{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5SXW43L3WHF5VXSW7V5VGB2ZIG","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":"e72db47757d5b4ab7304612092e33e86f6a066a909784defbf1178a0c340d4da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-17T17:18:54Z","title_canon_sha256":"d81f4f4437be5e5a93109b69159a18c173b67be50abc1ee438b9526d27355271"},"schema_version":"1.0","source":{"id":"2306.10393","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.10393","created_at":"2026-07-05T10:15:13Z"},{"alias_kind":"arxiv_version","alias_value":"2306.10393v2","created_at":"2026-07-05T10:15:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.10393","created_at":"2026-07-05T10:15:13Z"},{"alias_kind":"pith_short_12","alias_value":"5SXW43L3WHF5","created_at":"2026-07-05T10:15:13Z"},{"alias_kind":"pith_short_16","alias_value":"5SXW43L3WHF5VXSW","created_at":"2026-07-05T10:15:13Z"},{"alias_kind":"pith_short_8","alias_value":"5SXW43L3","created_at":"2026-07-05T10:15:13Z"}],"graph_snapshots":[{"event_id":"sha256:8e8d997b2b9240786b2ef19ae62823f8a2efc6c70c2a328b2c21ea7a2c521cb8","target":"graph","created_at":"2026-07-05T10:15:13Z","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/2306.10393/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any prime $p$ and $\\varepsilon>0$ we prove that for any sufficiently large positive odd integer $s$ at least $(c_p-\\varepsilon) \\sqrt{\\frac{s}{\\log s}}$ of the $p$-adic zeta values $\\zeta_p(3),\\zeta_p(5),\\dots,\\zeta_p(s)$ are irrational. The constant $c_p$ is positive and does only depend on $p$. This result establishes a $p$-adic version of the elimination technique used by Fischler--Sprang--Zudilin and Lai--Yu to prove a similar result on classical zeta values. The main difficulty consists in proving the non-vanishing of the resulting linear forms. We overcome this problem by using a new","authors_text":"Johannes Sprang, Li Lai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-17T17:18:54Z","title":"Many $p$-adic odd zeta values are irrational"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.10393","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":"sha256:67d38f96c47af49aedd94e8d2495100532ed4eda5b5fcb3d83e1f645252569f6","target":"record","created_at":"2026-07-05T10:15:13Z","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":"e72db47757d5b4ab7304612092e33e86f6a066a909784defbf1178a0c340d4da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-17T17:18:54Z","title_canon_sha256":"d81f4f4437be5e5a93109b69159a18c173b67be50abc1ee438b9526d27355271"},"schema_version":"1.0","source":{"id":"2306.10393","kind":"arxiv","version":2}},"canonical_sha256":"ecaf6e6d7bb1cbdade56fd7b53075941b60aa138cf3819dfa7e1f7d77391e21e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecaf6e6d7bb1cbdade56fd7b53075941b60aa138cf3819dfa7e1f7d77391e21e","first_computed_at":"2026-07-05T10:15:13.640730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:15:13.640730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FyR1y51AHUYL0FBJNzw5hAYT3qZ7sGQnMlIgXIfRTKP7dH6Zb9vZMobZZna0/eh2HC3rNIUgdCqwnT7Ln9L4Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T10:15:13.641197Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.10393","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67d38f96c47af49aedd94e8d2495100532ed4eda5b5fcb3d83e1f645252569f6","sha256:8e8d997b2b9240786b2ef19ae62823f8a2efc6c70c2a328b2c21ea7a2c521cb8"],"state_sha256":"be5797e54a4feab28fb5822504ef66370efd36707f0b024bc8a07054e4ce02c7"}