{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:KI4PG5TYNEBYKO3MNJTOIN6UID","short_pith_number":"pith:KI4PG5TY","schema_version":"1.0","canonical_sha256":"5238f376786903853b6c6a66e437d440c276ee01243eb0625039c9b5ce455db7","source":{"kind":"arxiv","id":"1203.4845","version":4},"attestation_state":"computed","paper":{"title":"Rational homological stability for groups of partially symmetric automorphisms of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Matthew C. B. Zaremsky","submitted_at":"2012-03-21T21:39:58Z","abstract_excerpt":"Let F_{n+m} be the free group of rank n+m, with generators x_1,...,x_{n+m}. An automorphism \\phi of F_{n+m} is called partially symmetric if for each 1 \\le i \\le m, \\phi(x_i) is conjugate to x_j or x_j^{-1} for some 1 \\le j \\le m. Let \\Sigma\\Aut_n^m be the group of partially symmetric automorphisms. We prove that for any m \\ge 0 the inclusion \\Sigma\\Aut_n^m \\to \\Sigma\\Aut_{n+1}^m induces an isomorphism in rational homology for dimensions i satisfying n \\ge (3(i+1)+m)/2, with a similar statement for the groups P\\Sigma\\Aut_n^m of pure partially symmetric automorphisms. We also prove that for any"},"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":"1203.4845","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-03-21T21:39:58Z","cross_cats_sorted":[],"title_canon_sha256":"e0bdee1bcebb0775cc26bcc21cb448049dd297edfd936976eb41e22d4967b5aa","abstract_canon_sha256":"d403d761f7cf0e8b07d34fa0aaaace6ab3219d87334c16de39f83cd762624ef4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:43.306264Z","signature_b64":"Ne6pNg/NjARXMJoxI8iX4oIATOHdjwrWTAgY3OrDyiSszdMRZIJA7Ks6qpKz9XS2MxN0yBUASSjdJhqu6xCcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5238f376786903853b6c6a66e437d440c276ee01243eb0625039c9b5ce455db7","last_reissued_at":"2026-05-18T02:41:43.305815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:43.305815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational homological stability for groups of partially symmetric automorphisms of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Matthew C. B. Zaremsky","submitted_at":"2012-03-21T21:39:58Z","abstract_excerpt":"Let F_{n+m} be the free group of rank n+m, with generators x_1,...,x_{n+m}. An automorphism \\phi of F_{n+m} is called partially symmetric if for each 1 \\le i \\le m, \\phi(x_i) is conjugate to x_j or x_j^{-1} for some 1 \\le j \\le m. Let \\Sigma\\Aut_n^m be the group of partially symmetric automorphisms. We prove that for any m \\ge 0 the inclusion \\Sigma\\Aut_n^m \\to \\Sigma\\Aut_{n+1}^m induces an isomorphism in rational homology for dimensions i satisfying n \\ge (3(i+1)+m)/2, with a similar statement for the groups P\\Sigma\\Aut_n^m of pure partially symmetric automorphisms. We also prove that for any"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4845","kind":"arxiv","version":4},"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":"1203.4845","created_at":"2026-05-18T02:41:43.305881+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.4845v4","created_at":"2026-05-18T02:41:43.305881+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4845","created_at":"2026-05-18T02:41:43.305881+00:00"},{"alias_kind":"pith_short_12","alias_value":"KI4PG5TYNEBY","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"KI4PG5TYNEBYKO3M","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"KI4PG5TY","created_at":"2026-05-18T12:27:11.947152+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/KI4PG5TYNEBYKO3MNJTOIN6UID","json":"https://pith.science/pith/KI4PG5TYNEBYKO3MNJTOIN6UID.json","graph_json":"https://pith.science/api/pith-number/KI4PG5TYNEBYKO3MNJTOIN6UID/graph.json","events_json":"https://pith.science/api/pith-number/KI4PG5TYNEBYKO3MNJTOIN6UID/events.json","paper":"https://pith.science/paper/KI4PG5TY"},"agent_actions":{"view_html":"https://pith.science/pith/KI4PG5TYNEBYKO3MNJTOIN6UID","download_json":"https://pith.science/pith/KI4PG5TYNEBYKO3MNJTOIN6UID.json","view_paper":"https://pith.science/paper/KI4PG5TY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.4845&json=true","fetch_graph":"https://pith.science/api/pith-number/KI4PG5TYNEBYKO3MNJTOIN6UID/graph.json","fetch_events":"https://pith.science/api/pith-number/KI4PG5TYNEBYKO3MNJTOIN6UID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KI4PG5TYNEBYKO3MNJTOIN6UID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KI4PG5TYNEBYKO3MNJTOIN6UID/action/storage_attestation","attest_author":"https://pith.science/pith/KI4PG5TYNEBYKO3MNJTOIN6UID/action/author_attestation","sign_citation":"https://pith.science/pith/KI4PG5TYNEBYKO3MNJTOIN6UID/action/citation_signature","submit_replication":"https://pith.science/pith/KI4PG5TYNEBYKO3MNJTOIN6UID/action/replication_record"}},"created_at":"2026-05-18T02:41:43.305881+00:00","updated_at":"2026-05-18T02:41:43.305881+00:00"}