{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AMECFK2BZJEFXDMBCLANO5LVZQ","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":"25bbec4207d30d62ca96bec6a97e2817e4a13b7f1a93b3c86291a75346a48933","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-24T01:02:34Z","title_canon_sha256":"51faab09a18ab952c5a3ea23bbf3f87f53ee98cf2805129a11794580391fe575"},"schema_version":"1.0","source":{"id":"2607.21883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21883","created_at":"2026-07-27T00:20:26Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21883v1","created_at":"2026-07-27T00:20:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21883","created_at":"2026-07-27T00:20:26Z"},{"alias_kind":"pith_short_12","alias_value":"AMECFK2BZJEF","created_at":"2026-07-27T00:20:26Z"},{"alias_kind":"pith_short_16","alias_value":"AMECFK2BZJEFXDMB","created_at":"2026-07-27T00:20:26Z"},{"alias_kind":"pith_short_8","alias_value":"AMECFK2B","created_at":"2026-07-27T00:20:26Z"}],"graph_snapshots":[{"event_id":"sha256:c57db4d8a5c03397641d9ae4904e3b7e007cc430ab8a94fdc9a87c82737330ef","target":"graph","created_at":"2026-07-27T00:20:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.21883/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Buchstab's function $\\omega(u)$ describes the distribution of integers without small prime factors. We establish numerically explicit upper and lower bounds for $\\omega(u)$ that are easy to evaluate, without the need to solve the delay differential equation numerically.","authors_text":"Andreas Weingartner","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-24T01:02:34Z","title":"Explicit bounds for Buchstab's function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21883","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":"sha256:9b3e21c8f1182ba3da70e26f573b603a329ffea2d9706602db24eab20d6bcc18","target":"record","created_at":"2026-07-27T00:20:26Z","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":"25bbec4207d30d62ca96bec6a97e2817e4a13b7f1a93b3c86291a75346a48933","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-24T01:02:34Z","title_canon_sha256":"51faab09a18ab952c5a3ea23bbf3f87f53ee98cf2805129a11794580391fe575"},"schema_version":"1.0","source":{"id":"2607.21883","kind":"arxiv","version":1}},"canonical_sha256":"030822ab41ca485b8d8112c0d77575cc1ac36a52df1b932b242d9dd34fc7ff38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"030822ab41ca485b8d8112c0d77575cc1ac36a52df1b932b242d9dd34fc7ff38","first_computed_at":"2026-07-27T00:20:26.123170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-27T00:20:26.123170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9cPtHP7edV2J/dkwlVA2U9eiKWE/tMJBdlo1Hu9Aow1YKDDMSJetJzirPidfA45ryslJdb55L+UZxM94fU9lBQ==","signature_status":"signed_v1","signed_at":"2026-07-27T00:20:26.123949Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.21883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b3e21c8f1182ba3da70e26f573b603a329ffea2d9706602db24eab20d6bcc18","sha256:c57db4d8a5c03397641d9ae4904e3b7e007cc430ab8a94fdc9a87c82737330ef"],"state_sha256":"9d442ad96b20bbbd8ac7c7db5513fb5fdb7a2312c33b2061c4516a505d0795c6"}