{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5XVWGX4WF3MHSKXNM3UNKETDWA","short_pith_number":"pith:5XVWGX4W","canonical_record":{"source":{"id":"1212.0007","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-30T21:00:04Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"bee5210cf94e7fbe9097c16ec8bf978fd208556fb0d908f7fb7fccdabc4717a6","abstract_canon_sha256":"9238031693bfb03135da4b8031a91bfbe7bf4db47927f9692db812c50d8f7175"},"schema_version":"1.0"},"canonical_sha256":"edeb635f962ed8792aed66e8d51263b02987b78c7d69c143f42361538604a5f8","source":{"kind":"arxiv","id":"1212.0007","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0007","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0007v3","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0007","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"5XVWGX4WF3MH","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5XVWGX4WF3MHSKXN","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5XVWGX4W","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5XVWGX4WF3MHSKXNM3UNKETDWA","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0007","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-30T21:00:04Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"bee5210cf94e7fbe9097c16ec8bf978fd208556fb0d908f7fb7fccdabc4717a6","abstract_canon_sha256":"9238031693bfb03135da4b8031a91bfbe7bf4db47927f9692db812c50d8f7175"},"schema_version":"1.0"},"canonical_sha256":"edeb635f962ed8792aed66e8d51263b02987b78c7d69c143f42361538604a5f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:38.463407Z","signature_b64":"qCxVQr1QMOc1POITubqIjr+mpPD+oWbVOoEnZ3oQlE3cz6lqVbfUj4+UWahcwyc7O+eyA2+qmhhCrlEXL6P4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edeb635f962ed8792aed66e8d51263b02987b78c7d69c143f42361538604a5f8","last_reissued_at":"2026-05-18T02:03:38.462704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:38.462704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0007","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"utjK18uVAR0tEGrnrt2eyGDtRncA1YH0aFILfwXpJBC1jFbUwE6Igvi9pJoLBIUubusNSOTTP81cvgCK/uMvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:20:07.882816Z"},"content_sha256":"06575707d15e0cc0abd69863d09db998930a9f04c2f8e739c6c4e0c9cf149b14","schema_version":"1.0","event_id":"sha256:06575707d15e0cc0abd69863d09db998930a9f04c2f8e739c6c4e0c9cf149b14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5XVWGX4WF3MHSKXNM3UNKETDWA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tagged mapping class groups: Auslander-Reiten translation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.RT","authors_text":"Thomas Br\\\"ustle, Yu Qiu","submitted_at":"2012-11-30T21:00:04Z","abstract_excerpt":"We give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface $\\mathbf{S}$ with marked points and non-empty boundary, which generalizes Br\\\"{u}stle-Zhang's result for the puncture free case.\n  As an application, we show that the intersection of the shifts in the 3-Calabi-Yau derived category $\\mathcal{D}(\\Gamma_{\\mathbf{S}})$ associated to the surface and the corresponding Seidel-Thomas braid group of $\\mathcal{D}(\\Gamma_{\\mathbf{S}})$ is empty, unless $\\mathbf{S}$ is a polygon with at most one puncture (i.e. of type A o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0007","kind":"arxiv","version":3},"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":"2026-05-18T02:03:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLQqjg35a6t0xD/6s43iAFg3mUv4K1i8+6P1jwrxcgcLvTNxplM7CxqUXs+wdvu02sruS3IZIK/FoQmO3/XyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:20:07.883163Z"},"content_sha256":"8e96d401f8caf81286fbef39d07c3a44bddc9ffc2b611b35b3206f1bac84b166","schema_version":"1.0","event_id":"sha256:8e96d401f8caf81286fbef39d07c3a44bddc9ffc2b611b35b3206f1bac84b166"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5XVWGX4WF3MHSKXNM3UNKETDWA/bundle.json","state_url":"https://pith.science/pith/5XVWGX4WF3MHSKXNM3UNKETDWA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5XVWGX4WF3MHSKXNM3UNKETDWA/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":"2026-06-03T15:20:07Z","links":{"resolver":"https://pith.science/pith/5XVWGX4WF3MHSKXNM3UNKETDWA","bundle":"https://pith.science/pith/5XVWGX4WF3MHSKXNM3UNKETDWA/bundle.json","state":"https://pith.science/pith/5XVWGX4WF3MHSKXNM3UNKETDWA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5XVWGX4WF3MHSKXNM3UNKETDWA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5XVWGX4WF3MHSKXNM3UNKETDWA","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":"9238031693bfb03135da4b8031a91bfbe7bf4db47927f9692db812c50d8f7175","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-30T21:00:04Z","title_canon_sha256":"bee5210cf94e7fbe9097c16ec8bf978fd208556fb0d908f7fb7fccdabc4717a6"},"schema_version":"1.0","source":{"id":"1212.0007","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0007","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0007v3","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0007","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"5XVWGX4WF3MH","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5XVWGX4WF3MHSKXN","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5XVWGX4W","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:8e96d401f8caf81286fbef39d07c3a44bddc9ffc2b611b35b3206f1bac84b166","target":"graph","created_at":"2026-05-18T02:03:38Z","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 geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface $\\mathbf{S}$ with marked points and non-empty boundary, which generalizes Br\\\"{u}stle-Zhang's result for the puncture free case.\n  As an application, we show that the intersection of the shifts in the 3-Calabi-Yau derived category $\\mathcal{D}(\\Gamma_{\\mathbf{S}})$ associated to the surface and the corresponding Seidel-Thomas braid group of $\\mathcal{D}(\\Gamma_{\\mathbf{S}})$ is empty, unless $\\mathbf{S}$ is a polygon with at most one puncture (i.e. of type A o","authors_text":"Thomas Br\\\"ustle, Yu Qiu","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-30T21:00:04Z","title":"Tagged mapping class groups: Auslander-Reiten translation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0007","kind":"arxiv","version":3},"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":"sha256:06575707d15e0cc0abd69863d09db998930a9f04c2f8e739c6c4e0c9cf149b14","target":"record","created_at":"2026-05-18T02:03:38Z","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":"9238031693bfb03135da4b8031a91bfbe7bf4db47927f9692db812c50d8f7175","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-30T21:00:04Z","title_canon_sha256":"bee5210cf94e7fbe9097c16ec8bf978fd208556fb0d908f7fb7fccdabc4717a6"},"schema_version":"1.0","source":{"id":"1212.0007","kind":"arxiv","version":3}},"canonical_sha256":"edeb635f962ed8792aed66e8d51263b02987b78c7d69c143f42361538604a5f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edeb635f962ed8792aed66e8d51263b02987b78c7d69c143f42361538604a5f8","first_computed_at":"2026-05-18T02:03:38.462704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:38.462704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qCxVQr1QMOc1POITubqIjr+mpPD+oWbVOoEnZ3oQlE3cz6lqVbfUj4+UWahcwyc7O+eyA2+qmhhCrlEXL6P4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:38.463407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0007","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06575707d15e0cc0abd69863d09db998930a9f04c2f8e739c6c4e0c9cf149b14","sha256:8e96d401f8caf81286fbef39d07c3a44bddc9ffc2b611b35b3206f1bac84b166"],"state_sha256":"a527d0bcb457b887d16273273debb2b2efb1688c20a8df089dc8bb172c04d2c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dZuXxe+9t35uv7+ZVrs2vdbGqLvgdGzEcAqzZrqrdSHabttWn321yTqw7vGrwntF9SpgvpcsbvutUODsKf3aDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:20:07.885123Z","bundle_sha256":"c1ae85c4349b11231a207fb30e42ecb485fa5de1ccb75d46de2107531ce257ab"}}