{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:S6UAJULS4EDKX2MFV3FEQS2TP7","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":"209f2971020ecfd26c709a2da4356a4ec72caf4cc8b907d83e3b2d5f4835b3aa","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.NT","submitted_at":"2006-06-01T19:10:20Z","title_canon_sha256":"cac732fa6f856d604bf632d4242f1adcca7d0a05e1587387ebba4152eb9811ab"},"schema_version":"1.0","source":{"id":"math/0606039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606039","created_at":"2026-07-04T14:55:07Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606039v1","created_at":"2026-07-04T14:55:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606039","created_at":"2026-07-04T14:55:07Z"},{"alias_kind":"pith_short_12","alias_value":"S6UAJULS4EDK","created_at":"2026-07-04T14:55:07Z"},{"alias_kind":"pith_short_16","alias_value":"S6UAJULS4EDKX2MF","created_at":"2026-07-04T14:55:07Z"},{"alias_kind":"pith_short_8","alias_value":"S6UAJULS","created_at":"2026-07-04T14:55:07Z"}],"graph_snapshots":[{"event_id":"sha256:690adb59d1f93f2bc6e6f5a2d45a410086913e7de52f18844c06dbb7fd88abee","target":"graph","created_at":"2026-07-04T14:55:07Z","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/math/0606039/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a relatively easy proof of the Erd\\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several related results in the literature.","authors_text":"Andrew Granville, K. Soundararajan","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2006-06-01T19:10:20Z","title":"Sieving and the Erd{\\H o}s-Kac theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606039","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:f010b4dc287c866c748c48c803a9546aee11ccd216ee11305daab802858e525c","target":"record","created_at":"2026-07-04T14:55:07Z","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":"209f2971020ecfd26c709a2da4356a4ec72caf4cc8b907d83e3b2d5f4835b3aa","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.NT","submitted_at":"2006-06-01T19:10:20Z","title_canon_sha256":"cac732fa6f856d604bf632d4242f1adcca7d0a05e1587387ebba4152eb9811ab"},"schema_version":"1.0","source":{"id":"math/0606039","kind":"arxiv","version":1}},"canonical_sha256":"97a804d172e106abe985aeca484b537ffe0af2c008a41a7aeb4659ef92faec89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97a804d172e106abe985aeca484b537ffe0af2c008a41a7aeb4659ef92faec89","first_computed_at":"2026-07-04T14:55:07.703416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:55:07.703416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4qHl5kWYgUN+yo64s74OHmZ9Lk/LFo+jwLHEF0XMzVNjeHaNTn11tTmK+Atpox5Zqw6Hdq8rCci1yLCSZubsBw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:55:07.703792Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f010b4dc287c866c748c48c803a9546aee11ccd216ee11305daab802858e525c","sha256:690adb59d1f93f2bc6e6f5a2d45a410086913e7de52f18844c06dbb7fd88abee"],"state_sha256":"7dd2a08c393432ecc7220b5b22ccccf236789c0d781c03f148c5c0b99b07eadb"}