{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FA337BJJRL2PQB6KN4OQOCAD5G","short_pith_number":"pith:FA337BJJ","canonical_record":{"source":{"id":"1109.2687","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-13T07:28:59Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"455e23a24d4d7656c401c3b5a035c6e9319d02c7ffbede1fcb8b14250a9aa15e","abstract_canon_sha256":"cb6c7e68318eb89065c6dfb519ea9cf79a14da1bf922590b7726a13a562a22f0"},"schema_version":"1.0"},"canonical_sha256":"2837bf85298af4f807ca6f1d070803e98522e2e80b04f27f77c7114a526e5839","source":{"kind":"arxiv","id":"1109.2687","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2687","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2687v3","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2687","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"FA337BJJRL2P","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FA337BJJRL2PQB6K","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FA337BJJ","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FA337BJJRL2PQB6KN4OQOCAD5G","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2687","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-13T07:28:59Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"455e23a24d4d7656c401c3b5a035c6e9319d02c7ffbede1fcb8b14250a9aa15e","abstract_canon_sha256":"cb6c7e68318eb89065c6dfb519ea9cf79a14da1bf922590b7726a13a562a22f0"},"schema_version":"1.0"},"canonical_sha256":"2837bf85298af4f807ca6f1d070803e98522e2e80b04f27f77c7114a526e5839","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:30.530105Z","signature_b64":"cr+bFMqspo3LhYTd2PLMlhC/YM5CI5YFHFpZ4cyKtgC2uqfCwpKNxDbnitxS/yV9IbMVc56TmixBiUgXQwijAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2837bf85298af4f807ca6f1d070803e98522e2e80b04f27f77c7114a526e5839","last_reissued_at":"2026-05-18T00:44:30.529574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:30.529574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2687","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TcFH9AQMJcWegkoI4kxtzkdNMCACfcyypHaQQkuLKrS1sEbdeS1W/tIG8MY1+BP6yepAieiLUsHBnN/zWPejAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:20:03.909791Z"},"content_sha256":"81529a90f40aa0657b0dcbccb22f33d08068d864de27fb6daf21f34088891c89","schema_version":"1.0","event_id":"sha256:81529a90f40aa0657b0dcbccb22f33d08068d864de27fb6daf21f34088891c89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FA337BJJRL2PQB6KN4OQOCAD5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spheres and Projections for $\\mathrm{Out}(F_n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Sebastian Hensel, Ursula Hamenst\\\"adt","submitted_at":"2011-09-13T07:28:59Z","abstract_excerpt":"The outer automorphism group Out(F_2g) of a free group on 2g generators naturally contains the mapping class group of a punctured surface as a subgroup. We define a subsurface projection of the sphere complex of the connected sum of n copies of S^1 x S^2 into the arc complex of the surface and use this to show that this subgroup is a Lipschitz retract of Out(F_2g). We also use subsurface projections to give a simple proof of a result of Handel and Mosher [HM10] stating that stabilizers of conjugacy classes of free splittings and corank 1 free factors in a free group Fn are Lipschitz retracts o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2687","kind":"arxiv","version":3},"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":"2026-05-18T00:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9BGfoK2ZddgPbaidh6z0KNwG09JERiInXQ8lKffyesG/gVU/H1uz7Iec8ynlHtc2uKCajGoLDhNnUfbkgSpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:20:03.910136Z"},"content_sha256":"9654e0c3692add4492152c9345d030115c453f079575e0037d5bbfc662fa129b","schema_version":"1.0","event_id":"sha256:9654e0c3692add4492152c9345d030115c453f079575e0037d5bbfc662fa129b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FA337BJJRL2PQB6KN4OQOCAD5G/bundle.json","state_url":"https://pith.science/pith/FA337BJJRL2PQB6KN4OQOCAD5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FA337BJJRL2PQB6KN4OQOCAD5G/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":"2026-06-05T10:20:03Z","links":{"resolver":"https://pith.science/pith/FA337BJJRL2PQB6KN4OQOCAD5G","bundle":"https://pith.science/pith/FA337BJJRL2PQB6KN4OQOCAD5G/bundle.json","state":"https://pith.science/pith/FA337BJJRL2PQB6KN4OQOCAD5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FA337BJJRL2PQB6KN4OQOCAD5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FA337BJJRL2PQB6KN4OQOCAD5G","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":"cb6c7e68318eb89065c6dfb519ea9cf79a14da1bf922590b7726a13a562a22f0","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-13T07:28:59Z","title_canon_sha256":"455e23a24d4d7656c401c3b5a035c6e9319d02c7ffbede1fcb8b14250a9aa15e"},"schema_version":"1.0","source":{"id":"1109.2687","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2687","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2687v3","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2687","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"FA337BJJRL2P","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FA337BJJRL2PQB6K","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FA337BJJ","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:9654e0c3692add4492152c9345d030115c453f079575e0037d5bbfc662fa129b","target":"graph","created_at":"2026-05-18T00:44:30Z","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":"The outer automorphism group Out(F_2g) of a free group on 2g generators naturally contains the mapping class group of a punctured surface as a subgroup. We define a subsurface projection of the sphere complex of the connected sum of n copies of S^1 x S^2 into the arc complex of the surface and use this to show that this subgroup is a Lipschitz retract of Out(F_2g). We also use subsurface projections to give a simple proof of a result of Handel and Mosher [HM10] stating that stabilizers of conjugacy classes of free splittings and corank 1 free factors in a free group Fn are Lipschitz retracts o","authors_text":"Sebastian Hensel, Ursula Hamenst\\\"adt","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-13T07:28:59Z","title":"Spheres and Projections for $\\mathrm{Out}(F_n)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2687","kind":"arxiv","version":3},"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":"sha256:81529a90f40aa0657b0dcbccb22f33d08068d864de27fb6daf21f34088891c89","target":"record","created_at":"2026-05-18T00:44:30Z","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":"cb6c7e68318eb89065c6dfb519ea9cf79a14da1bf922590b7726a13a562a22f0","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-13T07:28:59Z","title_canon_sha256":"455e23a24d4d7656c401c3b5a035c6e9319d02c7ffbede1fcb8b14250a9aa15e"},"schema_version":"1.0","source":{"id":"1109.2687","kind":"arxiv","version":3}},"canonical_sha256":"2837bf85298af4f807ca6f1d070803e98522e2e80b04f27f77c7114a526e5839","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2837bf85298af4f807ca6f1d070803e98522e2e80b04f27f77c7114a526e5839","first_computed_at":"2026-05-18T00:44:30.529574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:30.529574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cr+bFMqspo3LhYTd2PLMlhC/YM5CI5YFHFpZ4cyKtgC2uqfCwpKNxDbnitxS/yV9IbMVc56TmixBiUgXQwijAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:30.530105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2687","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81529a90f40aa0657b0dcbccb22f33d08068d864de27fb6daf21f34088891c89","sha256:9654e0c3692add4492152c9345d030115c453f079575e0037d5bbfc662fa129b"],"state_sha256":"676aea78ef36bf07a50746f773ec20919f6f725acbfcb4ca1fd6ed41c95e298b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4vGI9vFA5VxaqMFBrY2iCxqEzvw7tALCwwFZ5QUGYjY6eIbM/gaPC1o/I6yvrPz49H/v2A4QToYOJdUa8oTWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:20:03.912172Z","bundle_sha256":"9d62645b890b22098ec8de0d58f0e0a7c7cc243e330ee2ef183f2c4c5de00373"}}