{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3SQTYGO3HZIIVSD7D5NP2VEB55","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":"cf608cad77ce45d7f0857c7836c45ba5194f9460a4830e5eed54956059c5b2cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-04T04:44:57Z","title_canon_sha256":"3cd7ff5c936485c42102d738a1915a58e5de72440ac910a3a6838a6bb52584da"},"schema_version":"1.0","source":{"id":"1111.1040","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1040","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1040v4","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1040","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"3SQTYGO3HZII","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3SQTYGO3HZIIVSD7","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3SQTYGO3","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:e67e5e98d08277f212c804420af926258990c29fb130a07c64ab4aeb44d33f47","target":"graph","created_at":"2026-05-18T00:42:44Z","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 study the concentration of the distribution of an additive function, when the sequence of prime values of $f$ decays fast and has good spacing properties. In particular, we prove a conjecture by Erdos and Katai on the concentration of $f(n)=\\sum_{p|n}(\\log p)^{-c}$ when $c>1$.","authors_text":"Dimitris Koukoulopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-04T04:44:57Z","title":"On the concentration of certain additive functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1040","kind":"arxiv","version":4},"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":"sha256:2ec183d744b361d633eed0aac4b12b549a34180a096255035bfe9e227b851b51","target":"record","created_at":"2026-05-18T00:42:44Z","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":"cf608cad77ce45d7f0857c7836c45ba5194f9460a4830e5eed54956059c5b2cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-04T04:44:57Z","title_canon_sha256":"3cd7ff5c936485c42102d738a1915a58e5de72440ac910a3a6838a6bb52584da"},"schema_version":"1.0","source":{"id":"1111.1040","kind":"arxiv","version":4}},"canonical_sha256":"dca13c19db3e508ac87f1f5afd5481ef7135d1115ae4e937798d728688a25d59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dca13c19db3e508ac87f1f5afd5481ef7135d1115ae4e937798d728688a25d59","first_computed_at":"2026-05-18T00:42:44.763759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:44.763759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1SuzgQDV4dtUd6ql3+2igSJ/7L0rAK0ORUu6YczJLFpaDuGYrpBg3gCSmDheHv4XvDdruvR675RowhajG9qUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:44.764401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1040","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ec183d744b361d633eed0aac4b12b549a34180a096255035bfe9e227b851b51","sha256:e67e5e98d08277f212c804420af926258990c29fb130a07c64ab4aeb44d33f47"],"state_sha256":"0ebbc66d2e31285060b4ca4e2b7749a53c1947360c817047255bd798802ec237"}