{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KTRBUTTA4VNZFO3MB6QO5SASBQ","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":"e067cd2eb070cae50bebf466ebb61d7ea76a12ecde7a23c9d31e9d4b249c05a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-05T13:35:37Z","title_canon_sha256":"60eb7dd0b1e22e9892de99a5e25fdf27bfaaa5728fc505ced7b8c5bd8915982f"},"schema_version":"1.0","source":{"id":"1904.03060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03060","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03060v1","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03060","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"pith_short_12","alias_value":"KTRBUTTA4VNZ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KTRBUTTA4VNZFO3M","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KTRBUTTA","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:978f7264e98b75c4b4a42ee3acf1ca2e1fa5787c2e14370beff0665b6072bf24","target":"graph","created_at":"2026-05-17T23:49:18Z","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 prove that the integer part of the reciprocal of the tail of $\\zeta(s)$ at a rational number $s=\\frac{1}{p}$ for any integer with $p \\geq 5$ or $s=\\frac{2}{p}$ for any odd integer with $p \\geq 5$ can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\\frac{2}{p},$ we use a result on the finiteness of integral points of certain curves over $\\mathbb{Q}$.","authors_text":"Kyunghwan Song, WonTae Hwang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-05T13:35:37Z","title":"On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03060","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:e4cebea40112a8249e6ae7da7f5ce17ad37ee37ad5c5bac5a7a2f5800edabc94","target":"record","created_at":"2026-05-17T23:49:18Z","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":"e067cd2eb070cae50bebf466ebb61d7ea76a12ecde7a23c9d31e9d4b249c05a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-05T13:35:37Z","title_canon_sha256":"60eb7dd0b1e22e9892de99a5e25fdf27bfaaa5728fc505ced7b8c5bd8915982f"},"schema_version":"1.0","source":{"id":"1904.03060","kind":"arxiv","version":1}},"canonical_sha256":"54e21a4e60e55b92bb6c0fa0eec8120c300bf8ef6823e8f1922e25f366601ba9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54e21a4e60e55b92bb6c0fa0eec8120c300bf8ef6823e8f1922e25f366601ba9","first_computed_at":"2026-05-17T23:49:18.736209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:18.736209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PkRabD2FIygeoatPivRXzJe7jmSAfcQP9JQyQtRW8a6dDP8S5tCXSsf4y59CUYFFu6ZBPuILfUGgCrWRpvI7AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:18.736686Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4cebea40112a8249e6ae7da7f5ce17ad37ee37ad5c5bac5a7a2f5800edabc94","sha256:978f7264e98b75c4b4a42ee3acf1ca2e1fa5787c2e14370beff0665b6072bf24"],"state_sha256":"fc954b1ad741236583277463278f0808dc5770d057fa3ceaebe0834fe0d7fd85"}