{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MQIWWXQP3J2NXIY6Q7WIW6YMOB","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":"2ccb0473892ccd52e2d9850ac3125c5e4bfa0d36258b3e9f903664dc9544d82a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-05-03T06:51:05Z","title_canon_sha256":"7dc73be1d96f4425de55a9cac264f8aecaba01e5387f0533bc775558e0f5f28a"},"schema_version":"1.0","source":{"id":"1705.01269","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01269","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01269v1","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01269","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"MQIWWXQP3J2N","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MQIWWXQP3J2NXIY6","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MQIWWXQP","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:81ed0105864a50b382cc7855bbc14ba75c6b7125ad26153560cd42ac28757a09","target":"graph","created_at":"2026-05-18T00:45:05Z","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 this work, we derive relations between generating functions of double stuffle relations and double shuffle relations to express the alternating double Euler sums $\\zeta\\left(\\overline{r}, s\\right)$, $\\zeta\\left(r, \\overline{s}\\right)$ and $\\zeta\\left(\\overline{r}, \\overline{s}\\right)$ with $r+s$ odd in terms of zeta values. We also give a direct proof of a hypergeometric identity which is a limiting case of a basic hypergeometric identity of Andrews. Finally, we gave another proof for the formula of Zagier on the multiple zeta values $\\zeta(2,\\ldots,2,3,2,\\ldots,2)$.","authors_text":"Lee-Peng Teo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-05-03T06:51:05Z","title":"Alternating Double Euler Sums, Hypergeometric Identities and a Theorem of Zagier"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01269","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":"sha256:645480ef78db6d7c076a2078c9331f7ac179eb0611ef54be432a920e54a8eb58","target":"record","created_at":"2026-05-18T00:45:05Z","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":"2ccb0473892ccd52e2d9850ac3125c5e4bfa0d36258b3e9f903664dc9544d82a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-05-03T06:51:05Z","title_canon_sha256":"7dc73be1d96f4425de55a9cac264f8aecaba01e5387f0533bc775558e0f5f28a"},"schema_version":"1.0","source":{"id":"1705.01269","kind":"arxiv","version":1}},"canonical_sha256":"64116b5e0fda74dba31e87ec8b7b0c7079e6a2c2a57d4b43660e2f3444256d05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64116b5e0fda74dba31e87ec8b7b0c7079e6a2c2a57d4b43660e2f3444256d05","first_computed_at":"2026-05-18T00:45:05.517465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:05.517465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3PncBOH4PkeFGBqwyHzBDa7GSZHxgd27JSNoifFDP8ITICiJ1n4zrE8enU3M9NrAACgFs9b+o0S33xwkTTp0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:05.517876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01269","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:645480ef78db6d7c076a2078c9331f7ac179eb0611ef54be432a920e54a8eb58","sha256:81ed0105864a50b382cc7855bbc14ba75c6b7125ad26153560cd42ac28757a09"],"state_sha256":"3838abad5d92140ed0fa057d066b8bc4ceb38d7a73323cf021de10708a94a426"}