{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:SKNUCQI4P7A4KPEHYZ4FFCIGQU","short_pith_number":"pith:SKNUCQI4","canonical_record":{"source":{"id":"0712.1639","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-11T02:51:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f4861fd2d4ba95057ce7042eaa726a59a72bd3f9340c2cc900fa79d576d400cb","abstract_canon_sha256":"8a827459702caafa17ac5cc3b6e4f4e6eca25c945e1dd723baa38ed617b922d3"},"schema_version":"1.0"},"canonical_sha256":"929b41411c7fc1c53c87c67852890685262e86f074b316688844df5d315fbcad","source":{"kind":"arxiv","id":"0712.1639","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1639","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1639v2","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1639","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"SKNUCQI4P7A4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"SKNUCQI4P7A4KPEH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"SKNUCQI4","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:SKNUCQI4P7A4KPEHYZ4FFCIGQU","target":"record","payload":{"canonical_record":{"source":{"id":"0712.1639","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-11T02:51:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f4861fd2d4ba95057ce7042eaa726a59a72bd3f9340c2cc900fa79d576d400cb","abstract_canon_sha256":"8a827459702caafa17ac5cc3b6e4f4e6eca25c945e1dd723baa38ed617b922d3"},"schema_version":"1.0"},"canonical_sha256":"929b41411c7fc1c53c87c67852890685262e86f074b316688844df5d315fbcad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:05.636004Z","signature_b64":"Ikxw8z20jfqsobw1S8aondtI8Sm4NDU8+UAmj3ebHzlyqma5R5GNQUULNrV9ugVVIWyiiKIQmAhpMUnz7YC6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"929b41411c7fc1c53c87c67852890685262e86f074b316688844df5d315fbcad","last_reissued_at":"2026-05-18T03:39:05.635257Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:05.635257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.1639","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tK+yTlo0Yh3cJuRIAhDcN16J7I15DbyiExHEvtGjq95CPYJd1cWHHQ/mEtvOMWnJUJUBnnZzgcZi596/89NyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T15:44:53.162597Z"},"content_sha256":"a72f35597f090cd15c6029e44379c4b81b07941035c06ee8b26dba521a7c9048","schema_version":"1.0","event_id":"sha256:a72f35597f090cd15c6029e44379c4b81b07941035c06ee8b26dba521a7c9048"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:SKNUCQI4P7A4KPEHYZ4FFCIGQU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evaluations of multiple Dirichlet $L$-values via symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Yoshinori Yamasaki","submitted_at":"2007-12-11T02:51:05Z","abstract_excerpt":"We explicitly evaluate a special type of multiple Dirichlet $L$-values at positive integers in two different ways: One approach involves using symmetric functions, while the other involves using a generating function of the values. Equating these two expressions, we derive several summation formulae involving the Bernoulli and Euler numbers. Moreover, values at non-positive integers, called central limit values, are also studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1639","kind":"arxiv","version":2},"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":"2026-05-18T03:39:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8qPP17LOCvydeKOkLNIVC8rwGBBB7qjS7B8REFVALPtXeF5iGSbHbeSlBl1Hgvx2CQPe2iHFUUMQ7o6n1Uk9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T15:44:53.162954Z"},"content_sha256":"fae7d79bc4ee09c7fa0f701e37ed35e8f437d670bfd7bb6f3a813f63b9e7385a","schema_version":"1.0","event_id":"sha256:fae7d79bc4ee09c7fa0f701e37ed35e8f437d670bfd7bb6f3a813f63b9e7385a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKNUCQI4P7A4KPEHYZ4FFCIGQU/bundle.json","state_url":"https://pith.science/pith/SKNUCQI4P7A4KPEHYZ4FFCIGQU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKNUCQI4P7A4KPEHYZ4FFCIGQU/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":"2026-07-01T15:44:53Z","links":{"resolver":"https://pith.science/pith/SKNUCQI4P7A4KPEHYZ4FFCIGQU","bundle":"https://pith.science/pith/SKNUCQI4P7A4KPEHYZ4FFCIGQU/bundle.json","state":"https://pith.science/pith/SKNUCQI4P7A4KPEHYZ4FFCIGQU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKNUCQI4P7A4KPEHYZ4FFCIGQU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:SKNUCQI4P7A4KPEHYZ4FFCIGQU","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":"8a827459702caafa17ac5cc3b6e4f4e6eca25c945e1dd723baa38ed617b922d3","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-11T02:51:05Z","title_canon_sha256":"f4861fd2d4ba95057ce7042eaa726a59a72bd3f9340c2cc900fa79d576d400cb"},"schema_version":"1.0","source":{"id":"0712.1639","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1639","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1639v2","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1639","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"SKNUCQI4P7A4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"SKNUCQI4P7A4KPEH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"SKNUCQI4","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:fae7d79bc4ee09c7fa0f701e37ed35e8f437d670bfd7bb6f3a813f63b9e7385a","target":"graph","created_at":"2026-05-18T03:39:05Z","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":"We explicitly evaluate a special type of multiple Dirichlet $L$-values at positive integers in two different ways: One approach involves using symmetric functions, while the other involves using a generating function of the values. Equating these two expressions, we derive several summation formulae involving the Bernoulli and Euler numbers. Moreover, values at non-positive integers, called central limit values, are also studied.","authors_text":"Yoshinori Yamasaki","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-11T02:51:05Z","title":"Evaluations of multiple Dirichlet $L$-values via symmetric functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1639","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:a72f35597f090cd15c6029e44379c4b81b07941035c06ee8b26dba521a7c9048","target":"record","created_at":"2026-05-18T03:39:05Z","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":"8a827459702caafa17ac5cc3b6e4f4e6eca25c945e1dd723baa38ed617b922d3","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-11T02:51:05Z","title_canon_sha256":"f4861fd2d4ba95057ce7042eaa726a59a72bd3f9340c2cc900fa79d576d400cb"},"schema_version":"1.0","source":{"id":"0712.1639","kind":"arxiv","version":2}},"canonical_sha256":"929b41411c7fc1c53c87c67852890685262e86f074b316688844df5d315fbcad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"929b41411c7fc1c53c87c67852890685262e86f074b316688844df5d315fbcad","first_computed_at":"2026-05-18T03:39:05.635257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:05.635257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ikxw8z20jfqsobw1S8aondtI8Sm4NDU8+UAmj3ebHzlyqma5R5GNQUULNrV9ugVVIWyiiKIQmAhpMUnz7YC6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:05.636004Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.1639","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a72f35597f090cd15c6029e44379c4b81b07941035c06ee8b26dba521a7c9048","sha256:fae7d79bc4ee09c7fa0f701e37ed35e8f437d670bfd7bb6f3a813f63b9e7385a"],"state_sha256":"c527951cd009c9698f895130c6a707459c5888ce9fe17b7c834e28c42a1453f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PRC7NmHMMwKYcBQ+iZQf05UY7Th5+ziQ04oiUPzJBIecNzpjm8MF7G4Rre1/gHBgHqWuBk0BRu0sONEtM54JAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T15:44:53.164986Z","bundle_sha256":"a9a4583268c4c9bd16a23d94645c90444424b0241dacd08466352c88d6ed7946"}}