{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5YYEATX3ZNXEVNEELOSEFUZ2YK","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":"fcdea7e3528782d0dd6a79756835405e47cba15b4e0e75c0f7477631ec3831f7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-23T14:59:09Z","title_canon_sha256":"c0010980cda891772c19d92d02594c6b9745b886c991afc45526c1a2cbafd574"},"schema_version":"1.0","source":{"id":"1501.05820","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05820","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05820v2","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05820","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"5YYEATX3ZNXE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5YYEATX3ZNXEVNEE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5YYEATX3","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:284b84ddb4c7ef9411b42edd322968869ed98a6f4d7042523c7691edb958c125","target":"graph","created_at":"2026-05-18T00:48:20Z","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 show that the group $PSL(2,R)$ is a spherical subgroup in the group of $C^3$-diffeomorphisms of the circle. Also, the group of automorphisms of a Bruhat--Tits tree is a spherical subgroup in the group of hierarchomorphisms of the tree.","authors_text":"Yury A. Neretin","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-23T14:59:09Z","title":"The subgroup $PSL(2,R)$ is spherical in the group of diffeomorphisms of the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05820","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:b2e1025d89557c32d54ab0ae286320da1c22c1a17ea2d35f8072664a490343f3","target":"record","created_at":"2026-05-18T00:48:20Z","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":"fcdea7e3528782d0dd6a79756835405e47cba15b4e0e75c0f7477631ec3831f7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-23T14:59:09Z","title_canon_sha256":"c0010980cda891772c19d92d02594c6b9745b886c991afc45526c1a2cbafd574"},"schema_version":"1.0","source":{"id":"1501.05820","kind":"arxiv","version":2}},"canonical_sha256":"ee30404efbcb6e4ab4845ba442d33ac2af4ee22503632e44f6e3d19eababed31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee30404efbcb6e4ab4845ba442d33ac2af4ee22503632e44f6e3d19eababed31","first_computed_at":"2026-05-18T00:48:20.811063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:20.811063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bF0eHuKUBoXxc2EkUqAz9Mxgma5e3RQTk90miIbeJe4wkb7dTvY893j2GtjrfTBVpqUrTqF/rpIdJTO8Goo+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:20.811741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05820","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2e1025d89557c32d54ab0ae286320da1c22c1a17ea2d35f8072664a490343f3","sha256:284b84ddb4c7ef9411b42edd322968869ed98a6f4d7042523c7691edb958c125"],"state_sha256":"9b7f34afe8c1e445bbd8675f1b446b689c2ed077c5aaec73d8bdfeaa67cbf789"}