{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QUNDTVH4CH2Y5LBNWKPELDUXQ3","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":"9c9efb637a4df19292590602794a0e45197612767df93f46f99a1c22de5b1c00","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-15T14:00:00Z","title_canon_sha256":"902c00bbdc072e580cd6a61e82b24aaf43d03a0d86a115d1b6876965a7584edf"},"schema_version":"1.0","source":{"id":"1211.3608","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3608","created_at":"2026-05-18T01:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3608v2","created_at":"2026-05-18T01:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3608","created_at":"2026-05-18T01:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"QUNDTVH4CH2Y","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QUNDTVH4CH2Y5LBN","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QUNDTVH4","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:4da2aead70f104854c57c8b618db253b6d75b79bb41c58e3f536b63d88ff2a35","target":"graph","created_at":"2026-05-18T01:28:21Z","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 give a description of the boundary of a complex of free factors that is analogous to E. Klarreich's description of the boundary of a curve complex. The argument uses the geometry of folding paths developed by Bestvina and Feighn as well as structural results about very small trees developed by Coulbois, Hilion, Lustig, and Reynolds.","authors_text":"Mladen Bestvina, Patrick Reynolds","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-15T14:00:00Z","title":"The boundary of the complex of free factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3608","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:c32216928154da213b157c717bca15bf765fb8d1ace69a8dba54dec6ab2dcfd5","target":"record","created_at":"2026-05-18T01:28:21Z","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":"9c9efb637a4df19292590602794a0e45197612767df93f46f99a1c22de5b1c00","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-15T14:00:00Z","title_canon_sha256":"902c00bbdc072e580cd6a61e82b24aaf43d03a0d86a115d1b6876965a7584edf"},"schema_version":"1.0","source":{"id":"1211.3608","kind":"arxiv","version":2}},"canonical_sha256":"851a39d4fc11f58eac2db29e458e9786d587c9753933ce520f8889a163c61d64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"851a39d4fc11f58eac2db29e458e9786d587c9753933ce520f8889a163c61d64","first_computed_at":"2026-05-18T01:28:21.430834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:21.430834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lXWGgB7ODq9SLgkQknm29FYj8KaryX6X+bX1F2c1PLqJRbHppz/ECkyL8dTrfAE70YDfBYizWI5vxbrtERgUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:21.431330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3608","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c32216928154da213b157c717bca15bf765fb8d1ace69a8dba54dec6ab2dcfd5","sha256:4da2aead70f104854c57c8b618db253b6d75b79bb41c58e3f536b63d88ff2a35"],"state_sha256":"154472ea12eb1fb146f178f72c1e247c443b6aab65a2b005cb25e1dd099c7dc6"}