{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NLRRXY7ROLOC72AYOTJY4EML5P","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":"9984a166e0f51db839957d13dd259fb2f08dd5e3a4d94434f3b706d76645766e","cross_cats_sorted":["math.GT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-12-13T15:52:00Z","title_canon_sha256":"75e6cdbdc64e7cabba7ba4d72963cc3f63f909f52d5d7f543cd297f0005c5c31"},"schema_version":"1.0","source":{"id":"2512.12369","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.12369","created_at":"2026-06-10T01:09:50Z"},{"alias_kind":"arxiv_version","alias_value":"2512.12369v2","created_at":"2026-06-10T01:09:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.12369","created_at":"2026-06-10T01:09:50Z"},{"alias_kind":"pith_short_12","alias_value":"NLRRXY7ROLOC","created_at":"2026-06-10T01:09:50Z"},{"alias_kind":"pith_short_16","alias_value":"NLRRXY7ROLOC72AY","created_at":"2026-06-10T01:09:50Z"},{"alias_kind":"pith_short_8","alias_value":"NLRRXY7R","created_at":"2026-06-10T01:09:50Z"}],"graph_snapshots":[{"event_id":"sha256:de607c995c2d2098678288bcd0ef65db6802a45da447cce6b24e89b2f6eb5243","target":"graph","created_at":"2026-06-10T01:09:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.12369/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In [DP12], Delzant and Py showed that there exist continuous irreducible isometric actions of $\\mathrm{PSL}_2(\\mathbb{R})$ on the infinite-dimensional hyperbolic space $\\mathbb{H}^\\infty$. Such continuous irreducible actions do not exist on the hyperbolic spaces $\\mathbb{H}^n$ when $n>2$ and their associated embeddings $\\mathbb{H}^2 \\to \\mathbb{H}^\\infty$ given by the orbit maps were later called \\emph{exotic} by Monod and Py in [MP14]. In this article, we produce a continuous and irreducible representation of $\\mathrm{PSL}_2(\\mathbb{R})\\to \\mathrm{Isom}(\\mathbb{H}^\\infty)$ using the hyperboli","authors_text":"David Xu, Fran\\c{c}ois Fillastre, Yusen Long","cross_cats":["math.GT","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-12-13T15:52:00Z","title":"An explicit exotic representation of a rank-one simple Lie group via convex bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.12369","kind":"arxiv","version":2},"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":"sha256:4c3d60e1b45fefee02f35166d97db0e4e0232d89588416d97ed8ef123c863d66","target":"record","created_at":"2026-06-10T01:09:50Z","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":"9984a166e0f51db839957d13dd259fb2f08dd5e3a4d94434f3b706d76645766e","cross_cats_sorted":["math.GT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-12-13T15:52:00Z","title_canon_sha256":"75e6cdbdc64e7cabba7ba4d72963cc3f63f909f52d5d7f543cd297f0005c5c31"},"schema_version":"1.0","source":{"id":"2512.12369","kind":"arxiv","version":2}},"canonical_sha256":"6ae31be3f172dc2fe81874d38e118bebe0c78f6669ddc4861d003f21565ead29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ae31be3f172dc2fe81874d38e118bebe0c78f6669ddc4861d003f21565ead29","first_computed_at":"2026-06-10T01:09:50.141228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:09:50.141228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NC1S5XH2lwFmy4KLCvM4YElKqZ6UY0P+z5UcyrdIUHVineKrsSGzWh/AbX88uzu/5yNhkH2FvReOA5xMGrlBAg==","signature_status":"signed_v1","signed_at":"2026-06-10T01:09:50.142371Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.12369","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c3d60e1b45fefee02f35166d97db0e4e0232d89588416d97ed8ef123c863d66","sha256:de607c995c2d2098678288bcd0ef65db6802a45da447cce6b24e89b2f6eb5243"],"state_sha256":"eae3cbaf2c239bbe3ca1c4c430f31eb80abeb571dd2653d9f40d45ea82ead964"}