{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EURPNE4KYXM75K2NLKHDUGN443","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":"d388c557507e9a16cee95a16b11e0bc32efe2b33970a9724af291efb8853c5ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-06T10:11:45Z","title_canon_sha256":"bee2bc39da85cb4b184f238442905b65266f3f418be78f3f270a4df35889ef24"},"schema_version":"1.0","source":{"id":"1012.1113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1113","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1113v1","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1113","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"EURPNE4KYXM7","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EURPNE4KYXM75K2N","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EURPNE4K","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:c7326b7f6427d199b5562fcf6331d4472b1f6afa60dadf74ed3708791328b57b","target":"graph","created_at":"2026-05-18T04:34:01Z","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 generalize parts of a special non-Euclidean calculus of pseudodifferential operators, which was invented by S. Zelditch for hyperbolic surfaces, to symmetric spaces $X=G/K$ of the noncompact type and their compact quotients $Y=\\Gamma\\backslash G/K$. We sometimes restrict our results to the case of rank one symmetric spcaes. The non-Euclidean setting extends the defintion of so-called Patterson-Sullivan distributions, which were first defined by N. Anantharaman and S. Zelditch for hyperbolic systems, in a natural way to arbitrary symmetric spaces of the noncompact type. We find an explicit i","authors_text":"Michael Schroeder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-06T10:11:45Z","title":"Patterson-Sullivan distributions for symmetric spaces of the noncompact type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1113","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":"sha256:32f74e514212493f249be8f972a5bd26a75d8793a0ca3223a1fdd66431970769","target":"record","created_at":"2026-05-18T04:34:01Z","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":"d388c557507e9a16cee95a16b11e0bc32efe2b33970a9724af291efb8853c5ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-06T10:11:45Z","title_canon_sha256":"bee2bc39da85cb4b184f238442905b65266f3f418be78f3f270a4df35889ef24"},"schema_version":"1.0","source":{"id":"1012.1113","kind":"arxiv","version":1}},"canonical_sha256":"2522f6938ac5d9feab4d5a8e3a19bce6ff9fe38e9e050c70b2a12e22f9e84c3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2522f6938ac5d9feab4d5a8e3a19bce6ff9fe38e9e050c70b2a12e22f9e84c3e","first_computed_at":"2026-05-18T04:34:01.794528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:01.794528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CcomixUcFSCKTEER6K/P5lYmx06edLQO05VzHOlDuGOIf0mNcSoZ6mv+47Xfj41FYgVDr08nsuc7Yqw+v+0yAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:01.795013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32f74e514212493f249be8f972a5bd26a75d8793a0ca3223a1fdd66431970769","sha256:c7326b7f6427d199b5562fcf6331d4472b1f6afa60dadf74ed3708791328b57b"],"state_sha256":"fcefad19f1c7c7c8c55cbb0d41679284ae05df587b7fb71c6aa4d010f00a31d7"}