{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:ZFNR75323PKPAZ2RC47JENKA7E","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":"f6de37f646a5d44412165c30ebbe6aca9cb6c7e7b617b88b65bfb1f3a39f5512","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2003-06-27T15:06:33Z","title_canon_sha256":"75f218d72d7e5ada3b4adfe37a8500ed3d57684287f1649ed0361b2c12fa4959"},"schema_version":"1.0","source":{"id":"math/0306398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0306398","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0306398v1","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0306398","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"ZFNR75323PKP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZFNR75323PKPAZ2R","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZFNR7532","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:6208a153aa7ec0da913c57cdfbb60d4a2942387b126ae5c258126a8d5dfe6bf3","target":"graph","created_at":"2026-05-18T01:05:28Z","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 M and N be n-dimensional connected orientable finite-volume hyperbolic manifolds with geodesic boundary, and let f be a given isomorphism between the fundamental groups of M and N. We study the problem whether there exists an isometry between M and N which induces f.\n We show that this is always the case if the dimension of M and N is at least four, while in the three-dimensional case the existence of an isometry inducing f is proved under some (necessary) additional conditions on f. Such conditions are trivially satisfied if the boundaries of M and N are both compact.","authors_text":"Roberto Frigerio","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2003-06-27T15:06:33Z","title":"Hyperbolic manifolds with geodesic boundary which are determined by their fundamental group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306398","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:efa3d69bc457e8435a997577a210f0f0843261198b623336ac970d7e30f22d55","target":"record","created_at":"2026-05-18T01:05:28Z","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":"f6de37f646a5d44412165c30ebbe6aca9cb6c7e7b617b88b65bfb1f3a39f5512","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2003-06-27T15:06:33Z","title_canon_sha256":"75f218d72d7e5ada3b4adfe37a8500ed3d57684287f1649ed0361b2c12fa4959"},"schema_version":"1.0","source":{"id":"math/0306398","kind":"arxiv","version":1}},"canonical_sha256":"c95b1ff77adbd4f06751173e923540f938f5ea67af4246c477f78dfeddaff40e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c95b1ff77adbd4f06751173e923540f938f5ea67af4246c477f78dfeddaff40e","first_computed_at":"2026-05-18T01:05:28.780260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:28.780260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p6jjQAboflq5Q9Wt8rYuZHY3ayy2iKN5ZsKpvFT7KhyvOkzuFxdD3GBtN5Br4JusOO1MPW9LoFXwNkM8wh7tCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:28.780814Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0306398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efa3d69bc457e8435a997577a210f0f0843261198b623336ac970d7e30f22d55","sha256:6208a153aa7ec0da913c57cdfbb60d4a2942387b126ae5c258126a8d5dfe6bf3"],"state_sha256":"1f6913526210f5c7553e5c3f2a514fe5c28f2d59f72c1ce02a21d03556b09791"}