{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4A6HGQYOE3UJHYASMOYCGH3TBY","short_pith_number":"pith:4A6HGQYO","canonical_record":{"source":{"id":"1111.6506","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-11-28T16:31:34Z","cross_cats_sorted":[],"title_canon_sha256":"c2914f5373b2c264303f4afc082bc3d1fe76d9baaf7914c81105566c94c9dbf1","abstract_canon_sha256":"88ad0644550e5b9eb43432631d2cefcca3615d30a9f5b8f40790075f4e9e2305"},"schema_version":"1.0"},"canonical_sha256":"e03c73430e26e893e01263b0231f730e2c30847168bc3efe0aa0ec72aabf3423","source":{"kind":"arxiv","id":"1111.6506","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6506","created_at":"2026-05-18T03:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6506v3","created_at":"2026-05-18T03:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6506","created_at":"2026-05-18T03:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"4A6HGQYOE3UJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4A6HGQYOE3UJHYAS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4A6HGQYO","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4A6HGQYOE3UJHYASMOYCGH3TBY","target":"record","payload":{"canonical_record":{"source":{"id":"1111.6506","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-11-28T16:31:34Z","cross_cats_sorted":[],"title_canon_sha256":"c2914f5373b2c264303f4afc082bc3d1fe76d9baaf7914c81105566c94c9dbf1","abstract_canon_sha256":"88ad0644550e5b9eb43432631d2cefcca3615d30a9f5b8f40790075f4e9e2305"},"schema_version":"1.0"},"canonical_sha256":"e03c73430e26e893e01263b0231f730e2c30847168bc3efe0aa0ec72aabf3423","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:27.161080Z","signature_b64":"RCRrAUPOPtPORTvzpLiSB3Kf2q2w+yJ/3Q6oWhYUUmDkpYBTnMCm2H+AwKyw5CAeQdpyPOZ1Vbm3nnBMHde3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e03c73430e26e893e01263b0231f730e2c30847168bc3efe0aa0ec72aabf3423","last_reissued_at":"2026-05-18T03:59:27.160510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:27.160510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.6506","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":"2026-05-18T03:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dLOv0/G7CdmcG3gCiz6/f+yXirf6sc1w9YMaeXLaIgdd6v2WuaRyVuS9AWKhakp/GujP+nc7TLHlRvY+A+wQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T13:39:23.042418Z"},"content_sha256":"d5b141ff5de0b854571113c48612e419de6c00fa12d618f4838a9eec5764bc5f","schema_version":"1.0","event_id":"sha256:d5b141ff5de0b854571113c48612e419de6c00fa12d618f4838a9eec5764bc5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4A6HGQYOE3UJHYASMOYCGH3TBY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational homological stability for groups of 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":"2011-11-28T16:31:34Z","abstract_excerpt":"Let F_n be the free group of rank n, with generating set S=\\{x_1,...,x_n\\}. An automorphism \\phi of F_n is called symmetric if for each 1\\leq i\\leq n, \\phi(x_i) is conjugate to x_j or x_j^{-1} for some 1\\leq j\\leq n. Let \\Sigma Aut(F_n) be the group of symmetric automorphisms. We prove that the inclusion \\Sigma Aut(F_n) \\rightarrow \\Sigma Aut(F_{n+1}) induces an isomorphism in rational homology for n>(3i-1)/2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6506","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":"2026-05-18T03:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PfHy2yuVoTQOY+FpIB0OshoFKBi1QGpaZytx5xZW+m+UAwn8mS1HAGD0ImZdfHiE8RvaGaCSmnB4JIKT4QpVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T13:39:23.043092Z"},"content_sha256":"f6c7edb4116d595e7b6d59ee5d5e9a9d5ed73cafae825db7fb5199a247c4d586","schema_version":"1.0","event_id":"sha256:f6c7edb4116d595e7b6d59ee5d5e9a9d5ed73cafae825db7fb5199a247c4d586"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4A6HGQYOE3UJHYASMOYCGH3TBY/bundle.json","state_url":"https://pith.science/pith/4A6HGQYOE3UJHYASMOYCGH3TBY