{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:U2NEHUIEEIPPH2NB3GLUAWWSRT","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":"6e3909fff53244f6a3d42ca0697a695edf00aa123aa4c7d2e21e9ea3b8354789","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-18T18:23:57Z","title_canon_sha256":"7943ffb271b3902b2959f81207e2469e84051a509a52c11d03c9ed8983ed587b"},"schema_version":"1.0","source":{"id":"1108.3805","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3805","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3805v3","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3805","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"pith_short_12","alias_value":"U2NEHUIEEIPP","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U2NEHUIEEIPPH2NB","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U2NEHUIE","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:4e98dde76e550876f161076070a9cff4e69027bc50c78117907823c4b5c9020e","target":"graph","created_at":"2026-05-18T02:55:57Z","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":"For a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n\\le x such that q does not divide phi(n). Part of the analysis involves a careful study of the Euler-Kronecker constants for cyclotomic fields. In particular, we show that the prime k-tuples conjecture and a conjecture of Ihara about the distribution of these Euler-Kronecker constants cannot be both true.","authors_text":"Florian Luca, Kevin Ford, Pieter Moree","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-18T18:23:57Z","title":"Values of the Euler phi-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3805","kind":"arxiv","version":3},"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":"sha256:940157e06d0e438cb99ed49dc4e24406c1fcdb7e758412652f97d644e58d0723","target":"record","created_at":"2026-05-18T02:55:57Z","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":"6e3909fff53244f6a3d42ca0697a695edf00aa123aa4c7d2e21e9ea3b8354789","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-18T18:23:57Z","title_canon_sha256":"7943ffb271b3902b2959f81207e2469e84051a509a52c11d03c9ed8983ed587b"},"schema_version":"1.0","source":{"id":"1108.3805","kind":"arxiv","version":3}},"canonical_sha256":"a69a43d104221ef3e9a1d997405ad28cff4e5495e74fd3d0dd6a8a9f55ae731a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a69a43d104221ef3e9a1d997405ad28cff4e5495e74fd3d0dd6a8a9f55ae731a","first_computed_at":"2026-05-18T02:55:57.705205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:57.705205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6afTKgonLpj75vyQZKliN8biZF8p68pNsMff41uOkOY7DbgN2be+9ftqn/rqV4Gx5vRvE6LvlWNRR2iGt/h2BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:57.705717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3805","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:940157e06d0e438cb99ed49dc4e24406c1fcdb7e758412652f97d644e58d0723","sha256:4e98dde76e550876f161076070a9cff4e69027bc50c78117907823c4b5c9020e"],"state_sha256":"1a747995b33570df82b96d827fda0d1bf6144b96588e86401c3f08f86c7396f1"}