{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IFMLB6FBVVBHO5MMK5GAOACBTB","short_pith_number":"pith:IFMLB6FB","canonical_record":{"source":{"id":"1607.07031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-07-24T11:53:17Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"0114ca60412ae0924d1a05b83a2733711762da31af36f57800f62596168ec49d","abstract_canon_sha256":"20b614a87d9f77e587c539c78dfe25fff712bb1027314c59c7f5779d7bd8d216"},"schema_version":"1.0"},"canonical_sha256":"4158b0f8a1ad4277758c574c070041984ba349dc0304a31a07ad02612c05c71d","source":{"kind":"arxiv","id":"1607.07031","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07031","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07031v2","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07031","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"IFMLB6FBVVBH","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IFMLB6FBVVBHO5MM","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IFMLB6FB","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IFMLB6FBVVBHO5MMK5GAOACBTB","target":"record","payload":{"canonical_record":{"source":{"id":"1607.07031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-07-24T11:53:17Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"0114ca60412ae0924d1a05b83a2733711762da31af36f57800f62596168ec49d","abstract_canon_sha256":"20b614a87d9f77e587c539c78dfe25fff712bb1027314c59c7f5779d7bd8d216"},"schema_version":"1.0"},"canonical_sha256":"4158b0f8a1ad4277758c574c070041984ba349dc0304a31a07ad02612c05c71d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:59.289395Z","signature_b64":"ISBS55dr0iP17U486gKCLedjb36NuoA+oKXnbztXSJzMHnJ//wrIO59f4f1nQ83mtXK/GEIgQsfKX/Awefg7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4158b0f8a1ad4277758c574c070041984ba349dc0304a31a07ad02612c05c71d","last_reissued_at":"2026-05-18T00:20:59.288852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:59.288852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.07031","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9PISDHcJA5A1V/xK64mtsQ5J+dDE6/KhiQT9FGJYKAk6Q6VxEoCF/U6xONIRhGTkQy40IwNtvb4dA891kuwHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:59:47.887074Z"},"content_sha256":"f9198245c9df940d04ca576d76268ed339797d3f375ad2a88f1fa648048af498","schema_version":"1.0","event_id":"sha256:f9198245c9df940d04ca576d76268ed339797d3f375ad2a88f1fa648048af498"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IFMLB6FBVVBHO5MMK5GAOACBTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Outer actions of $\\mathrm{Out}(F_n)$ on small right-angled Artin groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Dawid Kielak","submitted_at":"2016-07-24T11:53:17Z","abstract_excerpt":"We determine the precise conditions under which $\\mathrm{SOut}(F_n)$, the unique index two subgroup of $\\mathrm{Out}(F_n)$, can act non-trivially via outer automorphisms on a RAAG whose defining graph has fewer than $\\frac 1 2 \\binom n 2 $ vertices.\n  We also show that the outer automorphism group of a RAAG cannot act faithfully via outer automorphisms on a RAAG with a strictly smaller (in number of vertices) defining graph.\n  Along the way we determine the minimal dimensions of non-trivial linear representations of congruence quotients of the integral special linear groups over algebraically "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07031","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OTK2v6YnxFpU1NxB06GF5TB2pAFO4JtW/uGMXkqfswUYMGu2QjRF6w+Gc7wh8eeVkI2B0WPK4gmL0/VO/H8gBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:59:47.887439Z"},"content_sha256":"ef3e81623fea43af4ac31120c1e8e1b9eae138379be034b755eabdeeb11673bf","schema_version":"1.0","event_id":"sha256:ef3e81623fea43af4ac31120c1e8e1b9eae138379be034b755eabdeeb11673bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IFMLB6FBVVBHO5MMK5GAOACBTB/bundle.json","state_url":"https://pith.science/pith/IFMLB6FBVVBHO5MMK5GAOACBTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IFMLB6FBVVBHO5MMK5GAOACBTB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T22:59:47Z","links":{"resolver":"https://pith.science/pith/IFMLB6FBVVBHO5MMK5GAOACBTB","bundle":"https://pith.science/pith/IFMLB6FBVVBHO5MMK5GAOACBTB/bundle.json","state":"https://pith.science/pith/IFMLB6FBVVBHO5MMK5GAOACBTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IFMLB6FBVVBHO5MMK5GAOACBTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IFMLB6FBVVBHO5MMK5GAOACBTB","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":"20b614a87d9f77e587c539c78dfe25fff712bb1027314c59c7f5779d7bd8d216","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-07-24T11:53:17Z","title_canon_sha256":"0114ca60412ae0924d1a05b83a2733711762da31af36f57800f62596168ec49d"},"schema_version":"1.0","source":{"id":"1607.07031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07031","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07031v2","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07031","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"IFMLB6FBVVBH","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IFMLB6FBVVBHO5MM","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IFMLB6FB","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:ef3e81623fea43af4ac31120c1e8e1b9eae138379be034b755eabdeeb11673bf","target":"graph","created_at":"2026-05-18T00:20:59Z","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 determine the precise conditions under which $\\mathrm{SOut}(F_n)$, the unique index two subgroup of $\\mathrm{Out}(F_n)$, can act non-trivially via outer automorphisms on a RAAG whose defining graph has fewer than $\\frac 1 2 \\binom n 2 $ vertices.\n  We also show that the outer automorphism group of a RAAG cannot act faithfully via outer automorphisms on a RAAG with a strictly smaller (in number of vertices) defining graph.\n  Along the way we determine the minimal dimensions of non-trivial linear representations of congruence quotients of the integral special linear groups over algebraically ","authors_text":"Dawid Kielak","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-07-24T11:53:17Z","title":"Outer actions of $\\mathrm{Out}(F_n)$ on small right-angled Artin groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07031","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:f9198245c9df940d04ca576d76268ed339797d3f375ad2a88f1fa648048af498","target":"record","created_at":"2026-05-18T00:20:59Z","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":"20b614a87d9f77e587c539c78dfe25fff712bb1027314c59c7f5779d7bd8d216","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-07-24T11:53:17Z","title_canon_sha256":"0114ca60412ae0924d1a05b83a2733711762da31af36f57800f62596168ec49d"},"schema_version":"1.0","source":{"id":"1607.07031","kind":"arxiv","version":2}},"canonical_sha256":"4158b0f8a1ad4277758c574c070041984ba349dc0304a31a07ad02612c05c71d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4158b0f8a1ad4277758c574c070041984ba349dc0304a31a07ad02612c05c71d","first_computed_at":"2026-05-18T00:20:59.288852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:59.288852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ISBS55dr0iP17U486gKCLedjb36NuoA+oKXnbztXSJzMHnJ//wrIO59f4f1nQ83mtXK/GEIgQsfKX/Awefg7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:59.289395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9198245c9df940d04ca576d76268ed339797d3f375ad2a88f1fa648048af498","sha256:ef3e81623fea43af4ac31120c1e8e1b9eae138379be034b755eabdeeb11673bf"],"state_sha256":"012fb6ebc7f3a2c683e66c6105682fd12890102cf3dc0c3e6373123ec6edcb66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nq07R9KqezU6R/UHSIsqlXtAI6nrtrBXmdATolS0bsCf2r3JlZMrjf/5DN1sFb6PfsMkpbxHt5izvcXdxDLSBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:59:47.889759Z","bundle_sha256":"8c0ace864c9bb21428fed660ff9a0b3ff8079f8eb66ba732099c91bf7fbc6789"}}