{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5EI3Y4OVZN3HCEXJFKIGSODDCU","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":"aacfe4fb296bb448fd7a348664a6c19e0b9df04240f9c42c2611637343017af4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-25T04:40:47Z","title_canon_sha256":"b428b7388963aa301809a78876b80467efc7cadce682d09b0061b953ee5ffa01"},"schema_version":"1.0","source":{"id":"1506.07612","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07612","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07612v2","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07612","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"5EI3Y4OVZN3H","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5EI3Y4OVZN3HCEXJ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5EI3Y4OV","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:e73d6cb1da35089f44b4bc46712b542b0624085e43961d253215629860c463d8","target":"graph","created_at":"2026-05-18T01:11:08Z","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 1998 Don Zagier introduced the modified Bernoulli numbers $B_{n}^{*}$ and showed that they satisfy amusing variants of some properties of Bernoulli numbers. In particular, he studied the asymptotic behavior of $B_{2n}^{*}$, and also obtained an exact formula for them, the motivation for which came from the representation of $B_{2n}$ in terms of the Riemann zeta function $\\zeta(2n)$. The modified Bernoulli numbers were recently generalized to Zagier polynomials $B_{n}^{*}(x)$. For $0<x<1$, an exact formula for $B_{2n}^{*}(x)$ involving infinite series of Bessel function of the second kind an","authors_text":"Atul Dixit, Christophe Vignat, M. Lawrence Glasser, Victor H. Moll","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-25T04:40:47Z","title":"Asymptotics and exact formulas for Zagier polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07612","kind":"arxiv","version":2},"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":"sha256:64af6b81e6871985e1af7cbe644cbe2dc09eb4ff0995bff41b4586fa7f6e7637","target":"record","created_at":"2026-05-18T01:11:08Z","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":"aacfe4fb296bb448fd7a348664a6c19e0b9df04240f9c42c2611637343017af4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-25T04:40:47Z","title_canon_sha256":"b428b7388963aa301809a78876b80467efc7cadce682d09b0061b953ee5ffa01"},"schema_version":"1.0","source":{"id":"1506.07612","kind":"arxiv","version":2}},"canonical_sha256":"e911bc71d5cb767112e92a9069386315142bd3b9888b8dbb5baeb1440c9fa515","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e911bc71d5cb767112e92a9069386315142bd3b9888b8dbb5baeb1440c9fa515","first_computed_at":"2026-05-18T01:11:08.574827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:08.574827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lYhiudrrIilnYXf1FDjilFwvsknypWu5pY9pAFwiWq2VPFdh4nELk5ewhBnAHci9ztKs2hajakO6lFooQSX/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:08.575414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07612","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64af6b81e6871985e1af7cbe644cbe2dc09eb4ff0995bff41b4586fa7f6e7637","sha256:e73d6cb1da35089f44b4bc46712b542b0624085e43961d253215629860c463d8"],"state_sha256":"b2886ceb334e1258e3a7105a563fb5ec4c8fcf8d9495d34a59b77cb0b13dd585"}