{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RAXAFB2ZWJ7S23EGA3LEFOXFRD","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":"a52f75d3a54efd8ff3dda67426c97198d4a61af3f830ac8d7df7c3e114ff7f68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-30T14:49:42Z","title_canon_sha256":"fee0b5d7ad0ec1bdb26538fb17b980590b050b9cd0ea24e446a134ef8f8a778f"},"schema_version":"1.0","source":{"id":"1304.0112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0112","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0112v1","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0112","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"RAXAFB2ZWJ7S","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RAXAFB2ZWJ7S23EG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RAXAFB2Z","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:e1196bcd28c393cc20e0db3bbfbafbf931857648f97b90f13ca8f90e2793c728","target":"graph","created_at":"2026-05-18T03:29:25Z","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 obtain a branched spherical CR structure on the complement of the figure eight knot with a given holonomy representation (called rho_2). There are essentially two boundary unipotent representations from the complement of the figure eight knot into PU(2,1), we call them rho_1 and rho_2. We make explicit some fundamental differences between these two representations. For instance, seeing the figure eight knot complement as a surface bundle over the circle, the behaviour of of the fundamental group of the fiber under the representation is a key difference between rho_1 and rho_2.","authors_text":"Elisha Falbel, Jieyan Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-30T14:49:42Z","title":"Branched Spherical CR structures on the complement of the figure eight knot"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0112","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":"sha256:11f98280b9cb8a8efae4705a9537ab3ea1d095eab923e3695d980451bd9be91a","target":"record","created_at":"2026-05-18T03:29:25Z","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":"a52f75d3a54efd8ff3dda67426c97198d4a61af3f830ac8d7df7c3e114ff7f68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-30T14:49:42Z","title_canon_sha256":"fee0b5d7ad0ec1bdb26538fb17b980590b050b9cd0ea24e446a134ef8f8a778f"},"schema_version":"1.0","source":{"id":"1304.0112","kind":"arxiv","version":1}},"canonical_sha256":"882e028759b27f2d6c8606d642bae588e6024ba78c80e5aa8d5327510ce0f205","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"882e028759b27f2d6c8606d642bae588e6024ba78c80e5aa8d5327510ce0f205","first_computed_at":"2026-05-18T03:29:25.958780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:25.958780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MoWlumZ+zgWpThHUrBC3tMSua7Q7wEoVoomRKYiL8gsOv3wmZ5S03yTjTBwqaY79s7NIfpjtXJ9mcCktstWpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:25.959591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11f98280b9cb8a8efae4705a9537ab3ea1d095eab923e3695d980451bd9be91a","sha256:e1196bcd28c393cc20e0db3bbfbafbf931857648f97b90f13ca8f90e2793c728"],"state_sha256":"0cf9d67c9d5b080fc953bcd53e66b912b8a0c6e0f8918621f203a22a9a2b9883"}