{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JM7SEAHL33L2XJAIYUTWRF6BPS","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":"fe5b6c625f0b294c977e01b2e75f0c39756b6d9bad0a6424bf08a461d08cc6de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-04T03:13:10Z","title_canon_sha256":"9bfcd1f7adbacd8decbde8a55fed570f77c1d6659cd005720eaf0ea850176623"},"schema_version":"1.0","source":{"id":"1310.1154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1154","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1154v1","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1154","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"JM7SEAHL33L2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JM7SEAHL33L2XJAI","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JM7SEAHL","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:14892a3941176dd9ef932137dbb6ea1598dbe60783e3d898d42bffe446c834d6","target":"graph","created_at":"2026-05-18T01:10:11Z","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":"Let $\\Gamma$ be a nonuniform lattice acting on real hyperbolic n-space. We show that in dimension greater than or equal to 4, the volume of a representation is constant on each connected component of the representation variety of $\\Gamma$ in SO(n,1). Furthermore, in dimensions 2 and 3, there is a semialgebraic subset of the representation variety such that the volume of a representation is constant on connected components of the semialgebraic subset. Our approach gives a new proof of the local rigidity theorem for nonuniform hyperbolic lattices and the analogue of Soma's theorem, which shows t","authors_text":"Inkang Kim, Sungwoon Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-04T03:13:10Z","title":"On deformation spaces of nonuniform hyperbolic lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1154","kind":"arxiv","version":1},"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":"sha256:0d35025fc37b66b52d55299b572e435c59b496e35f6fff121d708d5f0bb3616b","target":"record","created_at":"2026-05-18T01:10:11Z","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":"fe5b6c625f0b294c977e01b2e75f0c39756b6d9bad0a6424bf08a461d08cc6de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-04T03:13:10Z","title_canon_sha256":"9bfcd1f7adbacd8decbde8a55fed570f77c1d6659cd005720eaf0ea850176623"},"schema_version":"1.0","source":{"id":"1310.1154","kind":"arxiv","version":1}},"canonical_sha256":"4b3f2200ebded7aba408c5276897c17cbd46269de71d5bedc09a14cd5bb2e8d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b3f2200ebded7aba408c5276897c17cbd46269de71d5bedc09a14cd5bb2e8d0","first_computed_at":"2026-05-18T01:10:11.162920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:11.162920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nbvkZ4pNKWYOLQvAE46Knzo8i1u4HFz29uCxwArNM3OZ6tFicTBS+xGbXcsnXoehEFBG+aPDS4UXUfPeHRYeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:11.163451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d35025fc37b66b52d55299b572e435c59b496e35f6fff121d708d5f0bb3616b","sha256:14892a3941176dd9ef932137dbb6ea1598dbe60783e3d898d42bffe446c834d6"],"state_sha256":"d96d043ae4f341eca68776c7ab0e8a7e3a04d2356defa68a96d97edd1a4d3e28"}