{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QDPF4Q76RAZ4Q2C2SNQOAJZH3A","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":"ff98d0fee7d41b0fc29d8d180a8ca4600ac5ec6aaba3ce37a46b503e34d1530d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-04T00:30:50Z","title_canon_sha256":"3fce1d78b4b4cc353e0d9524d5dab8943073ea5b4284ea82b19ef99415719278"},"schema_version":"1.0","source":{"id":"1709.00778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00778","created_at":"2026-05-18T00:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00778v1","created_at":"2026-05-18T00:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00778","created_at":"2026-05-18T00:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"QDPF4Q76RAZ4","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QDPF4Q76RAZ4Q2C2","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QDPF4Q76","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:a331195bcc5494ed992ebcf576acc5b6d08dd3a2823ea62534eec4c989e79e47","target":"graph","created_at":"2026-05-18T00:36:05Z","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 sum of the $r$th powers of the descent set statistic and how many small prime factors occur in these numbers. Our results depend upon the base $p$ expansion of $n$ and $r$.","authors_text":"Alex Happ, Richard Ehrenborg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-04T00:30:50Z","title":"On the powers of the descent set statistic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00778","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:bc6fe54fcd6b18789d3d7bcf01e21abe6bbbeba8d77d3bf59a338b0c6f51b2b0","target":"record","created_at":"2026-05-18T00:36:05Z","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":"ff98d0fee7d41b0fc29d8d180a8ca4600ac5ec6aaba3ce37a46b503e34d1530d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-04T00:30:50Z","title_canon_sha256":"3fce1d78b4b4cc353e0d9524d5dab8943073ea5b4284ea82b19ef99415719278"},"schema_version":"1.0","source":{"id":"1709.00778","kind":"arxiv","version":1}},"canonical_sha256":"80de5e43fe8833c8685a9360e02727d83a9d4629c9557e23a03c05c66a68d527","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80de5e43fe8833c8685a9360e02727d83a9d4629c9557e23a03c05c66a68d527","first_computed_at":"2026-05-18T00:36:05.162986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:05.162986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+wx5FqmnJwBx6geb9SlAC1IojerSBwegAGXkgWH7nw93N08mdd4pHrfEEkGJCB1BVuZoMpEUVq3hXBvmFHVwDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:05.163615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc6fe54fcd6b18789d3d7bcf01e21abe6bbbeba8d77d3bf59a338b0c6f51b2b0","sha256:a331195bcc5494ed992ebcf576acc5b6d08dd3a2823ea62534eec4c989e79e47"],"state_sha256":"51fa3fb99f26fcae46be508088c4044d2d4ba90f3a76ee8f8654ee1d6c38b28d"}