{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YZCNRHZJEO7L5BS6JWGGRUP3YK","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":"9af9df642281b5163a26528db56ccbf94f9627bed418893dc3a8ac5e12868a2f","cross_cats_sorted":["math.DS","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-29T20:16:48Z","title_canon_sha256":"41e82977c7aadbb00b4c76bf019d5a827d60f3f65890915dc913ba220ae39fd3"},"schema_version":"1.0","source":{"id":"1008.4952","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4952","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4952v4","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4952","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"YZCNRHZJEO7L","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YZCNRHZJEO7L5BS6","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YZCNRHZJ","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:d77ffe3e5dd7e179eb95e40747b692a08858ed40baec9965fb6cb3cb52d229c2","target":"graph","created_at":"2026-05-17T23:53:36Z","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 obtain sharp estimates on the growth rate of stable commutator length on random (geodesic) words, and on random walks, in hyperbolic groups and groups acting nondegenerately on hyperbolic spaces. In either case, we show that with high probability stable commutator length of an element of length $n$ is of order $n/\\log{n}$.\n  This establishes quantitative refinements of qualitative results of Bestvina-Fujiwara and others on the infinite dimensionality of 2-dimensional bounded cohomology in groups acting suitably on hyperbolic spaces, in the sense that we can control the geometry of the unit ","authors_text":"Danny Calegari, Joseph Maher","cross_cats":["math.DS","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-29T20:16:48Z","title":"Statistics and compression of scl"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4952","kind":"arxiv","version":4},"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":"sha256:8d25076697a701273b3603543101160370741dd84e0ad90b360b9a034b845ae4","target":"record","created_at":"2026-05-17T23:53:36Z","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":"9af9df642281b5163a26528db56ccbf94f9627bed418893dc3a8ac5e12868a2f","cross_cats_sorted":["math.DS","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-29T20:16:48Z","title_canon_sha256":"41e82977c7aadbb00b4c76bf019d5a827d60f3f65890915dc913ba220ae39fd3"},"schema_version":"1.0","source":{"id":"1008.4952","kind":"arxiv","version":4}},"canonical_sha256":"c644d89f2923bebe865e4d8c68d1fbc2b912ef0158193c83d434651180bbe35d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c644d89f2923bebe865e4d8c68d1fbc2b912ef0158193c83d434651180bbe35d","first_computed_at":"2026-05-17T23:53:36.906458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.906458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iwMZ/6EJ4RYjtqG0H+9lN8iogD7zhPs8qLvu6KhyejuGLsByC1nt8LT0a4Hn3ZiCmuPuJinYcQq+sJUcsecUBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.907200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4952","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d25076697a701273b3603543101160370741dd84e0ad90b360b9a034b845ae4","sha256:d77ffe3e5dd7e179eb95e40747b692a08858ed40baec9965fb6cb3cb52d229c2"],"state_sha256":"57c58b965d8d18d7d660296dd0faf0198f5d9ab4659e9db89f5739433b08a6ae"}