{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LSSFKFKYQH66MRD7W533EU7AF3","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":"022b0a2412b4a7e9113539b5527e16f8618259ba4582ea85cd036128c1368f84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-04T21:11:04Z","title_canon_sha256":"e79825121e7f43ca2be92f5369c3305e9a0dd2075f718157c9742b10fbd70c0a"},"schema_version":"1.0","source":{"id":"1204.1078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1078","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1078v1","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1078","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"pith_short_12","alias_value":"LSSFKFKYQH66","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LSSFKFKYQH66MRD7","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LSSFKFKY","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:1872fc57490bd65af69215f6aaf364ab10a0a738c8787b1abf575a4f3fc8b3b1","target":"graph","created_at":"2026-05-18T03:58:36Z","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":"The inverse central binomial series {equation}S_k(z)=\\sum_{n=1}^{\\infty}\\frac{n^k z^n}{\\binom{2n}{n}}{equation} popularized by Ap\\'ery and Lehmer is evaluated for positive integers $k$ along with the asymptotic behavior for large $k$. It is found that value $z=2$, as commented on by D. H. Lehmer provides a unique relation to $\\pi$.","authors_text":"M. L. Glasser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-04T21:11:04Z","title":"A Generalized Apery Series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1078","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:e3d7f69568f5229ed76fadf98a7dc5febbd71c798072727ef28d3434f8272e65","target":"record","created_at":"2026-05-18T03:58:36Z","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":"022b0a2412b4a7e9113539b5527e16f8618259ba4582ea85cd036128c1368f84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-04T21:11:04Z","title_canon_sha256":"e79825121e7f43ca2be92f5369c3305e9a0dd2075f718157c9742b10fbd70c0a"},"schema_version":"1.0","source":{"id":"1204.1078","kind":"arxiv","version":1}},"canonical_sha256":"5ca455155881fde6447fb777b253e02edb67f2e3f27626f5305e9a6b67b903b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ca455155881fde6447fb777b253e02edb67f2e3f27626f5305e9a6b67b903b1","first_computed_at":"2026-05-18T03:58:36.457377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:36.457377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7VVMkB/Ngi6SUISLaP3weOmYYn+SzR2VUG+Kke+GxbH341R7nR1Ies9SCJA8WvX6ahmVCaldZHdp4zoRtXm8DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:36.457965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3d7f69568f5229ed76fadf98a7dc5febbd71c798072727ef28d3434f8272e65","sha256:1872fc57490bd65af69215f6aaf364ab10a0a738c8787b1abf575a4f3fc8b3b1"],"state_sha256":"099ffd60380af86867243b7515e7a7660fb730f7ef7f0dde7a92b7fef3c378fb"}