{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RXRBUQFH53ZU4CHBO2O5ACW4K3","short_pith_number":"pith:RXRBUQFH","schema_version":"1.0","canonical_sha256":"8de21a40a7eef34e08e1769dd00adc56edad3085210e2da88025da2d714eb4dc","source":{"kind":"arxiv","id":"1510.01617","version":2},"attestation_state":"computed","paper":{"title":"Automorphisms of the Baumslag-Gersten group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Boris Lishak","submitted_at":"2015-10-06T15:14:48Z","abstract_excerpt":"We classify homomorphisms of the Baumslag-Gersten group into itself. We prove it is Hopfian and co-Hopfian. We show that the group of outer automorphisms of the Baumslag-Gersten group is isomorphic to the dyadic rationals with the addition operation. These results are not new. They were obtained by Andrew M. Brunner in \\cite{Brunner}. However, our exposition is self-contained and, hopefully, more accessible for some readers."},"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":"1510.01617","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-06T15:14:48Z","cross_cats_sorted":[],"title_canon_sha256":"a662c0e192f1d4ac173171ff67fea17de1a7a9790358520f497688b072957da6","abstract_canon_sha256":"c2ebdf9a24a8b116d46e351d97a8734c1768050a4f3f73467fbf6850512bff17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:48.571070Z","signature_b64":"9WQE/HNXoHaWveRJEDJsfnmKKTWjJL1+LNSWtDaiKXs3PDM8olw0J4lp0XY6huwL2Ck/4HJK1wJ23lqJzG+YBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8de21a40a7eef34e08e1769dd00adc56edad3085210e2da88025da2d714eb4dc","last_reissued_at":"2026-05-18T01:30:48.570694Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:48.570694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphisms of the Baumslag-Gersten group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Boris Lishak","submitted_at":"2015-10-06T15:14:48Z","abstract_excerpt":"We classify homomorphisms of the Baumslag-Gersten group into itself. We prove it is Hopfian and co-Hopfian. We show that the group of outer automorphisms of the Baumslag-Gersten group is isomorphic to the dyadic rationals with the addition operation. These results are not new. They were obtained by Andrew M. Brunner in \\cite{Brunner}. However, our exposition is self-contained and, hopefully, more accessible for some readers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01617","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":"1510.01617","created_at":"2026-05-18T01:30:48.570759+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01617v2","created_at":"2026-05-18T01:30:48.570759+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01617","created_at":"2026-05-18T01:30:48.570759+00:00"},{"alias_kind":"pith_short_12","alias_value":"RXRBUQFH53ZU","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RXRBUQFH53ZU4CHB","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RXRBUQFH","created_at":"2026-05-18T12:29:39.896362+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/RXRBUQFH53ZU4CHBO2O5ACW4K3","json":"https://pith.science/pith/RXRBUQFH53ZU4CHBO2O5ACW4K3.json","graph_json":"https://pith.science/api/pith-number/RXRBUQFH53ZU4CHBO2O5ACW4K3/graph.json","events_json":"https://pith.science/api/pith-number/RXRBUQFH53ZU4CHBO2O5ACW4K3/events.json","paper":"https://pith.science/paper/RXRBUQFH"},"agent_actions":{"view_html":"https://pith.science/pith/RXRBUQFH53ZU4CHBO2O5ACW4K3","download_json":"https://pith.science/pith/RXRBUQFH53ZU4CHBO2O5ACW4K3.json","view_paper":"https://pith.science/paper/RXRBUQFH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01617&json=true","fetch_graph":"https://pith.science/api/pith-number/RXRBUQFH53ZU4CHBO2O5ACW4K3/graph.json","fetch_events":"https://pith.science/api/pith-number/RXRBUQFH53ZU4CHBO2O5ACW4K3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RXRBUQFH53ZU4CHBO2O5ACW4K3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RXRBUQFH53ZU4CHBO2O5ACW4K3/action/storage_attestation","attest_author":"https://pith.science/pith/RXRBUQFH53ZU4CHBO2O5ACW4K3/action/author_attestation","sign_citation":"https://pith.science/pith/RXRBUQFH53ZU4CHBO2O5ACW4K3/action/citation_signature","submit_replication":"https://pith.science/pith/RXRBUQFH53ZU4CHBO2O5ACW4K3/action/replication_record"}},"created_at":"2026-05-18T01:30:48.570759+00:00","updated_at":"2026-05-18T01:30:48.570759+00:00"}