{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DRHHVPFPQQXOTLMKMPYRHDUQPU","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":"c18102f6174c61d18ab16fb5c6d5fbec9b4c1b00c5a8b6f7b736037dfdd8e412","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-04T10:54:50Z","title_canon_sha256":"fe9bdf17e08286b84bd0d7de870244d2b1fdf2cb47ec220a2e04ef9d0bb9cc67"},"schema_version":"1.0","source":{"id":"1503.01277","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01277","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01277v2","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01277","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"pith_short_12","alias_value":"DRHHVPFPQQXO","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DRHHVPFPQQXOTLMK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DRHHVPFP","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:4982a3404312c46e0f44e1daa355bf8e3b72d6fba7b3b20534d2e4eaf88c5ccd","target":"graph","created_at":"2026-05-18T01:27:38Z","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":"The function $\\sum_{p\\leq x} \\frac{1}{p} - \\log\\log(x) - M$ is known to change sign infinitely often, but so far all calculated values are positive. In this paper we prove that the first sign change occurs well before $\\exp(495.702833165)$.","authors_text":"Jan B\\\"uthe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-04T10:54:50Z","title":"On the first sign change in Mertens' Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01277","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:e214f2df235dfa548ddd867522aba10c8b9e20f2ccedd67882ccf016f68a92f8","target":"record","created_at":"2026-05-18T01:27:38Z","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":"c18102f6174c61d18ab16fb5c6d5fbec9b4c1b00c5a8b6f7b736037dfdd8e412","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-04T10:54:50Z","title_canon_sha256":"fe9bdf17e08286b84bd0d7de870244d2b1fdf2cb47ec220a2e04ef9d0bb9cc67"},"schema_version":"1.0","source":{"id":"1503.01277","kind":"arxiv","version":2}},"canonical_sha256":"1c4e7abcaf842ee9ad8a63f1138e907d1d56acf2333187f6c77c2de3a8c42068","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c4e7abcaf842ee9ad8a63f1138e907d1d56acf2333187f6c77c2de3a8c42068","first_computed_at":"2026-05-18T01:27:38.440273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:38.440273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k5AeaovdhPgyouogTSQCMXdS3xoUBuazOlnDlkKz8i2nD2exKCQwfViVaS6f/9jm0uAsWotqgvfFdBvPR8VsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:38.440826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01277","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e214f2df235dfa548ddd867522aba10c8b9e20f2ccedd67882ccf016f68a92f8","sha256:4982a3404312c46e0f44e1daa355bf8e3b72d6fba7b3b20534d2e4eaf88c5ccd"],"state_sha256":"45a9703da8341b3a81290154d8e2a3306d8b6098d13ea8c59dea7acd0bda44eb"}