{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2OFATAPES5J3CJ3U2PJ7NXHFF3","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":"864a5ec52b7ebb4e5e9bf4c7591b58723a9fdbd8e00673a58b86adff004cec7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-20T21:16:20Z","title_canon_sha256":"225fd39e09010ea185f258b7fd082b0efb95e939239e2d1f32e417e040812255"},"schema_version":"1.0","source":{"id":"1510.06064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06064","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06064v1","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06064","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"2OFATAPES5J3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2OFATAPES5J3CJ3U","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2OFATAPE","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:1df1d1da7568f54ef5ecd8cd91343ee3fa1db8cd3d9c546a88b32edfa0d9a812","target":"graph","created_at":"2026-05-18T00:53:12Z","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":"Let $S_k(m):=1^k+2^k+\\cdots+(m-1)^k$ denote a power sum. In 2011 Bernd Kellner formulated the conjecture that for $m\\ge 4$ the ratio $S_k(m+1)/S_k(m)$ of two consecutive power sums is never an integer. We will develop some techniques that allow one to exclude many integers $\\rho$ as a ratio and combine them to exclude the integers $3\\le \\rho\\le 1501$ and, assuming a conjecture on irregular primes to be true, a set of density $1$ of ratios $\\rho$. To exclude a ratio $\\rho$ one has to show that the Erd\\H{o}s-Moser type equation $(\\rho-1)S_k(m)=m^k$ has no non-trivial solutions.","authors_text":"Ioulia N. Baoulina, Pieter Moree","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-20T21:16:20Z","title":"Forbidden integer ratios of consecutive power sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06064","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:fede66667e9ecec51dc8db9ee470113ffc049d7dd098327207b3b7dba2e2dbdc","target":"record","created_at":"2026-05-18T00:53:12Z","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":"864a5ec52b7ebb4e5e9bf4c7591b58723a9fdbd8e00673a58b86adff004cec7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-20T21:16:20Z","title_canon_sha256":"225fd39e09010ea185f258b7fd082b0efb95e939239e2d1f32e417e040812255"},"schema_version":"1.0","source":{"id":"1510.06064","kind":"arxiv","version":1}},"canonical_sha256":"d38a0981e49753b12774d3d3f6dce52ec39a88e1c8b5b3185b5a96166b91bef2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d38a0981e49753b12774d3d3f6dce52ec39a88e1c8b5b3185b5a96166b91bef2","first_computed_at":"2026-05-18T00:53:12.522933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:12.522933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"senuT4PsHlxCrrUZJRgxfeHM0crOMZYsRoBaRR0xRCKA2cO9gfy0LE1Y4N42eroh4o3VGoV+bwdEZLr60sgkBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:12.523481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fede66667e9ecec51dc8db9ee470113ffc049d7dd098327207b3b7dba2e2dbdc","sha256:1df1d1da7568f54ef5ecd8cd91343ee3fa1db8cd3d9c546a88b32edfa0d9a812"],"state_sha256":"867c0ca2db42812c5dae13522912db62f64a64f96026ef7a5add0c0f05b69040"}