{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IOZJFJOEP4V3C25AJ47ZU7NFWU","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":"abc07b7db0dcaf5951a38ec9375879b121c132364aa97b6d136b748a496dd234","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-15T13:31:55Z","title_canon_sha256":"5292cecffe8b6e80e2db12163a683e5f189d62bf37af870fe12f2bf7ca502abd"},"schema_version":"1.0","source":{"id":"1905.06171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.06171","created_at":"2026-05-17T23:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1905.06171v1","created_at":"2026-05-17T23:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06171","created_at":"2026-05-17T23:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"IOZJFJOEP4V3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IOZJFJOEP4V3C25A","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IOZJFJOE","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:c9db800c40528279d8e1db4aa9b834792b89a7fa7990068aebe462933ef00105","target":"graph","created_at":"2026-05-17T23:46:07Z","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 provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.","authors_text":"Ayhan Dil, Khristo N. Boyadzhiev","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-15T13:31:55Z","title":"Geometric Polynomials: Properties and Applications to Series with Zeta Values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06171","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:fdc9ad7d9aa380b2b286ad9a9adafb0e5bfe8b3ed4c6559e39314ac8372606a0","target":"record","created_at":"2026-05-17T23:46:07Z","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":"abc07b7db0dcaf5951a38ec9375879b121c132364aa97b6d136b748a496dd234","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-15T13:31:55Z","title_canon_sha256":"5292cecffe8b6e80e2db12163a683e5f189d62bf37af870fe12f2bf7ca502abd"},"schema_version":"1.0","source":{"id":"1905.06171","kind":"arxiv","version":1}},"canonical_sha256":"43b292a5c47f2bb16ba04f3f9a7da5b520a1d5c729ac1d38b58e9a04878655e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43b292a5c47f2bb16ba04f3f9a7da5b520a1d5c729ac1d38b58e9a04878655e3","first_computed_at":"2026-05-17T23:46:07.261901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:07.261901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3MaQ+3cpkOQngjkG5ZTJcf+wIWYf/zov9Fzxg6PfiwxzRwlXlp43nvy1EjB/fS4C/cbyaX4cTOap9Xj0R/JJAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:07.262638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.06171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdc9ad7d9aa380b2b286ad9a9adafb0e5bfe8b3ed4c6559e39314ac8372606a0","sha256:c9db800c40528279d8e1db4aa9b834792b89a7fa7990068aebe462933ef00105"],"state_sha256":"0e823836dffcb14198d87a81b77e5737198b4b4008f43482437c465344462f28"}