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4A6HGQYOE3UJHYASMOYCGH3TBY/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":"2026-06-07T13:39:23Z","links":{"resolver":"https://pith.science/pith/4A6HGQYOE3UJHYASMOYCGH3TBY","bundle":"https://pith.science/pith/4A6HGQYOE3UJHYASMOYCGH3TBY/bundle.json","state":"https://pith.science/pith/4A6HGQYOE3UJHYASMOYCGH3TBY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4A6HGQYOE3UJHYASMOYCGH3TBY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4A6HGQYOE3UJHYASMOYCGH3TBY","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":"88ad0644550e5b9eb43432631d2cefcca3615d30a9f5b8f40790075f4e9e2305","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-11-28T16:31:34Z","title_canon_sha256":"c2914f5373b2c264303f4afc082bc3d1fe76d9baaf7914c81105566c94c9dbf1"},"schema_version":"1.0","source":{"id":"1111.6506","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6506","created_at":"2026-05-18T03:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6506v3","created_at":"2026-05-18T03:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6506","created_at":"2026-05-18T03:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"4A6HGQYOE3UJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4A6HGQYOE3UJHYAS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4A6HGQYO","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:f6c7edb4116d595e7b6d59ee5d5e9a9d5ed73cafae825db7fb5199a247c4d586","target":"graph","created_at":"2026-05-18T03:59:27Z","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":"Let F_n be the free group of rank n, with generating set S=\\{x_1,...,x_n\\}. An automorphism \\phi of F_n is called symmetric if for each 1\\leq i\\leq n, \\phi(x_i) is conjugate to x_j or x_j^{-1} for some 1\\leq j\\leq n. Let \\Sigma Aut(F_n) be the group of symmetric automorphisms. We prove that the inclusion \\Sigma Aut(F_n) \\rightarrow \\Sigma Aut(F_{n+1}) induces an isomorphism in rational homology for n>(3i-1)/2.","authors_text":"Matthew C. B. Zaremsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-11-28T16:31:34Z","title":"Rational homological stability for groups of symmetric automorphisms of free groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6506","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:d5b141ff5de0b854571113c48612e419de6c00fa12d618f4838a9eec5764bc5f","target":"record","created_at":"2026-05-18T03:59:27Z","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":"88ad0644550e5b9eb43432631d2cefcca3615d30a9f5b8f40790075f4e9e2305","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-11-28T16:31:34Z","title_canon_sha256":"c2914f5373b2c264303f4afc082bc3d1fe76d9baaf7914c81105566c94c9dbf1"},"schema_version":"1.0","source":{"id":"1111.6506","kind":"arxiv","version":3}},"canonical_sha256":"e03c73430e26e893e01263b0231f730e2c30847168bc3efe0aa0ec72aabf3423","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e03c73430e26e893e01263b0231f730e2c30847168bc3efe0aa0ec72aabf3423","first_computed_at":"2026-05-18T03:59:27.160510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:27.160510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RCRrAUPOPtPORTvzpLiSB3Kf2q2w+yJ/3Q6oWhYUUmDkpYBTnMCm2H+AwKyw5CAeQdpyPOZ1Vbm3nnBMHde3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:27.161080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6506","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5b141ff5de0b854571113c48612e419de6c00fa12d618f4838a9eec5764bc5f","sha256:f6c7edb4116d595e7b6d59ee5d5e9a9d5ed73cafae825db7fb5199a247c4d586"],"state_sha256":"f94aeec2b21610525808c04d0e156ad87bdf947f2f210c57466829bd774c3352"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R781xpnKg0t5nBH42XDMp4CvVnb/w1wxKry/EagmTyZ5JpZr9mSohE6XL187rtox9+CANrLxuT2rkom53nD3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T13:39:23.048195Z","bundle_sha256":"c1a624a706b51c8f929b02789bda3426c80c0aa13289b6c7eaf1f2b35ef772cc"}}