{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XRG7DMV7QTCX4UL6VPAC7KVD44","short_pith_number":"pith:XRG7DMV7","canonical_record":{"source":{"id":"1304.0498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-01T23:34:50Z","cross_cats_sorted":[],"title_canon_sha256":"272e48ca094a13ad3771e2d46ad64591014b97e0ccfd730ada47dfc504aaa790","abstract_canon_sha256":"a587cbcfcb3f1195409ec76ead48a2ed16c61b272595c3bc39a2a5cc4f1e6cdd"},"schema_version":"1.0"},"canonical_sha256":"bc4df1b2bf84c57e517eabc02faaa3e70f352006fc67279fc743358f69e68610","source":{"kind":"arxiv","id":"1304.0498","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0498","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0498v2","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0498","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"XRG7DMV7QTCX","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XRG7DMV7QTCX4UL6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XRG7DMV7","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XRG7DMV7QTCX4UL6VPAC7KVD44","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-01T23:34:50Z","cross_cats_sorted":[],"title_canon_sha256":"272e48ca094a13ad3771e2d46ad64591014b97e0ccfd730ada47dfc504aaa790","abstract_canon_sha256":"a587cbcfcb3f1195409ec76ead48a2ed16c61b272595c3bc39a2a5cc4f1e6cdd"},"schema_version":"1.0"},"canonical_sha256":"bc4df1b2bf84c57e517eabc02faaa3e70f352006fc67279fc743358f69e68610","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:53.722675Z","signature_b64":"9goKjPWG0c7TsGZ9kXBB7KPt0IGv1K1I/rTvHlB0K4MbRMI/lvyAQnBu5ovTZB7GtWNMzHO4Z9+SGESIamXqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc4df1b2bf84c57e517eabc02faaa3e70f352006fc67279fc743358f69e68610","last_reissued_at":"2026-05-18T01:03:53.722114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:53.722114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0498","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":"2026-05-18T01:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SUVT2ddtbqHs2m/DXGlMtf7XVhJb8GeMSK8jm2OPQDv7MVNnHMOvHvWRb7ckEDQ6jRYjNAyvusBferjzXvwIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:09:04.086255Z"},"content_sha256":"fd4e959d3bc93e7f654bd462720f77d090207f1cf363f07f5cdd3160ec23a2cf","schema_version":"1.0","event_id":"sha256:fd4e959d3bc93e7f654bd462720f77d090207f1cf363f07f5cdd3160ec23a2cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XRG7DMV7QTCX4UL6VPAC7KVD44","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphisms of free groups, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Laurent Bartholdi","submitted_at":"2013-04-01T23:34:50Z","abstract_excerpt":"We describe, up to degree equal to the rank, the Lie algebra associated with the automorphism group of a free group. We compute in particular the ranks of its homogeneous components, and their structure as modules over the linear group.\n  Along the way, we infirm (but confirm a weaker form of) a conjecture by Andreadakis, and answer a question by Bryant-Gupta-Levin-Mochizuki."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0498","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":"2026-05-18T01:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HLWu3CbTr27i2YG/ncWUpLvLOt/IY26MnPPF72mx3H7HX7jqphU/GTvN/8JtPZPsW59RcYJZ80TPJilNEfqtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:09:04.086977Z"},"content_sha256":"9a90d506b1215a2a293b972ee45b449ddc709c5b978daf7e7a37f2e0aa915c8b","schema_version":"1.0","event_id":"sha256:9a90d506b1215a2a293b972ee45b449ddc709c5b978daf7e7a37f2e0aa915c8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XRG7DMV7QTCX4UL6VPAC7KVD44/bundle.json","state_url":"https://pith.science/pith/XRG7DMV7QTCX4UL6VPAC7KVD44/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XRG7DMV7QTCX4UL6VPAC7KVD44/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":"2026-06-09T17:09:04Z","links":{"resolver":"https://pith.science/pith/XRG7DMV7QTCX4UL6VPAC7KVD44","bundle":"https://pith.science/pith/XRG7DMV7QTCX4UL6VPAC7KVD44/bundle.json","state":"https://pith.science/pith/XRG7DMV7QTCX4UL6VPAC7KVD44/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XRG7DMV7QTCX4UL6VPAC7KVD44/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XRG7DMV7QTCX4UL6VPAC7KVD44","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":"a587cbcfcb3f1195409ec76ead48a2ed16c61b272595c3bc39a2a5cc4f1e6cdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-01T23:34:50Z","title_canon_sha256":"272e48ca094a13ad3771e2d46ad64591014b97e0ccfd730ada47dfc504aaa790"},"schema_version":"1.0","source":{"id":"1304.0498","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0498","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0498v2","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0498","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"XRG7DMV7QTCX","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XRG7DMV7QTCX4UL6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XRG7DMV7","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:9a90d506b1215a2a293b972ee45b449ddc709c5b978daf7e7a37f2e0aa915c8b","target":"graph","created_at":"2026-05-18T01:03:53Z","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 describe, up to degree equal to the rank, the Lie algebra associated with the automorphism group of a free group. We compute in particular the ranks of its homogeneous components, and their structure as modules over the linear group.\n  Along the way, we infirm (but confirm a weaker form of) a conjecture by Andreadakis, and answer a question by Bryant-Gupta-Levin-Mochizuki.","authors_text":"Laurent Bartholdi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-01T23:34:50Z","title":"Automorphisms of free groups, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0498","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:fd4e959d3bc93e7f654bd462720f77d090207f1cf363f07f5cdd3160ec23a2cf","target":"record","created_at":"2026-05-18T01:03:53Z","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":"a587cbcfcb3f1195409ec76ead48a2ed16c61b272595c3bc39a2a5cc4f1e6cdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-01T23:34:50Z","title_canon_sha256":"272e48ca094a13ad3771e2d46ad64591014b97e0ccfd730ada47dfc504aaa790"},"schema_version":"1.0","source":{"id":"1304.0498","kind":"arxiv","version":2}},"canonical_sha256":"bc4df1b2bf84c57e517eabc02faaa3e70f352006fc67279fc743358f69e68610","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc4df1b2bf84c57e517eabc02faaa3e70f352006fc67279fc743358f69e68610","first_computed_at":"2026-05-18T01:03:53.722114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:53.722114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9goKjPWG0c7TsGZ9kXBB7KPt0IGv1K1I/rTvHlB0K4MbRMI/lvyAQnBu5ovTZB7GtWNMzHO4Z9+SGESIamXqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:53.722675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0498","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd4e959d3bc93e7f654bd462720f77d090207f1cf363f07f5cdd3160ec23a2cf","sha256:9a90d506b1215a2a293b972ee45b449ddc709c5b978daf7e7a37f2e0aa915c8b"],"state_sha256":"4c0593fe87e1688faf5fbea58907c69a5745ae36bef1ef0c4f390e665bf72d16"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cTnzL5oNSa3m1Ay/oPOFgbPQ39c1FJECDzGKS8yjv9TgTV3x6iIJDC1Ue34MVDOQoS2XSFOAjNdQBtfMVwmrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:09:04.091043Z","bundle_sha256":"f62fcb671376e703a0dc70a9e9ed0f5c4f20f4c898796cd48a5ca430dee0f1d9"}}