{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HMPNLAXNXAA5HXDEROGK4NZY6H","short_pith_number":"pith:HMPNLAXN","canonical_record":{"source":{"id":"1105.0559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-03T11:44:26Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"81ca879a1ff68856da9d8e91f58d1f591847159eb8e6ab826133804d134b645c","abstract_canon_sha256":"d390e2499f93c4db093e4009f90c697a66ef9de851c2b3d5fd60574c80245149"},"schema_version":"1.0"},"canonical_sha256":"3b1ed582edb801d3dc648b8cae3738f1eaa0724430108a77f098f192744bcfe0","source":{"kind":"arxiv","id":"1105.0559","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0559","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0559v1","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0559","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"HMPNLAXNXAA5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HMPNLAXNXAA5HXDE","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HMPNLAXN","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HMPNLAXNXAA5HXDEROGK4NZY6H","target":"record","payload":{"canonical_record":{"source":{"id":"1105.0559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-03T11:44:26Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"81ca879a1ff68856da9d8e91f58d1f591847159eb8e6ab826133804d134b645c","abstract_canon_sha256":"d390e2499f93c4db093e4009f90c697a66ef9de851c2b3d5fd60574c80245149"},"schema_version":"1.0"},"canonical_sha256":"3b1ed582edb801d3dc648b8cae3738f1eaa0724430108a77f098f192744bcfe0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:20.474483Z","signature_b64":"BZjoqTYrNvjDHIsIqa9OUbKGyI7k04DllF3Z+UKufnhk8PCzcxauOWUcKWpTOZNdRi2tQNpPI0g89UlP2iSVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b1ed582edb801d3dc648b8cae3738f1eaa0724430108a77f098f192744bcfe0","last_reissued_at":"2026-05-18T03:09:20.473738Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:20.473738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.0559","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:09:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rz8myO1EJBsVaRmNRSj3a2OJol5N705cdN9UJ4ZDRWz8bPerBx4MTZGoRWyYjFBtHkjHumgWKP2OZ9bnVQY3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:53:59.697327Z"},"content_sha256":"05ad9c1f4c6d1afe0869bfd3625cfb1e82449b896b95c660c0dc279499796926","schema_version":"1.0","event_id":"sha256:05ad9c1f4c6d1afe0869bfd3625cfb1e82449b896b95c660c0dc279499796926"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HMPNLAXNXAA5HXDEROGK4NZY6H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotically rigid mapping class groups and Thompson's groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Christophe Kapoudjian, Louis Funar, Vlad Sergiescu","submitted_at":"2011-05-03T11:44:26Z","abstract_excerpt":"We consider Thompson's groups from the perspective of mapping class groups of surfaces of infinite type. This point of view leads us to the braided Thompson groups, which are extensions of Thompson's groups by infinite (spherical) braid groups. We will outline the main features of these groups and some applications to the quantization of Teichm\\\"uller spaces. The chapter provides an introduction to the subject with an emphasis on some of the authors results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0559","kind":"arxiv","version":1},"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":"2026-05-18T03:09:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VFqdEflS8NxJ8sP175pFSdaf6xDS3n23xwe2l3dG7k/H2HZcGT3WPa/fKvvTVcL26DodHf7KRd6RCLqnH5h9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:53:59.697671Z"},"content_sha256":"5b45d2558df7f94f1867abba9542f66ad7c35e27307c6713ec756733db37a334","schema_version":"1.0","event_id":"sha256:5b45d2558df7f94f1867abba9542f66ad7c35e27307c6713ec756733db37a334"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMPNLAXNXAA5HXDEROGK4NZY6H/bundle.json","state_url":"https://pith.science/pith/HMPNLAXNXAA5HXDEROGK4NZY6H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMPNLAXNXAA5HXDEROGK4NZY6H/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":"2026-06-01T03:53:59Z","links":{"resolver":"https://pith.science/pith/HMPNLAXNXAA5HXDEROGK4NZY6H","bundle":"https://pith.science/pith/HMPNLAXNXAA5HXDEROGK4NZY6H/bundle.json","state":"https://pith.science/pith/HMPNLAXNXAA5HXDEROGK4NZY6H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMPNLAXNXAA5HXDEROGK4NZY6H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HMPNLAXNXAA5HXDEROGK4NZY6H","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":"d390e2499f93c4db093e4009f90c697a66ef9de851c2b3d5fd60574c80245149","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-03T11:44:26Z","title_canon_sha256":"81ca879a1ff68856da9d8e91f58d1f591847159eb8e6ab826133804d134b645c"},"schema_version":"1.0","source":{"id":"1105.0559","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0559","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0559v1","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0559","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"HMPNLAXNXAA5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HMPNLAXNXAA5HXDE","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HMPNLAXN","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:5b45d2558df7f94f1867abba9542f66ad7c35e27307c6713ec756733db37a334","target":"graph","created_at":"2026-05-18T03:09:20Z","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 consider Thompson's groups from the perspective of mapping class groups of surfaces of infinite type. This point of view leads us to the braided Thompson groups, which are extensions of Thompson's groups by infinite (spherical) braid groups. We will outline the main features of these groups and some applications to the quantization of Teichm\\\"uller spaces. The chapter provides an introduction to the subject with an emphasis on some of the authors results.","authors_text":"Christophe Kapoudjian, Louis Funar, Vlad Sergiescu","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-03T11:44:26Z","title":"Asymptotically rigid mapping class groups and Thompson's groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0559","kind":"arxiv","version":1},"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":"sha256:05ad9c1f4c6d1afe0869bfd3625cfb1e82449b896b95c660c0dc279499796926","target":"record","created_at":"2026-05-18T03:09:20Z","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":"d390e2499f93c4db093e4009f90c697a66ef9de851c2b3d5fd60574c80245149","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-03T11:44:26Z","title_canon_sha256":"81ca879a1ff68856da9d8e91f58d1f591847159eb8e6ab826133804d134b645c"},"schema_version":"1.0","source":{"id":"1105.0559","kind":"arxiv","version":1}},"canonical_sha256":"3b1ed582edb801d3dc648b8cae3738f1eaa0724430108a77f098f192744bcfe0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b1ed582edb801d3dc648b8cae3738f1eaa0724430108a77f098f192744bcfe0","first_computed_at":"2026-05-18T03:09:20.473738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:20.473738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BZjoqTYrNvjDHIsIqa9OUbKGyI7k04DllF3Z+UKufnhk8PCzcxauOWUcKWpTOZNdRi2tQNpPI0g89UlP2iSVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:20.474483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.0559","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05ad9c1f4c6d1afe0869bfd3625cfb1e82449b896b95c660c0dc279499796926","sha256:5b45d2558df7f94f1867abba9542f66ad7c35e27307c6713ec756733db37a334"],"state_sha256":"e0da2ca9d9b9e0dcfce6dee399c93c4c3533e24b9f66d0bcc1fa6e4861b3123d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TXDSgqtpUC05xESJVbtZhv3Fu7M1g3nPv7ZlnKWVGEDSqIIZ5Og0Ca6pdVZt+6BS0qGA1U8YysSPfbyh3e9+Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T03:53:59.699783Z","bundle_sha256":"abb7ffd6e5cc938f1a89bb43c366b12dcf296271458dc79f2d3dc9e4a3a5bb53"}}