{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:X5SFJRJWLZ4PHE465UW3ID7K4I","short_pith_number":"pith:X5SFJRJW","schema_version":"1.0","canonical_sha256":"bf6454c5365e78f3939eed2db40feae22e651e4a9299a38fedc57eebe056cc2a","source":{"kind":"arxiv","id":"2411.15564","version":1},"attestation_state":"computed","paper":{"title":"On $L^1$-$L^2$ dichotomy for flat symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Nico Spronk, Sanjeev Kumar Gupta","submitted_at":"2024-11-23T13:46:45Z","abstract_excerpt":"For rank 1 flat symmetric spaces, continuous orbital measures admit absolutely continuous convolution squares, except for Cartan type AI. Hence $L^1$-$L^2$ dichotomy for these spaces holds true in parallel to the compact and non-compact rank 1 symmetric spaces. We also study $L^1$-$L^2$ dichotomy for flat symmetric spaces of ranks $p=2,3$ of type AIII, i.e.\\ associated with $SU(p,q)/S(U(p)\\times U(q))$ where $q\\geq p$. For continuous orbital measures given by regular points $L^1$-$L^2$ dichotomy holds. We study such measures given by certain singular points when $p=2$, and show that $L^1$-$L^2"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.15564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-11-23T13:46:45Z","cross_cats_sorted":[],"title_canon_sha256":"0b92ea7590d0d001a3f771d7cc5d584775c6dad55f720f7ab8a35788f564e433","abstract_canon_sha256":"85b56143522c9db7e8457df1e4dad6cfe3ba5687a75cd2222e6ea407952b3071"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:37.113865Z","signature_b64":"OkDUYiXWjjqGuhEVs7yCa+TMZ5XBRaQrZ9NWcAAcuwBa8aT2uU4GOETiPN3q+L67CzheQoib+6398qKkPxzwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf6454c5365e78f3939eed2db40feae22e651e4a9299a38fedc57eebe056cc2a","last_reissued_at":"2026-07-05T09:39:37.113421Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:37.113421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $L^1$-$L^2$ dichotomy for flat symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Nico Spronk, Sanjeev Kumar Gupta","submitted_at":"2024-11-23T13:46:45Z","abstract_excerpt":"For rank 1 flat symmetric spaces, continuous orbital measures admit absolutely continuous convolution squares, except for Cartan type AI. Hence $L^1$-$L^2$ dichotomy for these spaces holds true in parallel to the compact and non-compact rank 1 symmetric spaces. We also study $L^1$-$L^2$ dichotomy for flat symmetric spaces of ranks $p=2,3$ of type AIII, i.e.\\ associated with $SU(p,q)/S(U(p)\\times U(q))$ where $q\\geq p$. For continuous orbital measures given by regular points $L^1$-$L^2$ dichotomy holds. We study such measures given by certain singular points when $p=2$, and show that $L^1$-$L^2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15564","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.15564/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2411.15564","created_at":"2026-07-05T09:39:37.113480+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.15564v1","created_at":"2026-07-05T09:39:37.113480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15564","created_at":"2026-07-05T09:39:37.113480+00:00"},{"alias_kind":"pith_short_12","alias_value":"X5SFJRJWLZ4P","created_at":"2026-07-05T09:39:37.113480+00:00"},{"alias_kind":"pith_short_16","alias_value":"X5SFJRJWLZ4PHE46","created_at":"2026-07-05T09:39:37.113480+00:00"},{"alias_kind":"pith_short_8","alias_value":"X5SFJRJW","created_at":"2026-07-05T09:39:37.113480+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X5SFJRJWLZ4PHE465UW3ID7K4I","json":"https://pith.science/pith/X5SFJRJWLZ4PHE465UW3ID7K4I.json","graph_json":"https://pith.science/api/pith-number/X5SFJRJWLZ4PHE465UW3ID7K4I/graph.json","events_json":"https://pith.science/api/pith-number/X5SFJRJWLZ4PHE465UW3ID7K4I/events.json","paper":"https://pith.science/paper/X5SFJRJW"},"agent_actions":{"view_html":"https://pith.science/pith/X5SFJRJWLZ4PHE465UW3ID7K4I","download_json":"https://pith.science/pith/X5SFJRJWLZ4PHE465UW3ID7K4I.json","view_paper":"https://pith.science/paper/X5SFJRJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.15564&json=true","fetch_graph":"https://pith.science/api/pith-number/X5SFJRJWLZ4PHE465UW3ID7K4I/graph.json","fetch_events":"https://pith.science/api/pith-number/X5SFJRJWLZ4PHE465UW3ID7K4I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X5SFJRJWLZ4PHE465UW3ID7K4I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X5SFJRJWLZ4PHE465UW3ID7K4I/action/storage_attestation","attest_author":"https://pith.science/pith/X5SFJRJWLZ4PHE465UW3ID7K4I/action/author_attestation","sign_citation":"https://pith.science/pith/X5SFJRJWLZ4PHE465UW3ID7K4I/action/citation_signature","submit_replication":"https://pith.science/pith/X5SFJRJWLZ4PHE465UW3ID7K4I/action/replication_record"}},"created_at":"2026-07-05T09:39:37.113480+00:00","updated_at":"2026-07-05T09:39:37.113480+00:00"}