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We call w=s_1+...+s_{d} the weight and d the depth. When \\epsilon_j=-1 we say the jth component is alternating. We first consider Euler sums of the following special type:\n  \\xi(2s_1,...,2s_{d})=\\zeta(2s_1,...,2s_{d};(-1)^{s_1},...,(-","authors_text":"Jianqiang Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-23T12:02:43Z","title":"Restricted Sum Formula of Alternating Euler Sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5366","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:f23eb44fa3aeb4de0cfd0cd22e0d552e49d43529ecdb5bf004b9d798bb205968","target":"record","created_at":"2026-05-18T02:28:21Z","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":"d2169aa757764a9a8100ac031c4a820d4a8b3bddeadc806c0e5c261ecd10892b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-23T12:02:43Z","title_canon_sha256":"056bb4e38ccce0cd4d4420cce966a299ee5e8307ea48953679285eb6fe32fcbb"},"schema_version":"1.0","source":{"id":"1207.5366","kind":"arxiv","version":1}},"canonical_sha256":"86300e2e74493aaa54d3929c2529686cd8ce70ab3709a1eab14dd42368515a2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86300e2e74493aaa54d3929c2529686cd8ce70ab3709a1eab14dd42368515a2d","first_computed_at":"2026-05-18T02:28:21.231921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:21.231921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tA2B/MH6L4BuBlKP5NIB36RTIPOSJ3DXZAfVqRfo/Z6K9o32IUC3PdFXlENm4aHcWKWFrHKymLf5ik4qV/b8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:21.232530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f23eb44fa3aeb4de0cfd0cd22e0d552e49d43529ecdb5bf004b9d798bb205968","sha256:b4b125f4f424e130cfac9e6e97df6342f57b016aa88dbe24a830f55cdd57f8e3"],"state_sha256":"7411e87ee61d5f379bb2ec51940d6969476770981e12d1f64a2dc5818136bf25"}