{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KF5PZNHXMGQY55UCAK6AZ7THEX","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":"1272238ee50f36bded2ba2ffeaa438d60fbd2e0dcd2f5028b55eb3cf31f1f1b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-12T21:03:19Z","title_canon_sha256":"0983df0cdd0a17c97ca974ce91d88cc6cfd847cd8a11687f2f930e5aa3354978"},"schema_version":"1.0","source":{"id":"1803.04533","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04533","created_at":"2026-05-18T00:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04533v1","created_at":"2026-05-18T00:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04533","created_at":"2026-05-18T00:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"KF5PZNHXMGQY","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KF5PZNHXMGQY55UC","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KF5PZNHX","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:48da5c45dcd343733253fe609dc363d874d5647bfc29d4e794b095a4a05b2005","target":"graph","created_at":"2026-05-18T00:21:18Z","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":"The aim of this paper is to prove conjectures concerning $p$-adic valuations of Stirling numbers of the second kind $S(n,k)$, $n,k\\in\\mathbb{N}_+$, stated by Amdeberhan, Manna and Moll and Berrizbeitia et al., where $p$ is a prime number. The proof is based on elementary facts from $p$-adic analysis.","authors_text":"Piotr Miska","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-12T21:03:19Z","title":"A note on $p$-adic locally analytic functions with application to behavior of the $p$-adic valuations of Stirling numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04533","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":"sha256:8999cf80257aa78706be644caf288d70db6743c8b35d2e1d08455abb153e00fc","target":"record","created_at":"2026-05-18T00:21:18Z","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":"1272238ee50f36bded2ba2ffeaa438d60fbd2e0dcd2f5028b55eb3cf31f1f1b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-12T21:03:19Z","title_canon_sha256":"0983df0cdd0a17c97ca974ce91d88cc6cfd847cd8a11687f2f930e5aa3354978"},"schema_version":"1.0","source":{"id":"1803.04533","kind":"arxiv","version":1}},"canonical_sha256":"517afcb4f761a18ef68202bc0cfe6725faae99d79f3c56af03a5155b080178ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"517afcb4f761a18ef68202bc0cfe6725faae99d79f3c56af03a5155b080178ab","first_computed_at":"2026-05-18T00:21:18.797086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:18.797086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OXiHO0pZTo16oLaXSmjGfEsGZljPTYKi8KEQY+PDoVyVNqu1R6gul5EHZxXexaz61DIZCTCCS252k8a8DGwxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:18.798233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04533","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8999cf80257aa78706be644caf288d70db6743c8b35d2e1d08455abb153e00fc","sha256:48da5c45dcd343733253fe609dc363d874d5647bfc29d4e794b095a4a05b2005"],"state_sha256":"6c814f34528c24ce6609cdcd1f032721ae1f8070fc9c363204e438b1bfe614b7"}