{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:ZCII75MWDB4O3AZ4GMHBXPCLXP","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":"2457dd7cae4b96e62ec08b495dd89ec616a02fc1646dcce2586f081efa697f93","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"1998-11-17T00:00:00Z","title_canon_sha256":"51c2ba7fd362903e8b463c183c6575ca176fd47407895f84b54c4e7a797ba752"},"schema_version":"1.0","source":{"id":"math/9811181","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9811181","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/9811181v1","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9811181","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"pith_short_12","alias_value":"ZCII75MWDB4O","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"ZCII75MWDB4O3AZ4","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"ZCII75MW","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:2db254f0d86399fd863ef8a08edaef6d801645bd872d696a401ce76e9d93f3f9","target":"graph","created_at":"2026-05-18T01:05:33Z","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":"By using Thurston's bending construction we obtain a sequence of faithful discrete representations \\rho _n of the fundamental group of a closed hyperbolic 3-manifold fibering over the circle into the isometry group Iso H^4 of the hyperbolic space H^4. The algebraic limit of \\rho _n contains a finitely generated subgroup F whose 3-dimensional quotient \\Omega (F)/F has infinitely generated fundamental group, where \\Omega (F) is the discontinuity domain of F acting on the sphere at infinity. Moreover F is isomorphic to the fundamental group of a closed surface and contains infinitely many conjuga","authors_text":"Leonid Potyagailo","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"1998-11-17T00:00:00Z","title":"The boundary of the deformation space of the fundamental group of some hyperbolic 3-manifolds fibering over the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9811181","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":"sha256:5f6840076f4da9ca9b958e5373882060dc34835da7cd22cb9eb7452e13e14ab4","target":"record","created_at":"2026-05-18T01:05:33Z","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":"2457dd7cae4b96e62ec08b495dd89ec616a02fc1646dcce2586f081efa697f93","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"1998-11-17T00:00:00Z","title_canon_sha256":"51c2ba7fd362903e8b463c183c6575ca176fd47407895f84b54c4e7a797ba752"},"schema_version":"1.0","source":{"id":"math/9811181","kind":"arxiv","version":1}},"canonical_sha256":"c8908ff5961878ed833c330e1bbc4bbbe32261f3ff142b273ffb400b74ff5af7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8908ff5961878ed833c330e1bbc4bbbe32261f3ff142b273ffb400b74ff5af7","first_computed_at":"2026-05-18T01:05:33.511614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:33.511614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3rJoFEuVf+tiGJf8bPKO/mM3JtYwolK8MGWF/TW1KH7E52bnr+T0XiKyWrJhVKkT5f7RzgAA1K2Quq6TrOUjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:33.512391Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9811181","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f6840076f4da9ca9b958e5373882060dc34835da7cd22cb9eb7452e13e14ab4","sha256:2db254f0d86399fd863ef8a08edaef6d801645bd872d696a401ce76e9d93f3f9"],"state_sha256":"834a685eadd6e970b01121d9f00b7db657d2d6a76973b821881d7ef5c97d9753"}