{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:66X2APXIWBVYLMOAIWCRBTGSA5","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":"0aa472d889b19e640487bfbc09742b477918a27fbcbbb911c95d11d5c4c3292d","cross_cats_sorted":["math.AG","math.CA","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-08T07:22:25Z","title_canon_sha256":"2da9206f8eea44ccfbbcc8a0792dde83cf06b32f9cbc22bd08b1a6f8043ee306"},"schema_version":"1.0","source":{"id":"2505.05005","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.05005","created_at":"2026-05-28T01:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"2505.05005v2","created_at":"2026-05-28T01:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.05005","created_at":"2026-05-28T01:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"66X2APXIWBVY","created_at":"2026-05-28T01:04:06Z"},{"alias_kind":"pith_short_16","alias_value":"66X2APXIWBVYLMOA","created_at":"2026-05-28T01:04:06Z"},{"alias_kind":"pith_short_8","alias_value":"66X2APXI","created_at":"2026-05-28T01:04:06Z"}],"graph_snapshots":[{"event_id":"sha256:2a69466d79969e44cb76e32e520f5e1f729ee9b54af00f976928eef140762567","target":"graph","created_at":"2026-05-28T01:04:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.05005/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a spirit of Ap\\'ery's proof of the irrationality of $\\zeta(3)$, we construct a sequence $p_n/q_n$ of rational approximations to the $2$-adic zeta value $\\zeta_2(5)$ which satisfy $0 < |\\zeta_2(5)-p_n/q_n|_2 < \\max\\{|p_n|,|q_n|\\}^{-1-\\delta}$ for an explicit constant $\\delta>0$. This leads to a new proof of the irrationality of $\\zeta_2(5)$, the result established recently by Calegari, Dimitrov and Tang using a different method. Furthermore, our approximations allow us to obtain an upper bound for the irrationality measure of this $2$-adic quantity; namely, we show that $\\mu(\\zeta_2(5)) \\le ","authors_text":"Johannes Sprang, Li Lai, Wadim Zudilin","cross_cats":["math.AG","math.CA","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-08T07:22:25Z","title":"A note on the irrationality of $\\zeta_2(5)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.05005","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":"sha256:9918f5903d8a6cc49924627c94a1e83cb14852eaf2839cfebe828c783e63adf4","target":"record","created_at":"2026-05-28T01:04:06Z","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":"0aa472d889b19e640487bfbc09742b477918a27fbcbbb911c95d11d5c4c3292d","cross_cats_sorted":["math.AG","math.CA","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-08T07:22:25Z","title_canon_sha256":"2da9206f8eea44ccfbbcc8a0792dde83cf06b32f9cbc22bd08b1a6f8043ee306"},"schema_version":"1.0","source":{"id":"2505.05005","kind":"arxiv","version":2}},"canonical_sha256":"f7afa03ee8b06b85b1c0458510ccd2075099f86b0919d4dbea3ae441224ec585","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7afa03ee8b06b85b1c0458510ccd2075099f86b0919d4dbea3ae441224ec585","first_computed_at":"2026-05-28T01:04:06.966267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:06.966267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WTJiDPfPW9qPu5DCAslzxJ5cvgC61BGnAMIZvsmJYDqjtWVpDEcT0g90W3mmxe1Ld3tzA2lPCiMvxP7obWQqCQ==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:06.967053Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.05005","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9918f5903d8a6cc49924627c94a1e83cb14852eaf2839cfebe828c783e63adf4","sha256:2a69466d79969e44cb76e32e520f5e1f729ee9b54af00f976928eef140762567"],"state_sha256":"d28bcb198dabcacd4a1a871cfa337f80b30c40b712df4866b8ea1d10e804ceeb"}