{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:LFIHS5W63XC2CCIU4DD657XOJO","short_pith_number":"pith:LFIHS5W6","schema_version":"1.0","canonical_sha256":"59507976deddc5a10914e0c7eefeee4b9a0703683db35a689f5e609ea6fc2b27","source":{"kind":"arxiv","id":"math/0412136","version":2},"attestation_state":"computed","paper":{"title":"An ascending HNN extension of a free group inside SL(2,C)","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Danny Calegari, Nathan M. Dunfield","submitted_at":"2004-12-07T18:41:47Z","abstract_excerpt":"We give an example of a subgroup of SL(2,C) which is a strictly ascending HNN extension of a non-abelian finitely generated free group F. In particular, we exhibit a free group F in SL(2,C) of rank 6 which is conjugate to a proper subgroup of itself. This answers positively a question of Drutu and Sapir. The main ingredient in our construction is a specific finite volume (noncompact) hyperbolic 3-manifold M which is a surface bundle over the circle. In particular, most of F comes from the fundamental group of a surface fiber. A key feature of M is that there is an element of its fundamental gr"},"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":"math/0412136","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2004-12-07T18:41:47Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"e5ddc2adcbb1247467c0d73d751bbac2d482d4666032181a64e812f5cd3853c4","abstract_canon_sha256":"5a718ebf0bf3f25f9bfbf3db61717a4e3589dbb9567a3cdfc58a5d79588538c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:49:30.121528Z","signature_b64":"1sDcE/26Xxs32Brheg0CjhjKZJzG48IcZvQRDEEFHznPDtF0s4ahXDC0sfSFMMHMIsUUVDb5jTWVoI4zqyduAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59507976deddc5a10914e0c7eefeee4b9a0703683db35a689f5e609ea6fc2b27","last_reissued_at":"2026-07-04T14:49:30.121161Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:49:30.121161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An ascending HNN extension of a free group inside SL(2,C)","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Danny Calegari, Nathan M. Dunfield","submitted_at":"2004-12-07T18:41:47Z","abstract_excerpt":"We give an example of a subgroup of SL(2,C) which is a strictly ascending HNN extension of a non-abelian finitely generated free group F. In particular, we exhibit a free group F in SL(2,C) of rank 6 which is conjugate to a proper subgroup of itself. This answers positively a question of Drutu and Sapir. The main ingredient in our construction is a specific finite volume (noncompact) hyperbolic 3-manifold M which is a surface bundle over the circle. In particular, most of F comes from the fundamental group of a surface fiber. A key feature of M is that there is an element of its fundamental gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412136","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0412136/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0412136","created_at":"2026-07-04T14:49:30.121220+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0412136v2","created_at":"2026-07-04T14:49:30.121220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412136","created_at":"2026-07-04T14:49:30.121220+00:00"},{"alias_kind":"pith_short_12","alias_value":"LFIHS5W63XC2","created_at":"2026-07-04T14:49:30.121220+00:00"},{"alias_kind":"pith_short_16","alias_value":"LFIHS5W63XC2CCIU","created_at":"2026-07-04T14:49:30.121220+00:00"},{"alias_kind":"pith_short_8","alias_value":"LFIHS5W6","created_at":"2026-07-04T14:49:30.121220+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/LFIHS5W63XC2CCIU4DD657XOJO","json":"https://pith.science/pith/LFIHS5W63XC2CCIU4DD657XOJO.json","graph_json":"https://pith.science/api/pith-number/LFIHS5W63XC2CCIU4DD657XOJO/graph.json","events_json":"https://pith.science/api/pith-number/LFIHS5W63XC2CCIU4DD657XOJO/events.json","paper":"https://pith.science/paper/LFIHS5W6"},"agent_actions":{"view_html":"https://pith.science/pith/LFIHS5W63XC2CCIU4DD657XOJO","download_json":"https://pith.science/pith/LFIHS5W63XC2CCIU4DD657XOJO.json","view_paper":"https://pith.science/paper/LFIHS5W6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0412136&json=true","fetch_graph":"https://pith.science/api/pith-number/LFIHS5W63XC2CCIU4DD657XOJO/graph.json","fetch_events":"https://pith.science/api/pith-number/LFIHS5W63XC2CCIU4DD657XOJO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LFIHS5W63XC2CCIU4DD657XOJO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LFIHS5W63XC2CCIU4DD657XOJO/action/storage_attestation","attest_author":"https://pith.science/pith/LFIHS5W63XC2CCIU4DD657XOJO/action/author_attestation","sign_citation":"https://pith.science/pith/LFIHS5W63XC2CCIU4DD657XOJO/action/citation_signature","submit_replication":"https://pith.science/pith/LFIHS5W63XC2CCIU4DD657XOJO/action/replication_record"}},"created_at":"2026-07-04T14:49:30.121220+00:00","updated_at":"2026-07-04T14:49:30.121220+00:00"}