{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:MA7H57TKAQOV4VZ2EB6M4VM5Z5","short_pith_number":"pith:MA7H57TK","canonical_record":{"source":{"id":"dg-ga/9712009","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1997-12-20T12:55:16Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"d837f9227ccb0c41a89b8cc7531dd94c22bc4e1f2019970304ed4e4aab6b1136","abstract_canon_sha256":"29fd7af5f68f1769d39d0f285bd0f15252cc2a6d74b9572dc55c4f9bd584d7cc"},"schema_version":"1.0"},"canonical_sha256":"603e7efe6a041d5e573a207cce559dcf4587c56d002238a50ef0167e3fab40c5","source":{"kind":"arxiv","id":"dg-ga/9712009","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9712009","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9712009v1","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9712009","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"MA7H57TKAQOV","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"MA7H57TKAQOV4VZ2","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"MA7H57TK","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:MA7H57TKAQOV4VZ2EB6M4VM5Z5","target":"record","payload":{"canonical_record":{"source":{"id":"dg-ga/9712009","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1997-12-20T12:55:16Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"d837f9227ccb0c41a89b8cc7531dd94c22bc4e1f2019970304ed4e4aab6b1136","abstract_canon_sha256":"29fd7af5f68f1769d39d0f285bd0f15252cc2a6d74b9572dc55c4f9bd584d7cc"},"schema_version":"1.0"},"canonical_sha256":"603e7efe6a041d5e573a207cce559dcf4587c56d002238a50ef0167e3fab40c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:27.427795Z","signature_b64":"O9P1N4Q8XkJ13tdEIq3q4Ux9k8/KdcPx2EeFcsovlD3FUze94ip9Rqqn+CO4Xxom3Dp1YclwHdleFS4LZ6n9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"603e7efe6a041d5e573a207cce559dcf4587c56d002238a50ef0167e3fab40c5","last_reissued_at":"2026-05-18T03:36:27.427425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:27.427425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"dg-ga/9712009","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":"2026-05-18T03:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LEsWcrVEM2iyyJ4gZHuFO6908dxkhIN8tj9B7lj6kySV6589CyHO15WIa3b9RZumzrM/OPa+g1aufWHWIh1qBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T18:54:03.035839Z"},"content_sha256":"a126008d925d88e2abb991e17e5acb07a280a3b03a0cf067f68cc9c4ae4a5814","schema_version":"1.0","event_id":"sha256:a126008d925d88e2abb991e17e5acb07a280a3b03a0cf067f68cc9c4ae4a5814"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:MA7H57TKAQOV4VZ2EB6M4VM5Z5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on affine isometric actions of discrete groups","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"dg-ga","authors_text":"Yurii A. Neretin","submitted_at":"1997-12-20T12:55:16Z","abstract_excerpt":"Consider a lattice $\\Gamma$ in a group $G = SL_2(\\R), SO(1,n), SU(1,n)$, $SL_2(\\Q_p)$. We discuss actions of $\\Gamma$ by affine isometric transformations of Hilbert spaces. We show that for irreducible affine isometric action of $G$ its restriction to $\\Gamma$ is irreducible. We prove the existence of canonical irreducible affine isometric actions of $\\Gamma$ associated to actions of $\\Gamma$ on $\\R$- trees. Using such actions we construct irreducible representations of semigroup of probabilistic measures on $\\Gamma$ and construct the series of representations of the groups of diffeomorphisms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9712009","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":"2026-05-18T03:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJsKCG67lTSFhvy5+gsRiBMdQir+UnqI5tvTmlIj8QELvqIGZbQx/IhqLTStoijQD6fxG502lDy9j4pO7TCDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T18:54:03.036198Z"},"content_sha256":"82a52bacee05606aab66e4943d21386925d31743919c3fde8af577e1d91a95a8","schema_version":"1.0","event_id":"sha256:82a52bacee05606aab66e4943d21386925d31743919c3fde8af577e1d91a95a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MA7H57TKAQOV4VZ2EB6M4VM5Z5/bundle.json","state_url":"https://pith.science