{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:P64TERKGTLNBBUVXN4MAZTBVAS","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":"ab7b9cd24b09d88e86295c20f263f9837c2e55fd7eb24c381a6829240b5a5874","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-16T15:28:21Z","title_canon_sha256":"9992c9e2ee4415e95560e3507e11e8f92ac7b2bfc6f96ba21654fdc2afdf5551"},"schema_version":"1.0","source":{"id":"2412.11879","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.11879","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2412.11879v4","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11879","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"P64TERKGTLNB","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"P64TERKGTLNBBUVX","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"P64TERKG","created_at":"2026-05-28T01:04:25Z"}],"graph_snapshots":[{"event_id":"sha256:3dc7e43d81a96dd0e3072f12e00a5e4d2019f06a7dff9afd7d4e13992cd7aa6a","target":"graph","created_at":"2026-05-28T01:04:25Z","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/2412.11879/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove Witten zeta function of a root system $\\Phi$ has high-order vanishing at negative even integers, using an integral representation involving the Hurwitz zeta function. This settles a conjecture of Kurokawa and Ochiai for a large class of compact Lie groups. We also provide a qualitative description of the corresponding leading coefficient in terms of Riemann zeta values, in which the highest root of $\\Phi$ makes a natural appearance.","authors_text":"Kam Cheong Au","cross_cats":["math.CA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-16T15:28:21Z","title":"Vanishing of Witten zeta function at negative integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11879","kind":"arxiv","version":4},"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":"sha256:119db1437255327505765f16adee067c6b067429208475915f8fe3e5bb7b1ecb","target":"record","created_at":"2026-05-28T01:04:25Z","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":"ab7b9cd24b09d88e86295c20f263f9837c2e55fd7eb24c381a6829240b5a5874","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-16T15:28:21Z","title_canon_sha256":"9992c9e2ee4415e95560e3507e11e8f92ac7b2bfc6f96ba21654fdc2afdf5551"},"schema_version":"1.0","source":{"id":"2412.11879","kind":"arxiv","version":4}},"canonical_sha256":"7fb93245469ada10d2b76f180ccc3504990846b78061f238ecd1dc7128ea177f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fb93245469ada10d2b76f180ccc3504990846b78061f238ecd1dc7128ea177f","first_computed_at":"2026-05-28T01:04:25.895253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:25.895253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zpE/Hg+6+y4ZWKA7KGLxXGmvYnjs+Xz+SHmYI885tPg7YcWCqVKhZOhDMaO9GqdqDGZftS+8weRjM9evS+0YBg==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:25.895895Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.11879","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:119db1437255327505765f16adee067c6b067429208475915f8fe3e5bb7b1ecb","sha256:3dc7e43d81a96dd0e3072f12e00a5e4d2019f06a7dff9afd7d4e13992cd7aa6a"],"state_sha256":"c4e93b73bcd1bd35bfdfabaaa447d7ef34f3034a53991f71f6e1cd553868999a"}