{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2WYCVVKQJB46ZETXTDVGEBRLZV","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":"f518c29f57ea45577b03a68fe097b4d14896b5b3bfc0cd31b6ea792fdb7eca5b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2022-07-24T20:32:49Z","title_canon_sha256":"22cfb6066d58501f2fcfc62219136f2aba38c982dca00ba6b634974d27a6402c"},"schema_version":"1.0","source":{"id":"2207.11806","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.11806","created_at":"2026-07-05T05:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"2207.11806v3","created_at":"2026-07-05T05:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.11806","created_at":"2026-07-05T05:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"2WYCVVKQJB46","created_at":"2026-07-05T05:20:13Z"},{"alias_kind":"pith_short_16","alias_value":"2WYCVVKQJB46ZETX","created_at":"2026-07-05T05:20:13Z"},{"alias_kind":"pith_short_8","alias_value":"2WYCVVKQ","created_at":"2026-07-05T05:20:13Z"}],"graph_snapshots":[{"event_id":"sha256:6bbaf7cf81b6fe16f689622e6b70c6ffc0e679746c7fc3b9335d15de41807955","target":"graph","created_at":"2026-07-05T05:20:13Z","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/2207.11806/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define and study a $p$-adic analogue of the incomplete gamma function related to Morita's $p$-adic gamma function. We also discuss a combinatorial identity related to the Artin-Hasse series, which is a special case of the exponential principle in combinatorics. From this we deduce a curious $p$-adic property of $|\\mathrm{Hom} (G,S_n)|$ for a topologically finitely generated group $G$, using a characterization of $p$-adic continuity for certain functions $f \\colon \\mathbb Z_{>0} \\to \\mathbb Q_p$ due to O'Desky-Richman. In the end, we give an exposition of some standard properties of the Arti","authors_text":"Jay Reiter, Jin Yi, Napoleon Wang, Shiang Tang, Xiaojian Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2022-07-24T20:32:49Z","title":"P-adic incomplete gamma functions and Artin-Hasse-type series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.11806","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:f60c57711957d4a8ad8caa127625c059994d46728f2f7741af2f3dc413085b10","target":"record","created_at":"2026-07-05T05:20:13Z","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":"f518c29f57ea45577b03a68fe097b4d14896b5b3bfc0cd31b6ea792fdb7eca5b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2022-07-24T20:32:49Z","title_canon_sha256":"22cfb6066d58501f2fcfc62219136f2aba38c982dca00ba6b634974d27a6402c"},"schema_version":"1.0","source":{"id":"2207.11806","kind":"arxiv","version":3}},"canonical_sha256":"d5b02ad5504879ec927798ea62062bcd4ed448d1320c6634231a65c12f25972e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5b02ad5504879ec927798ea62062bcd4ed448d1320c6634231a65c12f25972e","first_computed_at":"2026-07-05T05:20:13.301725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:20:13.301725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eNappMhlN5oo78r5v/m812F9SiFxhcIW8LEtOpnxIywAdtWvMaxZdP7gS6NWlpywZ/3MrsYUTHiI/RwiP1gfBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:20:13.302196Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.11806","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f60c57711957d4a8ad8caa127625c059994d46728f2f7741af2f3dc413085b10","sha256:6bbaf7cf81b6fe16f689622e6b70c6ffc0e679746c7fc3b9335d15de41807955"],"state_sha256":"6e2e9c89ed67b18fea680a698d70b25989c2bf9caa3368480cde9016206c5f5f"}