/pith/MA7H57TKAQOV4VZ2EB6M4VM5Z5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MA7H57TKAQOV4VZ2EB6M4VM5Z5/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":"2026-06-30T18:54:03Z","links":{"resolver":"https://pith.science/pith/MA7H57TKAQOV4VZ2EB6M4VM5Z5","bundle":"https://pith.science/pith/MA7H57TKAQOV4VZ2EB6M4VM5Z5/bundle.json","state":"https://pith.science/pith/MA7H57TKAQOV4VZ2EB6M4VM5Z5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MA7H57TKAQOV4VZ2EB6M4VM5Z5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:MA7H57TKAQOV4VZ2EB6M4VM5Z5","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":"29fd7af5f68f1769d39d0f285bd0f15252cc2a6d74b9572dc55c4f9bd584d7cc","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1997-12-20T12:55:16Z","title_canon_sha256":"d837f9227ccb0c41a89b8cc7531dd94c22bc4e1f2019970304ed4e4aab6b1136"},"schema_version":"1.0","source":{"id":"dg-ga/9712009","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9712009","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9712009v1","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9712009","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"MA7H57TKAQOV","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"MA7H57TKAQOV4VZ2","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"MA7H57TK","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:82a52bacee05606aab66e4943d21386925d31743919c3fde8af577e1d91a95a8","target":"graph","created_at":"2026-05-18T03:36:27Z","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":"Consider a lattice $\\Gamma$ in a group $G = SL_2(\\R), SO(1,n), SU(1,n)$, $SL_2(\\Q_p)$. We discuss actions of $\\Gamma$ by affine isometric transformations of Hilbert spaces. We show that for irreducible affine isometric action of $G$ its restriction to $\\Gamma$ is irreducible. We prove the existence of canonical irreducible affine isometric actions of $\\Gamma$ associated to actions of $\\Gamma$ on $\\R$- trees. Using such actions we construct irreducible representations of semigroup of probabilistic measures on $\\Gamma$ and construct the series of representations of the groups of diffeomorphisms ","authors_text":"Yurii A. Neretin","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"dg-ga","submitted_at":"1997-12-20T12:55:16Z","title":"Notes on affine isometric actions of discrete groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9712009","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:a126008d925d88e2abb991e17e5acb07a280a3b03a0cf067f68cc9c4ae4a5814","target":"record","created_at":"2026-05-18T03:36:27Z","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":"29fd7af5f68f1769d39d0f285bd0f15252cc2a6d74b9572dc55c4f9bd584d7cc","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1997-12-20T12:55:16Z","title_canon_sha256":"d837f9227ccb0c41a89b8cc7531dd94c22bc4e1f2019970304ed4e4aab6b1136"},"schema_version":"1.0","source":{"id":"dg-ga/9712009","kind":"arxiv","version":1}},"canonical_sha256":"603e7efe6a041d5e573a207cce559dcf4587c56d002238a50ef0167e3fab40c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"603e7efe6a041d5e573a207cce559dcf4587c56d002238a50ef0167e3fab40c5","first_computed_at":"2026-05-18T03:36:27.427425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:27.427425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O9P1N4Q8XkJ13tdEIq3q4Ux9k8/KdcPx2EeFcsovlD3FUze94ip9Rqqn+CO4Xxom3Dp1YclwHdleFS4LZ6n9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:27.427795Z","signed_message":"canonical_sha256_bytes"},"source_id":"dg-ga/9712009","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a126008d925d88e2abb991e17e5acb07a280a3b03a0cf067f68cc9c4ae4a5814","sha256:82a52bacee05606aab66e4943d21386925d31743919c3fde8af577e1d91a95a8"],"state_sha256":"9ee924ea1033ff5e3262f4e6e918a7365557db53886e8af3f6344087873048b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"33sKSx9xlCXlGjv85jiI63s6fXfSYxQFlDqgh7XBXEDwu7eMdM+bPSHAgRG0oMmm7esAQU5rKDbRcAegqwMUCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T18:54:03.038198Z","bundle_sha256":"c65489bea4073f2dc14d36d2b58686c4f50f4beeb37bbb54407d2dbe3c768e8e"}}