{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:F2GFYLGV3PPQDYEVCBUSWQQRL7","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":"87e8cf0e65a65838836358014cc4ae0d49fb0ce746f612701b1b7b8d8a7290ae","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-29T13:55:46Z","title_canon_sha256":"98c537ac7a7a47e090548d44842aea6188441af333c8c849150ffd0075264ce5"},"schema_version":"1.0","source":{"id":"1105.5788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5788","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5788v1","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5788","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"F2GFYLGV3PPQ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F2GFYLGV3PPQDYEV","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F2GFYLGV","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:e9309311b1b850b0f58e0281f70ab6db55bf3cd94af5f6a1d5ab94c11d28251f","target":"graph","created_at":"2026-05-18T04:21:01Z","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":"For a compact locally symmetric space $\\XG$ of non-positive curvature, we consider sequences of normalized joint eigenfunctions which belong to the principal spectrum of the algebra of invariant differential operators. Using an $h$-\\psdiff\\ calculus on $\\XG$, we define and study lifted quantum limits as weak$^*$-limit points of Wigner distributions. The Helgason boundary values of the eigenfunctions allow us to construct Patterson--Sullivan distributions on the space of Weyl chambers. These distributions are asymptotic to lifted quantum limits and satisfy additional invariance properties, whic","authors_text":"Joachim Hilgert, Michael Schr\\\"oder, S\\\"onke Hansen","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-29T13:55:46Z","title":"Patterson--Sullivan distributions in higher rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5788","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:f6c40c2d00991532f641ef5ecd23d25e001e90f6ffe314115e46a7b3b0a3e77b","target":"record","created_at":"2026-05-18T04:21:01Z","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":"87e8cf0e65a65838836358014cc4ae0d49fb0ce746f612701b1b7b8d8a7290ae","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-29T13:55:46Z","title_canon_sha256":"98c537ac7a7a47e090548d44842aea6188441af333c8c849150ffd0075264ce5"},"schema_version":"1.0","source":{"id":"1105.5788","kind":"arxiv","version":1}},"canonical_sha256":"2e8c5c2cd5dbdf01e09510692b42115ff6a363a7c0e80bf1bf4231a6d7607c21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e8c5c2cd5dbdf01e09510692b42115ff6a363a7c0e80bf1bf4231a6d7607c21","first_computed_at":"2026-05-18T04:21:01.554540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:01.554540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v4cy2d613JRnQL+R6G+LuwISPz4kQk9d3+wqX13Y5V3xJkLB9zYyT6BbEvVt/tWHkCAsxv9wXXnAH+q/MoHVDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:01.555029Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5788","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6c40c2d00991532f641ef5ecd23d25e001e90f6ffe314115e46a7b3b0a3e77b","sha256:e9309311b1b850b0f58e0281f70ab6db55bf3cd94af5f6a1d5ab94c11d28251f"],"state_sha256":"f646eab28491bfb8dab89e169e121bf2138fd699ff5621b98562215a0f8a37ce"}