{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JADPXQJAOTQS2YLMWZKJRGXBZP","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":"cdcbe038a9e549dfeb8c2f0421a04055ab3a3259abc7fd1fb76afbd6e06cac54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-08-31T19:57:29Z","title_canon_sha256":"e4f98019e36c5a4362830ebd1cf3cd1cbf2afb043617bda384b3b03eb683ebb5"},"schema_version":"1.0","source":{"id":"1409.0258","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0258","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0258v2","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0258","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"JADPXQJAOTQS","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JADPXQJAOTQS2YLM","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JADPXQJA","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:258255cef49490991d97a9546783c02b44b2df1dffae4a0a4a2dfb260c914f64","target":"graph","created_at":"2026-05-17T23:43:38Z","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":"By the collective name of {\\it lattice counting} we refer to a setup introduced in Duke-Rudnick-Sarnak that aim to establish a relationship between arithmetic and randomness in the context of affine symmetric spaces. In this paper we extend the geometric setup from symmetric to real spherical spaces and continue to develop the approach with harmonic analysis which was initiated in Duke-Rudnick-Sarnak.","authors_text":"Bernhard Kr\\\"otz, Eitan Sayag, Henrik Schlichtkrull","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-08-31T19:57:29Z","title":"The harmonic analysis of lattice counting on real spherical spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0258","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":"sha256:09aeab5b5f298dd4a1326d86365c8bf371e0696e33a55aa1ca145d457ae65045","target":"record","created_at":"2026-05-17T23:43:38Z","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":"cdcbe038a9e549dfeb8c2f0421a04055ab3a3259abc7fd1fb76afbd6e06cac54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-08-31T19:57:29Z","title_canon_sha256":"e4f98019e36c5a4362830ebd1cf3cd1cbf2afb043617bda384b3b03eb683ebb5"},"schema_version":"1.0","source":{"id":"1409.0258","kind":"arxiv","version":2}},"canonical_sha256":"4806fbc12074e12d616cb654989ae1cbe8685c434d37dfc982f5d4d706f0ee94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4806fbc12074e12d616cb654989ae1cbe8685c434d37dfc982f5d4d706f0ee94","first_computed_at":"2026-05-17T23:43:38.635581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:38.635581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1giXf0MUtxrWf6+4VqqDSbw1Fb/QCS8Tu7vOU4KvtiqIej2TTTEthMIMRAKQOoARX8/O4Xf/hhFgEYQ5lOaLDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:38.636338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0258","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09aeab5b5f298dd4a1326d86365c8bf371e0696e33a55aa1ca145d457ae65045","sha256:258255cef49490991d97a9546783c02b44b2df1dffae4a0a4a2dfb260c914f64"],"state_sha256":"c9deb44685c6065faaeead9bd300d3d3661f977eab056479b052278e4d60bb32"}