{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HNZZQDUVP7RXS3VARF7XZKEKIF","short_pith_number":"pith:HNZZQDUV","canonical_record":{"source":{"id":"1201.3808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-01-18T15:00:42Z","cross_cats_sorted":[],"title_canon_sha256":"c034f03ad4f7fc7fd9f7bfc3a604fdb9356552c829ae0e49be617151aa3db019","abstract_canon_sha256":"9633d69a708ed182b1b2b9372cf90e59701bb233451295badd87bf42e9cc0fc2"},"schema_version":"1.0"},"canonical_sha256":"3b73980e957fe3796ea0897f7ca88a414ff386fe6f4e531efc9fece479bd3b45","source":{"kind":"arxiv","id":"1201.3808","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3808","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3808v1","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3808","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"HNZZQDUVP7RX","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HNZZQDUVP7RXS3VA","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HNZZQDUV","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HNZZQDUVP7RXS3VARF7XZKEKIF","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-01-18T15:00:42Z","cross_cats_sorted":[],"title_canon_sha256":"c034f03ad4f7fc7fd9f7bfc3a604fdb9356552c829ae0e49be617151aa3db019","abstract_canon_sha256":"9633d69a708ed182b1b2b9372cf90e59701bb233451295badd87bf42e9cc0fc2"},"schema_version":"1.0"},"canonical_sha256":"3b73980e957fe3796ea0897f7ca88a414ff386fe6f4e531efc9fece479bd3b45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:17.956303Z","signature_b64":"WUMxV+guW5rtvZZi/yP+3KAArA6n8opz+pmjN7+eFy2Ak2uTxm5gacdwUisXsEDgw57/Ws8aMgGsHGyQJRTaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b73980e957fe3796ea0897f7ca88a414ff386fe6f4e531efc9fece479bd3b45","last_reissued_at":"2026-05-18T04:04:17.955670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:17.955670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3808","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":"2026-05-18T04:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MtPQtU7hifzp/ehCpnPw3cmnQ18E1/AKSFDon2h+vrMbuSQyPstdqjrkx/lGkXA8eYXZt9pc163KX5XKUf9cCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:50:52.410195Z"},"content_sha256":"d1b4967a40dbe9bdc23038e2e75d07cb192b8bd9caf3dee89aafea20be8e5782","schema_version":"1.0","event_id":"sha256:d1b4967a40dbe9bdc23038e2e75d07cb192b8bd9caf3dee89aafea20be8e5782"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HNZZQDUVP7RXS3VARF7XZKEKIF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Marked fatgraph complexes and surface automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"R. C. Penner, Vladimir Turaev, Yusuke Kuno","submitted_at":"2012-01-18T15:00:42Z","abstract_excerpt":"Combinatorial aspects of the Torelli-Johnson-Morita theory of surface automorphisms are extended to certain subgroups of the mapping class groups. These subgroups are defined relative to a specified homomorphism from the fundamental group of the surface onto an arbitrary group $K$. For $K$ abelian, there is a combinatorial theory akin to the classical case, for example, providing an explicit cocycle representing the first Johnson homomophism with target $\\Lambda ^3 K$. Furthermore, the Earle class with coefficients in $K$ is represented by an explicit cocyle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3808","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":"2026-05-18T04:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kZEcl85q2Sk61mdsOjfa7+an21SIIeQpBxHTrdqR3Xihk3FgX6PbhAnPl3dqwOqD6oB0r5kWPjyfDhjXBnzZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:50:52.410832Z"},"content_sha256":"b38e190e03e537c73cdd257cde7362bb500efa9270073069d9687385b110eb1a","schema_version":"1.0","event_id":"sha256:b38e190e03e537c73cdd257cde7362bb500efa9270073069d9687385b110eb1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNZZQDUVP7RXS3VARF7XZKEKIF/bundle.json","state_url":"https://pith.science/pith/HNZZQDUVP7RXS3VARF7XZKEKIF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNZZQDUVP7RXS3VARF7XZKEKIF/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":"2026-05-31T15:50:52Z","links":{"resolver":"https://pith.science/pith/HNZZQDUVP7RXS3VARF7XZKEKIF","bundle":"https://pith.science/pith/HNZZQDUVP7RXS3VARF7XZKEKIF/bundle.json","state":"https://pith.science/pith/HNZZQDUVP7RXS3VARF7XZKEKIF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNZZQDUVP7RXS3VARF7XZKEKIF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HNZZQDUVP7RXS3VARF7XZKEKIF","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":"9633d69a708ed182b1b2b9372cf90e59701bb233451295badd87bf42e9cc0fc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-01-18T15:00:42Z","title_canon_sha256":"c034f03ad4f7fc7fd9f7bfc3a604fdb9356552c829ae0e49be617151aa3db019"},"schema_version":"1.0","source":{"id":"1201.3808","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3808","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3808v1","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3808","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"HNZZQDUVP7RX","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HNZZQDUVP7RXS3VA","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HNZZQDUV","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:b38e190e03e537c73cdd257cde7362bb500efa9270073069d9687385b110eb1a","target":"graph","created_at":"2026-05-18T04:04:17Z","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":"Combinatorial aspects of the Torelli-Johnson-Morita theory of surface automorphisms are extended to certain subgroups of the mapping class groups. These subgroups are defined relative to a specified homomorphism from the fundamental group of the surface onto an arbitrary group $K$. For $K$ abelian, there is a combinatorial theory akin to the classical case, for example, providing an explicit cocycle representing the first Johnson homomophism with target $\\Lambda ^3 K$. Furthermore, the Earle class with coefficients in $K$ is represented by an explicit cocyle.","authors_text":"R. C. Penner, Vladimir Turaev, Yusuke Kuno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-01-18T15:00:42Z","title":"Marked fatgraph complexes and surface automorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3808","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:d1b4967a40dbe9bdc23038e2e75d07cb192b8bd9caf3dee89aafea20be8e5782","target":"record","created_at":"2026-05-18T04:04:17Z","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":"9633d69a708ed182b1b2b9372cf90e59701bb233451295badd87bf42e9cc0fc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-01-18T15:00:42Z","title_canon_sha256":"c034f03ad4f7fc7fd9f7bfc3a604fdb9356552c829ae0e49be617151aa3db019"},"schema_version":"1.0","source":{"id":"1201.3808","kind":"arxiv","version":1}},"canonical_sha256":"3b73980e957fe3796ea0897f7ca88a414ff386fe6f4e531efc9fece479bd3b45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b73980e957fe3796ea0897f7ca88a414ff386fe6f4e531efc9fece479bd3b45","first_computed_at":"2026-05-18T04:04:17.955670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:17.955670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WUMxV+guW5rtvZZi/yP+3KAArA6n8opz+pmjN7+eFy2Ak2uTxm5gacdwUisXsEDgw57/Ws8aMgGsHGyQJRTaCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:17.956303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1b4967a40dbe9bdc23038e2e75d07cb192b8bd9caf3dee89aafea20be8e5782","sha256:b38e190e03e537c73cdd257cde7362bb500efa9270073069d9687385b110eb1a"],"state_sha256":"744c9493409ad11cd4135eae9753835a9019e8e2ab57a1383da35dabcadff391"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3qaSSuZE7WgvHUGVcT2XxMPef0LpkuFUfqXL73iXFb3NDsjmZD9e7Phf2H91XQ72CJdgtGgZ/Db/VAOGcksKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:50:52.414722Z","bundle_sha256":"7204322e0177ed3108b1eb9564ba56aa99c64c72c2788335c0b3028c7a811499"}}