuK2k4uD2dvKlnN5VVSNmAcL6lv5uyAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:59.095307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2643","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8146cdc030e949456ccd928b4da61198527a7830219c75e6e9b0949e5e730c2","sha256:e6c322d5b098edf86d3fedcdcc8722f9129280617f072ee868c7df2311de78e4"],"state_sha256":"5662fd3359c24155dc5ba91b902802e32aecc05917832529bdccb92542e91fed"}