{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UVLP2LXR2IQ5KNJXCJV4KZU3KW","short_pith_number":"pith:UVLP2LXR","canonical_record":{"source":{"id":"1805.08056","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-17T01:59:18Z","cross_cats_sorted":[],"title_canon_sha256":"24a40d5f92b12f2664dbc7000aa7d43b44e17d5d404e16c2a78dead59bfebfc9","abstract_canon_sha256":"7db059d941cae2cfc672c7652380dd072074b9628257a58ed9163661584d0f64"},"schema_version":"1.0"},"canonical_sha256":"a556fd2ef1d221d53537126bc5669b559ac4636d741e75beebb97881ba4cb41a","source":{"kind":"arxiv","id":"1805.08056","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08056","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08056v3","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08056","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"UVLP2LXR2IQ5","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UVLP2LXR2IQ5KNJX","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UVLP2LXR","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UVLP2LXR2IQ5KNJXCJV4KZU3KW","target":"record","payload":{"canonical_record":{"source":{"id":"1805.08056","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-17T01:59:18Z","cross_cats_sorted":[],"title_canon_sha256":"24a40d5f92b12f2664dbc7000aa7d43b44e17d5d404e16c2a78dead59bfebfc9","abstract_canon_sha256":"7db059d941cae2cfc672c7652380dd072074b9628257a58ed9163661584d0f64"},"schema_version":"1.0"},"canonical_sha256":"a556fd2ef1d221d53537126bc5669b559ac4636d741e75beebb97881ba4cb41a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:25.126568Z","signature_b64":"qUucZ70evF0S9fEFU+SETPv2imymFeIgrwvnUKwwJ6WjsWfqazVLwJp0CV1+cfzsaeapt51iLT1yLqKFpDpiDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a556fd2ef1d221d53537126bc5669b559ac4636d741e75beebb97881ba4cb41a","last_reissued_at":"2026-05-17T23:41:25.125931Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:25.125931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.08056","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ux7LZGTFVEXJUsCcx+gALmxL/ZXGTxfsDy6TkwIEEzu56iuHjTfe41CA0nEiJY77RlWFqWCCyq8tdYR10eAOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:24:50.986128Z"},"content_sha256":"23eeb76980a6709116675c00780c34994aa4fa11377eba31b073f5a047c27d27","schema_version":"1.0","event_id":"sha256:23eeb76980a6709116675c00780c34994aa4fa11377eba31b073f5a047c27d27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UVLP2LXR2IQ5KNJXCJV4KZU3KW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit formulas of Euler sums via multiple zeta values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ce Xu, Weiping Wang","submitted_at":"2018-05-17T01:59:18Z","abstract_excerpt":"Flajolet and Salvy pointed out that every Euler sum is a $\\mathbb{Q}$-linear combination of multiple zeta values. However, in the literature, there is no formula completely revealing this relation. In this paper, using permutations and compositions, we establish two explicit formulas for the Euler sums, and show that all the Euler sums are indeed expressible in terms of MZVs. Moreover, we apply this method to the alternating Euler sums, and show that all the alternating Euler sums are reducible to alternating MZVs. Some famous results, such as the Euler theorem, the Borwein--Borwein--Girgensoh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08056","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yxY/xeQ9Qb+nZDQofHOZKHNV+tTnLVFDwRHxv0tsipu5EE4yB3aADzIHWY839Q7CekwVbUyTDlIiq3htHmx4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:24:50.986488Z"},"content_sha256":"51d5fe08ac5a1fc426c204cfb85091f6da9379f5c5f73a9f538635837107895c","schema_version":"1.0","event_id":"sha256:51d5fe08ac5a1fc426c204cfb85091f6da9379f5c5f73a9f538635837107895c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UVLP2LXR2IQ5KNJXCJV4KZU3KW/bundle.json","state_url":"https://pith.science/pith/UVLP2LXR2IQ5KNJXCJV4KZU3KW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UVLP2LXR2IQ5KNJXCJV4KZU3KW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T04:24:50Z","links":{"resolver":"https://pith.science/pith/UVLP2LXR2IQ5KNJXCJV4KZU3KW","bundle":"https://pith.science/pith/UVLP2LXR2IQ5KNJXCJV4KZU3KW/bundle.json","state":"https://pith.science/pith/UVLP2LXR2IQ5KNJXCJV4KZU3KW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UVLP2LXR2IQ5KNJXCJV4KZU3KW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UVLP2LXR2IQ5KNJXCJV4KZU3KW","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":"7db059d941cae2cfc672c7652380dd072074b9628257a58ed9163661584d0f64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-17T01:59:18Z","title_canon_sha256":"24a40d5f92b12f2664dbc7000aa7d43b44e17d5d404e16c2a78dead59bfebfc9"},"schema_version":"1.0","source":{"id":"1805.08056","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08056","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08056v3","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08056","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"UVLP2LXR2IQ5","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UVLP2LXR2IQ5KNJX","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UVLP2LXR","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:51d5fe08ac5a1fc426c204cfb85091f6da9379f5c5f73a9f538635837107895c","target":"graph","created_at":"2026-05-17T23:41:25Z","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":"Flajolet and Salvy pointed out that every Euler sum is a $\\mathbb{Q}$-linear combination of multiple zeta values. However, in the literature, there is no formula completely revealing this relation. In this paper, using permutations and compositions, we establish two explicit formulas for the Euler sums, and show that all the Euler sums are indeed expressible in terms of MZVs. Moreover, we apply this method to the alternating Euler sums, and show that all the alternating Euler sums are reducible to alternating MZVs. Some famous results, such as the Euler theorem, the Borwein--Borwein--Girgensoh","authors_text":"Ce Xu, Weiping Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-17T01:59:18Z","title":"Explicit formulas of Euler sums via multiple zeta values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08056","kind":"arxiv","version":3},"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":"sha256:23eeb76980a6709116675c00780c34994aa4fa11377eba31b073f5a047c27d27","target":"record","created_at":"2026-05-17T23:41:25Z","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":"7db059d941cae2cfc672c7652380dd072074b9628257a58ed9163661584d0f64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-17T01:59:18Z","title_canon_sha256":"24a40d5f92b12f2664dbc7000aa7d43b44e17d5d404e16c2a78dead59bfebfc9"},"schema_version":"1.0","source":{"id":"1805.08056","kind":"arxiv","version":3}},"canonical_sha256":"a556fd2ef1d221d53537126bc5669b559ac4636d741e75beebb97881ba4cb41a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a556fd2ef1d221d53537126bc5669b559ac4636d741e75beebb97881ba4cb41a","first_computed_at":"2026-05-17T23:41:25.125931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:25.125931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qUucZ70evF0S9fEFU+SETPv2imymFeIgrwvnUKwwJ6WjsWfqazVLwJp0CV1+cfzsaeapt51iLT1yLqKFpDpiDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:25.126568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.08056","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23eeb76980a6709116675c00780c34994aa4fa11377eba31b073f5a047c27d27","sha256:51d5fe08ac5a1fc426c204cfb85091f6da9379f5c5f73a9f538635837107895c"],"state_sha256":"14e42e6ed1d6fecfb0af1f028e0da40fd02d024f02c6367109ac1eca24a48b58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YZgZtk8gmz+rqoSIBoIZqrEf3dihTawrZmurx6L9kmF1Kn4uKK73o6gHIgunS/yw/nRe4xvw+aYgu3HAY5UJDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:24:50.988418Z","bundle_sha256":"d1e6cf18515a21f26bbc581ef0778567928c540ccd72f538f48c1cf00947ad5d"}}