{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:C4HBGABQI2RMPTSWSLDH6EJWG7","short_pith_number":"pith:C4HBGABQ","canonical_record":{"source":{"id":"1410.2089","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-08T13:01:13Z","cross_cats_sorted":["math.DG","math.RT"],"title_canon_sha256":"3e18bcffd5353971e3e354f98e13ca4ac1b1da1025e626f900cd17b230dafbef","abstract_canon_sha256":"978fef87107ca9276712a6f4fb70bff06ca90a1cc12009f1ceeff4b53fdeb547"},"schema_version":"1.0"},"canonical_sha256":"170e13003046a2c7ce5692c67f113637e548fa86b78880f4bb2994b858ad808a","source":{"kind":"arxiv","id":"1410.2089","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2089","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2089v3","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2089","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"C4HBGABQI2RM","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C4HBGABQI2RMPTSW","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C4HBGABQ","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:C4HBGABQI2RMPTSWSLDH6EJWG7","target":"record","payload":{"canonical_record":{"source":{"id":"1410.2089","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-08T13:01:13Z","cross_cats_sorted":["math.DG","math.RT"],"title_canon_sha256":"3e18bcffd5353971e3e354f98e13ca4ac1b1da1025e626f900cd17b230dafbef","abstract_canon_sha256":"978fef87107ca9276712a6f4fb70bff06ca90a1cc12009f1ceeff4b53fdeb547"},"schema_version":"1.0"},"canonical_sha256":"170e13003046a2c7ce5692c67f113637e548fa86b78880f4bb2994b858ad808a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:22.747786Z","signature_b64":"Ks/haAXb6Zrj1rRwLVKlGhbroHMGCmtL2wAGFzOibaxP/wBBoAcqbEC5tT6Oi5FbxftTghLKxzOpjSkkiJ2PDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"170e13003046a2c7ce5692c67f113637e548fa86b78880f4bb2994b858ad808a","last_reissued_at":"2026-05-18T00:45:22.747172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:22.747172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.2089","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":"2026-05-18T00:45:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qav9AF1h1RxZHs2IXez5tiTi4ARp9ZdlzrhGnBkuQ31aQTaXjh6B1nLIUD+lZcnLcnx7OzpcCCjhAIDORJfTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:15:22.910862Z"},"content_sha256":"b7e479b3813dd3a4792e20fa0098591fcd738d8d6eed2ecfb897227df33f51ff","schema_version":"1.0","event_id":"sha256:b7e479b3813dd3a4792e20fa0098591fcd738d8d6eed2ecfb897227df33f51ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:C4HBGABQI2RMPTSWSLDH6EJWG7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toledo invariant of lattices in SU(2,1) via symmetric square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.RT"],"primary_cat":"math.GT","authors_text":"Genkai Zhang, Inkang Kim","submitted_at":"2014-10-08T13:01:13Z","abstract_excerpt":"In this paper, we address the issue of quaternionic Toledo invariant to study the character variety of two dimensional complex hyperbolic uniform lattices into $SU(n,2)$. We construct four distinct representations to prove that the character variety contains at least four distinct components. We also address the existence of holomorphic horizontal lift to various period domains of $SU(n,2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2089","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":"2026-05-18T00:45:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8LA1XjJmyz/bxJklmjhKpB5XNxkJU28DjGsC0GX2ZYRtTJ+bZnbfNo4boQLyJL32whWkuFT0DZb4efcv6SFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:15:22.911220Z"},"content_sha256":"b82d24d9df01655a05e97302ca648312a3d303d72af2bad40f50961b7311d5b2","schema_version":"1.0","event_id":"sha256:b82d24d9df01655a05e97302ca648312a3d303d72af2bad40f50961b7311d5b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4HBGABQI2RMPTSWSLDH6EJWG7/bundle.json","state_url":"https://pith.science/pith/C4HBGABQI2RMPTSWSLDH6EJWG7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4HBGABQI2RMPTSWSLDH6EJWG7/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":"2026-05-30T14:15:22Z","links":{"resolver":"https://pith.science/pith/C4HBGABQI2RMPTSWSLDH6EJWG7","bundle":"https://pith.science/pith/C4HBGABQI2RMPTSWSLDH6EJWG7/bundle.json","state":"https://pith.science/pith/C4HBGABQI2RMPTSWSLDH6EJWG7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4HBGABQI2RMPTSWSLDH6EJWG7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C4HBGABQI2RMPTSWSLDH6EJWG7","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":"978fef87107ca9276712a6f4fb70bff06ca90a1cc12009f1ceeff4b53fdeb547","cross_cats_sorted":["math.DG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-08T13:01:13Z","title_canon_sha256":"3e18bcffd5353971e3e354f98e13ca4ac1b1da1025e626f900cd17b230dafbef"},"schema_version":"1.0","source":{"id":"1410.2089","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2089","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2089v3","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2089","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"C4HBGABQI2RM","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C4HBGABQI2RMPTSW","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C4HBGABQ","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:b82d24d9df01655a05e97302ca648312a3d303d72af2bad40f50961b7311d5b2","target":"graph","created_at":"2026-05-18T00:45:22Z","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":"In this paper, we address the issue of quaternionic Toledo invariant to study the character variety of two dimensional complex hyperbolic uniform lattices into $SU(n,2)$. We construct four distinct representations to prove that the character variety contains at least four distinct components. We also address the existence of holomorphic horizontal lift to various period domains of $SU(n,2)$.","authors_text":"Genkai Zhang, Inkang Kim","cross_cats":["math.DG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-08T13:01:13Z","title":"Toledo invariant of lattices in SU(2,1) via symmetric square"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2089","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:b7e479b3813dd3a4792e20fa0098591fcd738d8d6eed2ecfb897227df33f51ff","target":"record","created_at":"2026-05-18T00:45:22Z","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":"978fef87107ca9276712a6f4fb70bff06ca90a1cc12009f1ceeff4b53fdeb547","cross_cats_sorted":["math.DG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-08T13:01:13Z","title_canon_sha256":"3e18bcffd5353971e3e354f98e13ca4ac1b1da1025e626f900cd17b230dafbef"},"schema_version":"1.0","source":{"id":"1410.2089","kind":"arxiv","version":3}},"canonical_sha256":"170e13003046a2c7ce5692c67f113637e548fa86b78880f4bb2994b858ad808a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"170e13003046a2c7ce5692c67f113637e548fa86b78880f4bb2994b858ad808a","first_computed_at":"2026-05-18T00:45:22.747172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:22.747172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ks/haAXb6Zrj1rRwLVKlGhbroHMGCmtL2wAGFzOibaxP/wBBoAcqbEC5tT6Oi5FbxftTghLKxzOpjSkkiJ2PDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:22.747786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2089","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7e479b3813dd3a4792e20fa0098591fcd738d8d6eed2ecfb897227df33f51ff","sha256:b82d24d9df01655a05e97302ca648312a3d303d72af2bad40f50961b7311d5b2"],"state_sha256":"d75ade3aa8ee7c55cd2de1da18fae0d52b2fbd469919d0b566d85bae20604849"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2pK/86anWfuVLBzjTof10gCckLPGoVjVxGZQmFS83rPVgd/EnpmSGCYuos0jmH5bLpDysC/GCP4v2z+huZ2eDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:15:22.915329Z","bundle_sha256":"0bb08da7588bb695f21ee71f840fd252e86de51102a6375ec790a7411f71899e"}}