{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5Z5UNYKKZV7FHBAY5YOLWRAT34","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":"e230cb47ef469a589d2bedec88a78781afc2c70f848d93934c57e5e9ed0abd67","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T22:07:28Z","title_canon_sha256":"56340aa5b65d79128f08954bceabfa6ec126aa35d715e54c63df6a8c05a8efb8"},"schema_version":"1.0","source":{"id":"1205.6222","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6222","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6222v3","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6222","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"pith_short_12","alias_value":"5Z5UNYKKZV7F","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5Z5UNYKKZV7FHBAY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5Z5UNYKK","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:50debde908d400748ede4785547e2b13e74c5f6bb52ce7cd5234e7a37ca31a42","target":"graph","created_at":"2026-05-18T01:11:05Z","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":"There is a well known link between (maximal) polar representations and isotropy representations of symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns-Spatzier provides a link between irreducible symmetric spaces of non-compact type of rank at least three and irreducible topological spherical buildings of rank at least three.\n  We discover and exploit a rich structure of a (connected) chamber system of finite (Coxeter) type M associated with any polar action of cohomogeneity at least two on any simply connected closed positively curved manifold. Although this chamber sys","authors_text":"Fuquan Fang, Gudlaugur Thorbergsson, Karsten Grove","cross_cats":["math.GR","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T22:07:28Z","title":"Tits Geometry and Positive Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6222","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:b42482e3111b7ed047e5424076e3f2ec71e52e0e81622b37fd54f63e89dec13d","target":"record","created_at":"2026-05-18T01:11:05Z","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":"e230cb47ef469a589d2bedec88a78781afc2c70f848d93934c57e5e9ed0abd67","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T22:07:28Z","title_canon_sha256":"56340aa5b65d79128f08954bceabfa6ec126aa35d715e54c63df6a8c05a8efb8"},"schema_version":"1.0","source":{"id":"1205.6222","kind":"arxiv","version":3}},"canonical_sha256":"ee7b46e14acd7e538418ee1cbb4413df3d6fbb342d7d3dfdfb3c9e8d1ef07c75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee7b46e14acd7e538418ee1cbb4413df3d6fbb342d7d3dfdfb3c9e8d1ef07c75","first_computed_at":"2026-05-18T01:11:05.449942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:05.449942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"63VlQuyhfmfwPJtuhUG/8BFba+ngYhNFupuEN0i7ki7a0lrhqV4vukZYU7LCBATC+s4+VLETAQIIGhdejcxPCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:05.450561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6222","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b42482e3111b7ed047e5424076e3f2ec71e52e0e81622b37fd54f63e89dec13d","sha256:50debde908d400748ede4785547e2b13e74c5f6bb52ce7cd5234e7a37ca31a42"],"state_sha256":"09182244c19e51b8629e5c3e17bb1f8f1af3e69305f4cad3527aeb209c0d3483"}