{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KEIXUR37ILXC3QJ4GSCAGH2XUD","short_pith_number":"pith:KEIXUR37","canonical_record":{"source":{"id":"1311.2804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-11-12T15:08:24Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"4478df822c7096ff58d4f4aac771bd27a6abd2807a5b40ad5f13010b6e038a23","abstract_canon_sha256":"0450a2712ab162ef707e59ba332a50e2233e52200a36d134f7e320c3013153de"},"schema_version":"1.0"},"canonical_sha256":"51117a477f42ee2dc13c3484031f57a0f6f6032e611929f799cb2135c1569ac6","source":{"kind":"arxiv","id":"1311.2804","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2804","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2804v1","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2804","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"pith_short_12","alias_value":"KEIXUR37ILXC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KEIXUR37ILXC3QJ4","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KEIXUR37","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KEIXUR37ILXC3QJ4GSCAGH2XUD","target":"record","payload":{"canonical_record":{"source":{"id":"1311.2804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-11-12T15:08:24Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"4478df822c7096ff58d4f4aac771bd27a6abd2807a5b40ad5f13010b6e038a23","abstract_canon_sha256":"0450a2712ab162ef707e59ba332a50e2233e52200a36d134f7e320c3013153de"},"schema_version":"1.0"},"canonical_sha256":"51117a477f42ee2dc13c3484031f57a0f6f6032e611929f799cb2135c1569ac6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:24.680489Z","signature_b64":"6WB11pOWzgswKhh98Ve5xWacmlfmrrCBlxIQXWo0OiG8jz7EorhHYcMWXT0m4uuIXL9k8BG5ZKH+PbB6sSlkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51117a477f42ee2dc13c3484031f57a0f6f6032e611929f799cb2135c1569ac6","last_reissued_at":"2026-05-18T01:22:24.679931Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:24.679931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.2804","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":"2026-05-18T01:22:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ertg4hv5Ym7pZvd1xBR4otMwUKeZpUEnj6sUwd4ycpbNvYKKT88oZFO144R8PoHYDwN+fwyjJrKvXG7ersf0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:09:35.422153Z"},"content_sha256":"1ee3881ac547edac971488f931040c6a713dbcd058548a5b965f662e9554e27c","schema_version":"1.0","event_id":"sha256:1ee3881ac547edac971488f931040c6a713dbcd058548a5b965f662e9554e27c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KEIXUR37ILXC3QJ4GSCAGH2XUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compact anti-de Sitter 3-manifolds and folded hyperbolic structures on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Fanny Kassel, Fran\\c{c}ois Gu\\'eritaud, Maxime Wolff","submitted_at":"2013-11-12T15:08:24Z","abstract_excerpt":"We prove that any nonabelian, non-Fuchsian representation of a surface group into PSL(2,R) is the holonomy of a folded hyperbolic structure on the surface. Using similar ideas, we establish that any non-Fuchsian representation rho of a surface group into PSL(2,R) is strictly dominated by some Fuchsian representation j, in the sense that the hyperbolic translation lengths for j are uniformly larger than for rho; conversely, any Fuchsian representation j strictly dominates some non-Fuchsian representation rho, whose Euler class can be prescribed. This has applications to compact anti-de Sitter 3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2804","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":"2026-05-18T01:22:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juTWH2qF7sz2Uh2ldvBYVdU8Dgv2YkeSm4rz9ooSRoruRBIVmyHDuWfPum2mWCtCOi26TfWwLAVZWUPDF+L+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:09:35.422517Z"},"content_sha256":"6d01b418d698efeadcd851b7312d17217414c5a85968e1e3add12fdde1bf0571","schema_version":"1.0","event_id":"sha256:6d01b418d698efeadcd851b7312d17217414c5a85968e1e3add12fdde1bf0571"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KEIXUR37ILXC3QJ4GSCAGH2XUD/bundle.json","state