{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GZ6ZI4MXQCWXZGMYFXHHO6KDGR","short_pith_number":"pith:GZ6ZI4MX","schema_version":"1.0","canonical_sha256":"367d94719780ad7c99982dce777943346d835d0fae275daf75617cb7a8aaa73f","source":{"kind":"arxiv","id":"1205.4787","version":2},"attestation_state":"computed","paper":{"title":"Volume invariant and maximal representations of discrete subgroups of Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Inkang Kim, Sungwoon Kim","submitted_at":"2012-05-22T01:55:58Z","abstract_excerpt":"Let $\\Gamma$ be a lattice in a connected semisimple Lie group $G$ with trivial center and no compact factors. We introduce a volume invariant for representations of $\\Gamma$ into $G$, which generalizes the volume invariant for representations of uniform lattices introduced by Goldman. Then, we show that the maximality of this volume invariant exactly characterizes discrete, faithful representations of $\\Gamma$ into $G$ except for $\\Gamma\\subset \\mathrm{PSL_2 \\mathbb{C}}$ a nonuniform lattice."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.4787","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-05-22T01:55:58Z","cross_cats_sorted":[],"title_canon_sha256":"c0741770abaaec98afd80ed45b913a8af936126133b09abde5850ae94f588862","abstract_canon_sha256":"6cdde86a73687525c7e5305e8013870c08e1cd456be9763bb1093f58811f6dc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:10.515506Z","signature_b64":"oOoOwNA80sCQ3AVvMybjEQXmkyutvIfQ3670HtBc9qldQwkMC/4erGQqHworb2U59g9Ajh6w/GB/Q6aMdHRdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"367d94719780ad7c99982dce777943346d835d0fae275daf75617cb7a8aaa73f","last_reissued_at":"2026-05-18T03:45:10.514901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:10.514901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Volume invariant and maximal representations of discrete subgroups of Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Inkang Kim, Sungwoon Kim","submitted_at":"2012-05-22T01:55:58Z","abstract_excerpt":"Let $\\Gamma$ be a lattice in a connected semisimple Lie group $G$ with trivial center and no compact factors. We introduce a volume invariant for representations of $\\Gamma$ into $G$, which generalizes the volume invariant for representations of uniform lattices introduced by Goldman. Then, we show that the maximality of this volume invariant exactly characterizes discrete, faithful representations of $\\Gamma$ into $G$ except for $\\Gamma\\subset \\mathrm{PSL_2 \\mathbb{C}}$ a nonuniform lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4787","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.4787","created_at":"2026-05-18T03:45:10.514965+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.4787v2","created_at":"2026-05-18T03:45:10.514965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4787","created_at":"2026-05-18T03:45:10.514965+00:00"},{"alias_kind":"pith_short_12","alias_value":"GZ6ZI4MXQCWX","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GZ6ZI4MXQCWXZGMY","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GZ6ZI4MX","created_at":"2026-05-18T12:27:06.952714+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GZ6ZI4MXQCWXZGMYFXHHO6KDGR","json":"https://pith.science/pith/GZ6ZI4MXQCWXZGMYFXHHO6KDGR.json","graph_json":"https://pith.science/api/pith-number/GZ6ZI4MXQCWXZGMYFXHHO6KDGR/graph.json","events_json":"https://pith.science/api/pith-number/GZ6ZI4MXQCWXZGMYFXHHO6KDGR/events.json","paper":"https://pith.science/paper/GZ6ZI4MX"},"agent_actions":{"view_html":"https://pith.science/pith/GZ6ZI4MXQCWXZGMYFXHHO6KDGR","download_json":"https://pith.science/pith/GZ6ZI4MXQCWXZGMYFXHHO6KDGR.json","view_paper":"https://pith.science/paper/GZ6ZI4MX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.4787&json=true","fetch_graph":"https://pith.science/api/pith-number/GZ6ZI4MXQCWXZGMYFXHHO6KDGR/graph.json","fetch_events":"https://pith.science/api/pith-number/GZ6ZI4MXQCWXZGMYFXHHO6KDGR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GZ6ZI4MXQCWXZGMYFXHHO6KDGR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GZ6ZI4MXQCWXZGMYFXHHO6KDGR/action/storage_attestation","attest_author":"https://pith.science/pith/GZ6ZI4MXQCWXZGMYFXHHO6KDGR/action/author_attestation","sign_citation":"https://pith.science/pith/GZ6ZI4MXQCWXZGMYFXHHO6KDGR/action/citation_signature","submit_replication":"https://pith.science/pith/GZ6ZI4MXQCWXZGMYFXHHO6KDGR/action/replication_record"}},"created_at":"2026-05-18T03:45:10.514965+00:00","updated_at":"2026-05-18T03:45:10.514965+00:00"}