{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:7E5GT76YFOTT44UG3WTNBOW6HL","short_pith_number":"pith:7E5GT76Y","canonical_record":{"source":{"id":"0710.1127","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2007-10-05T03:06:44Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"de52e23bb40b7f36be474e52ae36203fecc561758a949814bbed1905170f34ce","abstract_canon_sha256":"3bd00275ef7904380817fdf6945e3eb687cbba5e80a25cf4432af9f05e79b0c0"},"schema_version":"1.0"},"canonical_sha256":"f93a69ffd82ba73e7286dda6d0bade3af371f82da41c812510e3de730cce6134","source":{"kind":"arxiv","id":"0710.1127","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.1127","created_at":"2026-05-18T01:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"0710.1127v1","created_at":"2026-05-18T01:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.1127","created_at":"2026-05-18T01:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"7E5GT76YFOTT","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"7E5GT76YFOTT44UG","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"7E5GT76Y","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:7E5GT76YFOTT44UG3WTNBOW6HL","target":"record","payload":{"canonical_record":{"source":{"id":"0710.1127","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2007-10-05T03:06:44Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"de52e23bb40b7f36be474e52ae36203fecc561758a949814bbed1905170f34ce","abstract_canon_sha256":"3bd00275ef7904380817fdf6945e3eb687cbba5e80a25cf4432af9f05e79b0c0"},"schema_version":"1.0"},"canonical_sha256":"f93a69ffd82ba73e7286dda6d0bade3af371f82da41c812510e3de730cce6134","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:59.758716Z","signature_b64":"ZRjB34x0TE/V6cNJwoh2yHuqcTvhuBDoGHanPTS5rc9recU+2IPVF01Om96M86bO5yGgVrfLRwcZ93SmvSo1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f93a69ffd82ba73e7286dda6d0bade3af371f82da41c812510e3de730cce6134","last_reissued_at":"2026-05-18T01:02:59.758048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:59.758048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.1127","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"42WmP1JJVfaIh0bAg8tZeu/UESuTrX3z1PRqLlorGELz/gDD2l5DoLIXQQx8ZY7vAvESfO4e1uIoIZ7cHVMdCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:29:34.310591Z"},"content_sha256":"0a90818e4d5f4c1c715847845b94a466f85614663147a45df91ca8c76e02d1c2","schema_version":"1.0","event_id":"sha256:0a90818e4d5f4c1c715847845b94a466f85614663147a45df91ca8c76e02d1c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:7E5GT76YFOTT44UG3WTNBOW6HL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The values of an Euler sum at negative integers and relation to a convolution of Bernoulli numbers","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"H. Gopalkrishna Gadiyar, Khristo N. Boyadzhiev, R. Padma","submitted_at":"2007-10-05T03:06:44Z","abstract_excerpt":"We study a special Dirichlet series studied before by Apostol and Matsuoka and specify its values at negative integers. These values are related to a certain convolution of Bernoulli numbers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.1127","kind":"arxiv","version":1},"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":"2026-05-18T01:02:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0u9j2fvowZhpLvUK53QqOEpOo88GgGrTCfLYV1h/OlT6HZkkXsIWq6IjdHNqYhMG+ZlPH2go/S27+xTD2zKGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:29:34.311411Z"},"content_sha256":"09ca04937519c724eef0f58681f53abc6e5ac49db8053f56493c19d49e382f72","schema_version":"1.0","event_id":"sha256:09ca04937519c724eef0f58681f53abc6e5ac49db8053f56493c19d49e382f72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7E5GT76YFOTT44UG3WTNBOW6HL/bundle.json","state_url":"https://pith.science/pith/7E5GT76YFOTT44UG3WTNBOW6HL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7E5GT76YFOTT44UG3WTNBOW6HL/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":"2026-05-31T15:29:34Z","links":{"resolver":"https://pith.science/pith/7E5GT76YFOTT44UG3WTNBOW6HL","bundle":"https://pith.science/pith/7E5GT76YFOTT44UG3WTNBOW6HL/bundle.json","state":"https://pith.science/pith/7E5GT76YFOTT44UG3WTNBOW6HL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7E5GT76YFOTT44UG3WTNBOW6HL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:7E5GT76YFOTT44UG3WTNBOW6HL","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":"3bd00275ef7904380817fdf6945e3eb687cbba5e80a25cf4432af9f05e79b0c0","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.CA","submitted_at":"2007-10-05T03:06:44Z","title_canon_sha256":"de52e23bb40b7f36be474e52ae36203fecc561758a949814bbed1905170f34ce"},"schema_version":"1.0","source":{"id":"0710.1127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.1127","created_at":"2026-05-18T01:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"0710.1127v1","created_at":"2026-05-18T01:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.1127","created_at":"2026-05-18T01:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"7E5GT76YFOTT","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"7E5GT76YFOTT44UG","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"7E5GT76Y","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:09ca04937519c724eef0f58681f53abc6e5ac49db8053f56493c19d49e382f72","target":"graph","created_at":"2026-05-18T01:02:59Z","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 study a special Dirichlet series studied before by Apostol and Matsuoka and specify its values at negative integers. These values are related to a certain convolution of Bernoulli numbers","authors_text":"H. Gopalkrishna Gadiyar, Khristo N. Boyadzhiev, R. Padma","cross_cats":["math.NT"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2007-10-05T03:06:44Z","title":"The values of an Euler sum at negative integers and relation to a convolution of Bernoulli numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.1127","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":"sha256:0a90818e4d5f4c1c715847845b94a466f85614663147a45df91ca8c76e02d1c2","target":"record","created_at":"2026-05-18T01:02:59Z","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":"3bd00275ef7904380817fdf6945e3eb687cbba5e80a25cf4432af9f05e79b0c0","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.CA","submitted_at":"2007-10-05T03:06:44Z","title_canon_sha256":"de52e23bb40b7f36be474e52ae36203fecc561758a949814bbed1905170f34ce"},"schema_version":"1.0","source":{"id":"0710.1127","kind":"arxiv","version":1}},"canonical_sha256":"f93a69ffd82ba73e7286dda6d0bade3af371f82da41c812510e3de730cce6134","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f93a69ffd82ba73e7286dda6d0bade3af371f82da41c812510e3de730cce6134","first_computed_at":"2026-05-18T01:02:59.758048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:59.758048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZRjB34x0TE/V6cNJwoh2yHuqcTvhuBDoGHanPTS5rc9recU+2IPVF01Om96M86bO5yGgVrfLRwcZ93SmvSo1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:59.758716Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.1127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a90818e4d5f4c1c715847845b94a466f85614663147a45df91ca8c76e02d1c2","sha256:09ca04937519c724eef0f58681f53abc6e5ac49db8053f56493c19d49e382f72"],"state_sha256":"0b768a1a199728a4903538239aaee308eb7183468ef6d43118e67e98b258003b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i5qUndsZq1/SAVx+17hiRmX9YLvi13PrxHJIOvdz1rqgNZV8mgPvRA/EWo13IxtJ3XylBXdaCWJHPzfidmh9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:29:34.316297Z","bundle_sha256":"f10820d190e938e242ad2678c4d16d333e20e2c92289758e20117564f03d3e94"}}