{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:VX4AHC3ODVBG57PMVYJMDIR64O","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":"5fde958547d06da0eb6d77cc3ebbf5f1ccce2f0faf1ae96fcd90be523d15c94a","cross_cats_sorted":["cs.IT","math.IT","math.NT"],"license":"","primary_cat":"math.QA","submitted_at":"2003-09-25T22:08:05Z","title_canon_sha256":"0ccfd978c7d8ec6e46099c3c53e733da2a3d869107be55edeab66627f6032fd1"},"schema_version":"1.0","source":{"id":"math/0309425","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0309425","created_at":"2026-07-04T15:05:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/0309425v2","created_at":"2026-07-04T15:05:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0309425","created_at":"2026-07-04T15:05:18Z"},{"alias_kind":"pith_short_12","alias_value":"VX4AHC3ODVBG","created_at":"2026-07-04T15:05:18Z"},{"alias_kind":"pith_short_16","alias_value":"VX4AHC3ODVBG57PM","created_at":"2026-07-04T15:05:18Z"},{"alias_kind":"pith_short_8","alias_value":"VX4AHC3O","created_at":"2026-07-04T15:05:18Z"}],"graph_snapshots":[{"event_id":"sha256:90e6cdd4d6ff5f2e8d54ffefb8780e271059727e8f943d12d4506ec60bd1cb3e","target":"graph","created_at":"2026-07-04T15:05:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0309425/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Multiple zeta values have been studied by a wide variety of methods. In this article we summarize some of the results about them that can be obtained by an algebraic approach. This involves \"coding\" the multiple zeta values by monomials in two noncommuting variables x and y. Multiple zeta values can then be thought of as defining a map \\zeta: H^0 -> R, where H^0 is the graded rational vector space generated by the \"admissible words\" of the noncommutative polynomial algebra Q<x,y>. Now H^0 admits two (commutative) products making \\zeta a homomorphism: the shuffle product and the \"harmonic\" prod","authors_text":"Michael E. Hoffman","cross_cats":["cs.IT","math.IT","math.NT"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2003-09-25T22:08:05Z","title":"Algebraic Aspects of Multiple Zeta Values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309425","kind":"arxiv","version":2},"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":"sha256:99ffc03d059c6282a00720da6d90a2cf0e3fe1ac4f04aafba67b36589046948f","target":"record","created_at":"2026-07-04T15:05:18Z","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":"5fde958547d06da0eb6d77cc3ebbf5f1ccce2f0faf1ae96fcd90be523d15c94a","cross_cats_sorted":["cs.IT","math.IT","math.NT"],"license":"","primary_cat":"math.QA","submitted_at":"2003-09-25T22:08:05Z","title_canon_sha256":"0ccfd978c7d8ec6e46099c3c53e733da2a3d869107be55edeab66627f6032fd1"},"schema_version":"1.0","source":{"id":"math/0309425","kind":"arxiv","version":2}},"canonical_sha256":"adf8038b6e1d426efdecae12c1a23ee3a33ef0846e6e9a3ae7a7c432edc85d55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adf8038b6e1d426efdecae12c1a23ee3a33ef0846e6e9a3ae7a7c432edc85d55","first_computed_at":"2026-07-04T15:05:18.124997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:05:18.124997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n0Qz3ZQes2PGP37dh5GDlwo/Vwyw8yCnWe1lubWq8GU23u3UJphh0+R34V3o6KYPvXoQy/OWOfjIfNdwuBWyBw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:05:18.125398Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0309425","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99ffc03d059c6282a00720da6d90a2cf0e3fe1ac4f04aafba67b36589046948f","sha256:90e6cdd4d6ff5f2e8d54ffefb8780e271059727e8f943d12d4506ec60bd1cb3e"],"state_sha256":"45cb5a102da610577598369a80364708621c016eef193d739df07616252ce4ec"}