{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YK4SZAICBKCXRZBLSB5HDIPTFV","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":"a4734aeea23129f6a88671234ba05fe6a67ce99b46139cf97f7f99e62c680a47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-08T20:47:01Z","title_canon_sha256":"648773a51366032059b9bcb2cc2241839760edebc3888e5d2e60122c42f59fe2"},"schema_version":"1.0","source":{"id":"1103.1624","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1624","created_at":"2026-05-18T01:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1624v2","created_at":"2026-05-18T01:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1624","created_at":"2026-05-18T01:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"YK4SZAICBKCX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YK4SZAICBKCXRZBL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YK4SZAIC","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:99db729c3f422b60cde116aa237bc7fa7df251cfc2630d599f87482113922d7d","target":"graph","created_at":"2026-05-18T01:56:00Z","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":"We study the existence of homomorphisms between Out(F_n) and Out(F_m) for n > 5 and m < n(n-1)/2, and conclude that if m is not equal to n then each such homomorphism factors through the finite group of order 2. In particular this provides an answer to a question of Bogopol'skii and Puga. In the course of the argument linear representations of Out(F_n) in dimension less than n(n+1)/2 over fields of characteristic zero are completely classified. It is shown that each such representation has to factor through the natural projection from Out(F_n) to GL(n,Z) coming from the action of Out(F_n) on t","authors_text":"Dawid Kielak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-08T20:47:01Z","title":"Outer automorphism groups of free groups: linear and free representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1624","kind":"arxiv","version":2},"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":"sha256:150e594bcb58d9e2dfabea75f06999875c50ab98026ff8119fb183ccaf58d4c9","target":"record","created_at":"2026-05-18T01:56:00Z","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":"a4734aeea23129f6a88671234ba05fe6a67ce99b46139cf97f7f99e62c680a47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-08T20:47:01Z","title_canon_sha256":"648773a51366032059b9bcb2cc2241839760edebc3888e5d2e60122c42f59fe2"},"schema_version":"1.0","source":{"id":"1103.1624","kind":"arxiv","version":2}},"canonical_sha256":"c2b92c81020a8578e42b907a71a1f32d669ebefc167ddef8ffab759f5ae798b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2b92c81020a8578e42b907a71a1f32d669ebefc167ddef8ffab759f5ae798b9","first_computed_at":"2026-05-18T01:56:00.220031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:00.220031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YSJvZx4Gt7glF7SZa8EYA4G24GuRmoEhzLV4BGOnqoBxqQm9+xFk56QDve918XiGiJhU7Xh5CzRdFNUbNq7LCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:00.220629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1624","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:150e594bcb58d9e2dfabea75f06999875c50ab98026ff8119fb183ccaf58d4c9","sha256:99db729c3f422b60cde116aa237bc7fa7df251cfc2630d599f87482113922d7d"],"state_sha256":"6a6d54d09d889b7c452bbe27acd29ad00c5d845ad5871ea13829986ad95a4a71"}