{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX","short_pith_number":"pith:WJ6NUZAE","canonical_record":{"source":{"id":"1505.03589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-14T01:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"9382011fad02ca3cd1794faf8a8ea4f1cf0cdbfe3e4c8883b537007a03f425d1","abstract_canon_sha256":"a3ac1e93b444f5339498c2ee6770d25758cabcd8a02363a8422d6ab2969ea91a"},"schema_version":"1.0"},"canonical_sha256":"b27cda6404cea7b57722762c7870dfbdca7b672f874f0611c12a3ffbf5e64534","source":{"kind":"arxiv","id":"1505.03589","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03589","created_at":"2026-05-18T02:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03589v1","created_at":"2026-05-18T02:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03589","created_at":"2026-05-18T02:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"WJ6NUZAEZ2T3","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WJ6NUZAEZ2T3K5ZC","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WJ6NUZAE","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX","target":"record","payload":{"canonical_record":{"source":{"id":"1505.03589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-14T01:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"9382011fad02ca3cd1794faf8a8ea4f1cf0cdbfe3e4c8883b537007a03f425d1","abstract_canon_sha256":"a3ac1e93b444f5339498c2ee6770d25758cabcd8a02363a8422d6ab2969ea91a"},"schema_version":"1.0"},"canonical_sha256":"b27cda6404cea7b57722762c7870dfbdca7b672f874f0611c12a3ffbf5e64534","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:53.632846Z","signature_b64":"ZO+6B8Fa/lx8RX43Vf6avJP1E/FyAfhikirUYn+BEQcmaFpGJT/gj8ogn/5QQGd9MOjyCywetuGfGNoJhz9KBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b27cda6404cea7b57722762c7870dfbdca7b672f874f0611c12a3ffbf5e64534","last_reissued_at":"2026-05-18T02:09:53.632155Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:53.632155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.03589","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":"2026-05-18T02:09:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R4VUv02ut+7FmCrtZoa4Kty5Rp9vk+PPy0JahDM6JN3WeFcFfFKVKIcOPSNxIHiuW1/V1XeRPMrO6P44UQUoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:04:13.981154Z"},"content_sha256":"7d26273605333d9c3102dc0bf6973eaeded458103f6922a15e95c2f54d825054","schema_version":"1.0","event_id":"sha256:7d26273605333d9c3102dc0bf6973eaeded458103f6922a15e95c2f54d825054"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sign changes in Mertens' first and second theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jeffrey P.S. Lay","submitted_at":"2015-05-14T01:17:37Z","abstract_excerpt":"We show that the functions $\\sum_{p\\leq x} (\\log p)/p - \\log x - E$ and $\\sum_{p\\leq x} 1/p - \\log \\log x -B$ change sign infinitely often, and that under certain assumptions, they exhibit a strong bias towards positive values. These results build on recent work of Diamond & Pintz and Lamzouri concerning oscillation of Mertens' product formula, and answers to the affirmative a question posed by Rosser and Schoenfeld."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03589","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":"2026-05-18T02:09:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttEAZV4WrMPI2DYKX6Uka84fBpB4OVmn3BPLeuCX7zPPACTJRe9Ci9IF7mh3XnBdR7hpzcEtMpgVKMS1sigJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:04:13.981562Z"},"content_sha256":"d7ea0aaec0a535455b6d9c84bc0759b77a055c54270811b473d067ce98fb9839","schema_version":"1.0","event_id":"sha256:d7ea0aaec0a535455b6d9c84bc0759b77a055c54270811b473d067ce98fb9839"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX/bundle.json","state_url":"https://pith.science/pith/WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX/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":"2026-06-11T11:04:13Z","links":{"resolver":"https://pith.science/pith/WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX","bundle":"https://pith.science/pith/WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX/bundle.json","state":"https://pith.science/pith/WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WJ6NUZAEZ2T3K5ZCOYWHQ4G7XX","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":"a3ac1e93b444f5339498c2ee6770d25758cabcd8a02363a8422d6ab2969ea91a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-14T01:17:37Z","title_canon_sha256":"9382011fad02ca3cd1794faf8a8ea4f1cf0cdbfe3e4c8883b537007a03f425d1"},"schema_version":"1.0","source":{"id":"1505.03589","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03589","created_at":"2026-05-18T02:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03589v1","created_at":"2026-05-18T02:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03589","created_at":"2026-05-18T02:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"WJ6NUZAEZ2T3","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WJ6NUZAEZ2T3K5ZC","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WJ6NUZAE","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:d7ea0aaec0a535455b6d9c84bc0759b77a055c54270811b473d067ce98fb9839","target":"graph","created_at":"2026-05-18T02:09:53Z","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 show that the functions $\\sum_{p\\leq x} (\\log p)/p - \\log x - E$ and $\\sum_{p\\leq x} 1/p - \\log \\log x -B$ change sign infinitely often, and that under certain assumptions, they exhibit a strong bias towards positive values. These results build on recent work of Diamond & Pintz and Lamzouri concerning oscillation of Mertens' product formula, and answers to the affirmative a question posed by Rosser and Schoenfeld.","authors_text":"Jeffrey P.S. Lay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-14T01:17:37Z","title":"Sign changes in Mertens' first and second theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03589","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":"sha256:7d26273605333d9c3102dc0bf6973eaeded458103f6922a15e95c2f54d825054","target":"record","created_at":"2026-05-18T02:09:53Z","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":"a3ac1e93b444f5339498c2ee6770d25758cabcd8a02363a8422d6ab2969ea91a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-14T01:17:37Z","title_canon_sha256":"9382011fad02ca3cd1794faf8a8ea4f1cf0cdbfe3e4c8883b537007a03f425d1"},"schema_version":"1.0","source":{"id":"1505.03589","kind":"arxiv","version":1}},"canonical_sha256":"b27cda6404cea7b57722762c7870dfbdca7b672f874f0611c12a3ffbf5e64534","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b27cda6404cea7b57722762c7870dfbdca7b672f874f0611c12a3ffbf5e64534","first_computed_at":"2026-05-18T02:09:53.632155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:53.632155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZO+6B8Fa/lx8RX43Vf6avJP1E/FyAfhikirUYn+BEQcmaFpGJT/gj8ogn/5QQGd9MOjyCywetuGfGNoJhz9KBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:53.632846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03589","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d26273605333d9c3102dc0bf6973eaeded458103f6922a15e95c2f54d825054","sha256:d7ea0aaec0a535455b6d9c84bc0759b77a055c54270811b473d067ce98fb9839"],"state_sha256":"a2362bf3829143bd920cca32710b111b534ae90f1fb1fe3a963848e45d1085bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2lyajXGcjaknSU1sd9lq6jBAQIg0kMxXaiOrFQiVAobZYdAy4KJF9zHvhuqhsUXLE+ifGip8CxwzAcIXlETBCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:04:13.984054Z","bundle_sha256":"b1abd87c1062f08cd1675eacce91084b208183afd16c2cec80f2221dcc5b8596"}}