{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:XBJT6NVM5P2D5ZZDX263XWAWMV","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":"ae6d498357169b6e5da05ce8f5609b15a54e2165a9459ef0bb81e4045989ee65","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.NT","submitted_at":"2004-01-23T16:28:20Z","title_canon_sha256":"84ab2c36f2873e89bb3944099c002fb479edb09a3e7ee5ca49fc70311516e22d"},"schema_version":"1.0","source":{"id":"math/0401319","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401319","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401319v3","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401319","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"XBJT6NVM5P2D","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XBJT6NVM5P2D5ZZD","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XBJT6NVM","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:d99bcfb120bef2b24f6432daf8961962240ca1997e784eddbc10e9556346a7d4","target":"graph","created_at":"2026-05-18T01:03:12Z","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":"We present a number of results about (finite) multiple harmonic sums modulo a prime, which provide interesting parallels to known results about multiple zeta values (i.e., infinite multiple harmonic series). In particular, we prove a \"duality\" result for mod p multiple harmonic sums similar to (but distinct from) that for multiple zeta values. We also exploit the Hopf algebra structure of the quasi-symmetric functions to do calculations with multiple harmonic sums mod p, and obtain, for each weight through 9, a set of generators for the space of weight-n multiple harmonic sums mod p. When comb","authors_text":"Michael E. Hoffman","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.NT","submitted_at":"2004-01-23T16:28:20Z","title":"Quasi-symmetric functions and mod p multiple harmonic sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401319","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:e6993e1284cfa8d0123de3d6a88cc4522b42aa0580b3d3366a32403f1f94c95d","target":"record","created_at":"2026-05-18T01:03:12Z","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":"ae6d498357169b6e5da05ce8f5609b15a54e2165a9459ef0bb81e4045989ee65","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.NT","submitted_at":"2004-01-23T16:28:20Z","title_canon_sha256":"84ab2c36f2873e89bb3944099c002fb479edb09a3e7ee5ca49fc70311516e22d"},"schema_version":"1.0","source":{"id":"math/0401319","kind":"arxiv","version":3}},"canonical_sha256":"b8533f36acebf43ee723bebdbbd81665435cbd203ab10a91494598198f5a7ed6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8533f36acebf43ee723bebdbbd81665435cbd203ab10a91494598198f5a7ed6","first_computed_at":"2026-05-18T01:03:12.310895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:12.310895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q885h2HIqIeiE9V8QiMz8pZ7w4yBgLh8KK7HS1AhY7J2JetEM9ersQ2Ikq6cnvbv8UaHCO7TbSOfs9QO/bYPCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:12.311471Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0401319","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6993e1284cfa8d0123de3d6a88cc4522b42aa0580b3d3366a32403f1f94c95d","sha256:d99bcfb120bef2b24f6432daf8961962240ca1997e784eddbc10e9556346a7d4"],"state_sha256":"b111940f118cf7db269eabaa72235d2bbceb8967778d46d5bda937279c1a0720"}