{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CIACMALBDWYJQIBI6UT4MNIBST","short_pith_number":"pith:CIACMALB","schema_version":"1.0","canonical_sha256":"12002601611db0982028f527c6350194d836604a372845c3ddb35bbccdde04a6","source":{"kind":"arxiv","id":"1205.5747","version":2},"attestation_state":"computed","paper":{"title":"Criterion for Cannon's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GT","authors_text":"Vladimir Markovic","submitted_at":"2012-05-25T16:36:22Z","abstract_excerpt":"The Cannon Conjecture from the geometric group theory asserts that a word hyperbolic group that acts effectively on its boundary, and whose boundary is homeomorphic to the 2-sphere, is isomorphic to a Kleinian group. We prove the following Criterion for Cannon's Conjecture: A hyperbolic group $G$ (that acts effectively on its boundary) whose boundary is homeomorphic to the 2-sphere is isomorphic to a Kleinian group if and only if every two points in the boundary of $G$ are separated by a quasi-convex surface subgroup. Thus, the Cannon's conjecture is reduced to showing that such a group contai"},"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":"1205.5747","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-05-25T16:36:22Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"e7d5fb793d67b38f5a8df37828e452d0cc8ea1c937d6d5f80e74524c35d49dd7","abstract_canon_sha256":"4fa6aa08b9ee7db56c14613e77975d88ae51b304f3da1e8c075f5662fff49184"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:22.361862Z","signature_b64":"lejdhCmiJeTzL1RwdAz1Q55s+SOuctPIFZMs7CCmbf9UA1RMy9bmg+HOe0+EDEFIn4VseBL3MqdmQQplXTfnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12002601611db0982028f527c6350194d836604a372845c3ddb35bbccdde04a6","last_reissued_at":"2026-05-18T03:42:22.361168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:22.361168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Criterion for Cannon's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GT","authors_text":"Vladimir Markovic","submitted_at":"2012-05-25T16:36:22Z","abstract_excerpt":"The Cannon Conjecture from the geometric group theory asserts that a word hyperbolic group that acts effectively on its boundary, and whose boundary is homeomorphic to the 2-sphere, is isomorphic to a Kleinian group. We prove the following Criterion for Cannon's Conjecture: A hyperbolic group $G$ (that acts effectively on its boundary) whose boundary is homeomorphic to the 2-sphere is isomorphic to a Kleinian group if and only if every two points in the boundary of $G$ are separated by a quasi-convex surface subgroup. Thus, the Cannon's conjecture is reduced to showing that such a group contai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5747","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":"1205.5747","created_at":"2026-05-18T03:42:22.361267+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.5747v2","created_at":"2026-05-18T03:42:22.361267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5747","created_at":"2026-05-18T03:42:22.361267+00:00"},{"alias_kind":"pith_short_12","alias_value":"CIACMALBDWYJ","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CIACMALBDWYJQIBI","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CIACMALB","created_at":"2026-05-18T12:27:01.376967+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/CIACMALBDWYJQIBI6UT4MNIBST","json":"https://pith.science/pith/CIACMALBDWYJQIBI6UT4MNIBST.json","graph_json":"https://pith.science/api/pith-number/CIACMALBDWYJQIBI6UT4MNIBST/graph.json","events_json":"https://pith.science/api/pith-number/CIACMALBDWYJQIBI6UT4MNIBST/events.json","paper":"https://pith.science/paper/CIACMALB"},"agent_actions":{"view_html":"https://pith.science/pith/CIACMALBDWYJQIBI6UT4MNIBST","download_json":"https://pith.science/pith/CIACMALBDWYJQIBI6UT4MNIBST.json","view_paper":"https://pith.science/paper/CIACMALB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.5747&json=true","fetch_graph":"https://pith.science/api/pith-number/CIACMALBDWYJQIBI6UT4MNIBST/graph.json","fetch_events":"https://pith.science/api/pith-number/CIACMALBDWYJQIBI6UT4MNIBST/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CIACMALBDWYJQIBI6UT4MNIBST/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CIACMALBDWYJQIBI6UT4MNIBST/action/storage_attestation","attest_author":"https://pith.science/pith/CIACMALBDWYJQIBI6UT4MNIBST/action/author_attestation","sign_citation":"https://pith.science/pith/CIACMALBDWYJQIBI6UT4MNIBST/action/citation_signature","submit_replication":"https://pith.science/pith/CIACMALBDWYJQIBI6UT4MNIBST/action/replication_record"}},"created_at":"2026-05-18T03:42:22.361267+00:00","updated_at":"2026-05-18T03:42:22.361267+00:00"}