{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:O6FR472ML57MQVVAEQFA7OSJWX","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":"c23f1bb0f50a7bbe8cdb07b58abd4c2f838ac97f8288ea300031d65c295dced3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-06-30T18:28:48Z","title_canon_sha256":"672b02605b28cb3561f68c8ebaa66096941cbe9693793bd1cd97752271210de2"},"schema_version":"1.0","source":{"id":"0906.5601","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5601","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5601v2","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5601","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"O6FR472ML57M","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"O6FR472ML57MQVVA","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"O6FR472M","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:e51931befb6d1ad917db0d460d2adaf061bdce09eaf7ec81c45ce805f987c570","target":"graph","created_at":"2026-05-18T04:42:44Z","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":"Fixing a closed hyperbolic surface S, we define a moduli space AI(S) of unmarked hyperbolic 3-manifolds homotopy equivalent to S. This 3-dimensional analogue of the moduli space M(S) of unmarked hyperbolic surfaces homeomorphic to S has bizarre local topology, possessing many points that are not closed. There is, however, a natural embedding of M(S) into AI(S) and a compactification of AI(S) such that this embedding extends to an embedding of the Deligne-Mumford compactification of M(S) into the compactification of AI(S).","authors_text":"Peter Storm, Richard Canary","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-06-30T18:28:48Z","title":"The curious moduli spaces of unmarked Kleinian surface groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5601","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:e463891b7b4d7a752d0fac11661a599bf4e3b882eeb6023ce8508c062428c19a","target":"record","created_at":"2026-05-18T04:42:44Z","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":"c23f1bb0f50a7bbe8cdb07b58abd4c2f838ac97f8288ea300031d65c295dced3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-06-30T18:28:48Z","title_canon_sha256":"672b02605b28cb3561f68c8ebaa66096941cbe9693793bd1cd97752271210de2"},"schema_version":"1.0","source":{"id":"0906.5601","kind":"arxiv","version":2}},"canonical_sha256":"778b1e7f4c5f7ec856a0240a0fba49b5d016b63dceec64f439e5cddedcca23d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"778b1e7f4c5f7ec856a0240a0fba49b5d016b63dceec64f439e5cddedcca23d7","first_computed_at":"2026-05-18T04:42:44.698865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:44.698865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"75pnxPf393yP7PZo6/JnfJUJk6afdWnGxmzNpx3kq/UzFhEp99jBGxce2qPTf6CQMBC54sS4zp2iS1v8Z4UQCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:44.699419Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.5601","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e463891b7b4d7a752d0fac11661a599bf4e3b882eeb6023ce8508c062428c19a","sha256:e51931befb6d1ad917db0d460d2adaf061bdce09eaf7ec81c45ce805f987c570"],"state_sha256":"92f3719d9ad9876cdfe37d76475879f11138733a68b00d2e3ccbb1d00f083e3c"}