_url":"https://pith.science/pith/KEIXUR37ILXC3QJ4GSCAGH2XUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KEIXUR37ILXC3QJ4GSCAGH2XUD/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":"2026-05-21T23:09:35Z","links":{"resolver":"https://pith.science/pith/KEIXUR37ILXC3QJ4GSCAGH2XUD","bundle":"https://pith.science/pith/KEIXUR37ILXC3QJ4GSCAGH2XUD/bundle.json","state":"https://pith.science/pith/KEIXUR37ILXC3QJ4GSCAGH2XUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KEIXUR37ILXC3QJ4GSCAGH2XUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KEIXUR37ILXC3QJ4GSCAGH2XUD","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":"0450a2712ab162ef707e59ba332a50e2233e52200a36d134f7e320c3013153de","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-11-12T15:08:24Z","title_canon_sha256":"4478df822c7096ff58d4f4aac771bd27a6abd2807a5b40ad5f13010b6e038a23"},"schema_version":"1.0","source":{"id":"1311.2804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2804","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2804v1","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2804","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"pith_short_12","alias_value":"KEIXUR37ILXC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KEIXUR37ILXC3QJ4","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KEIXUR37","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:6d01b418d698efeadcd851b7312d17217414c5a85968e1e3add12fdde1bf0571","target":"graph","created_at":"2026-05-18T01:22:24Z","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 prove that any nonabelian, non-Fuchsian representation of a surface group into PSL(2,R) is the holonomy of a folded hyperbolic structure on the surface. Using similar ideas, we establish that any non-Fuchsian representation rho of a surface group into PSL(2,R) is strictly dominated by some Fuchsian representation j, in the sense that the hyperbolic translation lengths for j are uniformly larger than for rho; conversely, any Fuchsian representation j strictly dominates some non-Fuchsian representation rho, whose Euler class can be prescribed. This has applications to compact anti-de Sitter 3","authors_text":"Fanny Kassel, Fran\\c{c}ois Gu\\'eritaud, Maxime Wolff","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-11-12T15:08:24Z","title":"Compact anti-de Sitter 3-manifolds and folded hyperbolic structures on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2804","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":"sha256:1ee3881ac547edac971488f931040c6a713dbcd058548a5b965f662e9554e27c","target":"record","created_at":"2026-05-18T01:22:24Z","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":"0450a2712ab162ef707e59ba332a50e2233e52200a36d134f7e320c3013153de","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-11-12T15:08:24Z","title_canon_sha256":"4478df822c7096ff58d4f4aac771bd27a6abd2807a5b40ad5f13010b6e038a23"},"schema_version":"1.0","source":{"id":"1311.2804","kind":"arxiv","version":1}},"canonical_sha256":"51117a477f42ee2dc13c3484031f57a0f6f6032e611929f799cb2135c1569ac6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51117a477f42ee2dc13c3484031f57a0f6f6032e611929f799cb2135c1569ac6","first_computed_at":"2026-05-18T01:22:24.679931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:24.679931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6WB11pOWzgswKhh98Ve5xWacmlfmrrCBlxIQXWo0OiG8jz7EorhHYcMWXT0m4uuIXL9k8BG5ZKH+PbB6sSlkAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:24.680489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ee3881ac547edac971488f931040c6a713dbcd058548a5b965f662e9554e27c","sha256:6d01b418d698efeadcd851b7312d17217414c5a85968e1e3add12fdde1bf0571"],"state_sha256":"c18b387bee436c85420a0e2f4689cb3ef01b7e916dac94d981b8f38de514b175"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sE+TwgiOCHO9sc0vmI56Hf+8FpKYdXjdFliKGToVR5psZGKD7BwNECC47h/PZ3J3Jw9RMkR2LW9Q8d3Fvfj4CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T23:09:35.424783Z","bundle_sha256":"507983c26935e33ab557c312e6e6f198d5967389465eca820019f1f0afbf5bed"}}