{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7CD4XOBEBKPKR34UMDGEZQ4CUJ","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":"e2bcc0825a8d23ab25d4d4873e1a319fd4468a0465c0ae22115725ddd95ec5e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-01T14:03:56Z","title_canon_sha256":"697727a97d367a805cd251925f583aa497569c71233568335a29e081fcb9bb53"},"schema_version":"1.0","source":{"id":"1011.0323","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0323","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0323v3","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0323","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"7CD4XOBEBKPK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7CD4XOBEBKPKR34U","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7CD4XOBE","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:30e6342b763dd09413d6a833c8f0ad0099e4c9e47499118dd49961f56c31a5a1","target":"graph","created_at":"2026-05-18T01:16:07Z","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 define zeta-functions of weight lattices of compact connected semisimple Lie groups. If the group is simply-connected, these zeta-functions coincide with ordinary zeta-functions of root systems of associated Lie algebras. In this paper we consider the general connected (but not necessarily simply-connected) case, prove the explicit form of Witten's volume formulas for these zeta-functions, and further prove functional relations among them which include their volume formulas.","authors_text":"Hirofumi Tsumura, Kohji Matsumoto, Yasushi Komori","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-01T14:03:56Z","title":"Zeta-functions of weight lattices of compact connected semisimple Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0323","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":"sha256:7313c5bcbcfd457a3d7742e4e94b28b52f38ca3d2135ae912d15621a15ccba9a","target":"record","created_at":"2026-05-18T01:16:07Z","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":"e2bcc0825a8d23ab25d4d4873e1a319fd4468a0465c0ae22115725ddd95ec5e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-01T14:03:56Z","title_canon_sha256":"697727a97d367a805cd251925f583aa497569c71233568335a29e081fcb9bb53"},"schema_version":"1.0","source":{"id":"1011.0323","kind":"arxiv","version":3}},"canonical_sha256":"f887cbb8240a9ea8ef9460cc4cc382a273c7886a014de16af75eb6ab6436908d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f887cbb8240a9ea8ef9460cc4cc382a273c7886a014de16af75eb6ab6436908d","first_computed_at":"2026-05-18T01:16:07.742947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:07.742947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5+/X41GhwfbAljPe5cv6C1C9VEXkU4kxZ/pagqUojneU57VnAgz5Ozz4uQhUXtZe8g38Vt4Dp9TfKfK/Iuu9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:07.743429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0323","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7313c5bcbcfd457a3d7742e4e94b28b52f38ca3d2135ae912d15621a15ccba9a","sha256:30e6342b763dd09413d6a833c8f0ad0099e4c9e47499118dd49961f56c31a5a1"],"state_sha256":"817e90f4ee13ce89dc2e4f8eacb14c859691e5c05e415068fdfad77c02815591"}