{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QU5NHCWOEDXW2FGFATZPN6KHR5","short_pith_number":"pith:QU5NHCWO","canonical_record":{"source":{"id":"1212.6117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-26T05:44:49Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"a578a0af8951de171be28fd520405cb68581f5b26680bab12519494b96061bda","abstract_canon_sha256":"d5c4fde5fef5f138a14858e83003c0afedd0eca77f2d467903cd93aadfda1a74"},"schema_version":"1.0"},"canonical_sha256":"853ad38ace20ef6d14c504f2f6f9478f77e99b9d618693ef4cebf72b3d8bd58d","source":{"kind":"arxiv","id":"1212.6117","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6117","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6117v1","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6117","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"QU5NHCWOEDXW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QU5NHCWOEDXW2FGF","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QU5NHCWO","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QU5NHCWOEDXW2FGFATZPN6KHR5","target":"record","payload":{"canonical_record":{"source":{"id":"1212.6117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-26T05:44:49Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"a578a0af8951de171be28fd520405cb68581f5b26680bab12519494b96061bda","abstract_canon_sha256":"d5c4fde5fef5f138a14858e83003c0afedd0eca77f2d467903cd93aadfda1a74"},"schema_version":"1.0"},"canonical_sha256":"853ad38ace20ef6d14c504f2f6f9478f77e99b9d618693ef4cebf72b3d8bd58d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:25.865365Z","signature_b64":"zz0OLrqxeGF3EyzJMW7aftdesri4hV9NZuevxoRzVRj3oRHXq1lf4oD4/irw+q+pIhemOyludTigIA6OtRqQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"853ad38ace20ef6d14c504f2f6f9478f77e99b9d618693ef4cebf72b3d8bd58d","last_reissued_at":"2026-05-18T01:22:25.864673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:25.864673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.6117","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":"2026-05-18T01:22:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3juHIGOtVt/3rmqEF/CDnPdlCopfrvrnC3+OdEeBJsLj0fcT7dIBIpQci853DtFan506+XsA9VD11g8H+52yCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:10:06.518519Z"},"content_sha256":"36a33dc89a3c682af16927f4ea02a8b983e89fa8b2f49e970c35fbd7d6493713","schema_version":"1.0","event_id":"sha256:36a33dc89a3c682af16927f4ea02a8b983e89fa8b2f49e970c35fbd7d6493713"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QU5NHCWOEDXW2FGFATZPN6KHR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On stable commutator length in hyperelliptic mapping class groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Danny Calegari, Masatoshi Sato, Naoyuki Monden","submitted_at":"2012-12-26T05:44:49Z","abstract_excerpt":"We give a new upper bound on the stable commutator length of Dehn twists in hyperelliptic mapping class groups, and determine the stable commutator length of some elements. We also calculate values and the defects of homogeneous quasimorphisms derived from \\omega-signatures, and show that they are linearly independent in the mapping class groups of pointed 2-spheres when the number of points is small."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6117","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":"2026-05-18T01:22:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pdyGYib3gCuNDbNbhXST736GZ9e2JAE5IyWTW3SMflULgie1vu0Hb/PIwfipqQJ3PDScYxjPxFJgMUbJwavKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:10:06.519188Z"},"content_sha256":"424570864939e8244c3cb9b6d753b86187a5af69d634a73bff8f9d916ae7a4e8","schema_version":"1.0","event_id":"sha256:424570864939e8244c3cb9b6d753b86187a5af69d634a73bff8f9d916ae7a4e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QU5NHCWOEDXW2FGFATZPN6KHR5/bundle.json","state_url":"https://pith.science/pith/QU5NHCWOEDXW2FGFATZPN6KHR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QU5NHCWOEDXW2FGFATZPN6KHR5/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":"2026-05-27T15:10:06Z","links":{"resolver":"https://pith.science/pith/QU5NHCWOEDXW2FGFATZPN6KHR5","bundle":"https://pith.science/pith/QU5NHCWOEDXW2FGFATZPN6KHR5/bundle.json","state":"https://pith.science/pith/QU5NHCWOEDXW2FGFATZPN6KHR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QU5NHCWOEDXW2FGFATZPN6KHR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QU5NHCWOEDXW2FGFATZPN6KHR5","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":"d5c4fde5fef5f138a14858e83003c0afedd0eca77f2d467903cd93aadfda1a74","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-26T05:44:49Z","title_canon_sha256":"a578a0af8951de171be28fd520405cb68581f5b26680bab12519494b96061bda"},"schema_version":"1.0","source":{"id":"1212.6117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6117","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6117v1","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6117","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"QU5NHCWOEDXW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QU5NHCWOEDXW2FGF","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QU5NHCWO","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:424570864939e8244c3cb9b6d753b86187a5af69d634a73bff8f9d916ae7a4e8","target":"graph","created_at":"2026-05-18T01:22:25Z","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 new upper bound on the stable commutator length of Dehn twists in hyperelliptic mapping class groups, and determine the stable commutator length of some elements. We also calculate values and the defects of homogeneous quasimorphisms derived from \\omega-signatures, and show that they are linearly independent in the mapping class groups of pointed 2-spheres when the number of points is small.","authors_text":"Danny Calegari, Masatoshi Sato, Naoyuki Monden","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-26T05:44:49Z","title":"On stable commutator length in hyperelliptic mapping class groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6117","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":"sha256:36a33dc89a3c682af16927f4ea02a8b983e89fa8b2f49e970c35fbd7d6493713","target":"record","created_at":"2026-05-18T01:22:25Z","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":"d5c4fde5fef5f138a14858e83003c0afedd0eca77f2d467903cd93aadfda1a74","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-26T05:44:49Z","title_canon_sha256":"a578a0af8951de171be28fd520405cb68581f5b26680bab12519494b96061bda"},"schema_version":"1.0","source":{"id":"1212.6117","kind":"arxiv","version":1}},"canonical_sha256":"853ad38ace20ef6d14c504f2f6f9478f77e99b9d618693ef4cebf72b3d8bd58d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"853ad38ace20ef6d14c504f2f6f9478f77e99b9d618693ef4cebf72b3d8bd58d","first_computed_at":"2026-05-18T01:22:25.864673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:25.864673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zz0OLrqxeGF3EyzJMW7aftdesri4hV9NZuevxoRzVRj3oRHXq1lf4oD4/irw+q+pIhemOyludTigIA6OtRqQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:25.865365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36a33dc89a3c682af16927f4ea02a8b983e89fa8b2f49e970c35fbd7d6493713","sha256:424570864939e8244c3cb9b6d753b86187a5af69d634a73bff8f9d916ae7a4e8"],"state_sha256":"f5d9192ccefcf40760e06e02658fa659c3e9e4ca74c089b65e33a336b09ecce3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0C5oH+8T/OWKlMgp7QXR9HDzuDjwy0lXatpL70CwxiWz8R6+IxE5g2k70g5+QiUTcA6bvV4fwQchpTXzrZtQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:10:06.522811Z","bundle_sha256":"2f3ebe5e00953823fdb8687344244895964d2813905f895aa1a832e3fe7c4566"}}