{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:HH7LWVAI4UKEJMNRLDAX6NAFFI","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":"b582d199222f8556405e2072d2f7ee162aa36f08d254dbbeaa2f4f757ff178b1","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2007-03-17T00:57:15Z","title_canon_sha256":"86555cc04faac039743725dae5cbb8bbe03e41d5892c355c52c78a539732b4cd"},"schema_version":"1.0","source":{"id":"math/0703508","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703508","created_at":"2026-05-17T23:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703508v2","created_at":"2026-05-17T23:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703508","created_at":"2026-05-17T23:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"HH7LWVAI4UKE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"HH7LWVAI4UKEJMNR","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"HH7LWVAI","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:8707fec7a744f8a6f4eb5cb0af666144ad59a8afe91c0f63b4d580e24c220238","target":"graph","created_at":"2026-05-17T23:47:21Z","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 define a family {$\\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent monotonicity is investigated. We also prove that a certain property of these numbers is equivalent to the Riemann Hypothesis.","authors_text":"Harold G. Diamond, Kevin Ford","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2007-03-17T00:57:15Z","title":"Generalized Euler constants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703508","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:e7d4bfce042d3eaca1f9602a107a439df9edae2341301ca0e79dd493586b137f","target":"record","created_at":"2026-05-17T23:47:21Z","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":"b582d199222f8556405e2072d2f7ee162aa36f08d254dbbeaa2f4f757ff178b1","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2007-03-17T00:57:15Z","title_canon_sha256":"86555cc04faac039743725dae5cbb8bbe03e41d5892c355c52c78a539732b4cd"},"schema_version":"1.0","source":{"id":"math/0703508","kind":"arxiv","version":2}},"canonical_sha256":"39febb5408e51444b1b158c17f34052a0ad418f57b26500373ed9b2d5be593ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39febb5408e51444b1b158c17f34052a0ad418f57b26500373ed9b2d5be593ef","first_computed_at":"2026-05-17T23:47:21.383087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:21.383087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZZthGw4oeMOMnWq1HL7SW3TLLN+s1j1lJrC2yWZMaeUdqOjb9vgj3Jk1B8hD9PcL0JLMsX8IR+cMOOF2WS4+DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:21.383462Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0703508","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7d4bfce042d3eaca1f9602a107a439df9edae2341301ca0e79dd493586b137f","sha256:8707fec7a744f8a6f4eb5cb0af666144ad59a8afe91c0f63b4d580e24c220238"],"state_sha256":"c2cae18ad7cc9313d0be9a7a786ecdfb417152989853a55b251144c7565c1bc1"}