{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IJI4TMZQR4D6EMQZNKBNEOUVDD","short_pith_number":"pith:IJI4TMZQ","schema_version":"1.0","canonical_sha256":"4251c9b3308f07e232196a82d23a9518d0a6680358a2abe002aa136c7d3aa3d0","source":{"kind":"arxiv","id":"1008.0740","version":1},"attestation_state":"computed","paper":{"title":"$L_p$-nested symmetric distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.OT","authors_text":"Fabian Sinz, Matthias Bethge","submitted_at":"2010-08-04T10:44:30Z","abstract_excerpt":"Tractable generalizations of the Gaussian distribution play an important role for the analysis of high-dimensional data. One very general super-class of Normal distributions is the class of $\\nu$-spherical distributions whose random variables can be represented as the product $\\x = r\\cdot \\u$ of a uniformly distribution random variable $\\u$ on the $1$-level set of a positively homogeneous function $\\nu$ and arbitrary positive radial random variable $r$. Prominent subclasses of $\\nu$-spherical distributions are spherically symmetric distributions ($\\nu(\\x)=\\|\\x\\|_2$) which have been further gen"},"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":"1008.0740","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2010-08-04T10:44:30Z","cross_cats_sorted":[],"title_canon_sha256":"e32be19e67ef6b848a6adfb1353f2f66b5fd16a56b8de28e0f200cba09c458d7","abstract_canon_sha256":"fcdbc9cbdcb496e2c4fd9e93bfdb57842487a469fb6509efec58ae566aee7a81"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:35.730101Z","signature_b64":"He26nTx6LiVF1gW4JioQy24BQWRQjgffqKV8NHQZqpTEQ9FtMwFKkEj7efe+vf1VyT1u/8WSTxL5hyE1ArojBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4251c9b3308f07e232196a82d23a9518d0a6680358a2abe002aa136c7d3aa3d0","last_reissued_at":"2026-05-18T04:42:35.729449Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:35.729449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$L_p$-nested symmetric distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.OT","authors_text":"Fabian Sinz, Matthias Bethge","submitted_at":"2010-08-04T10:44:30Z","abstract_excerpt":"Tractable generalizations of the Gaussian distribution play an important role for the analysis of high-dimensional data. One very general super-class of Normal distributions is the class of $\\nu$-spherical distributions whose random variables can be represented as the product $\\x = r\\cdot \\u$ of a uniformly distribution random variable $\\u$ on the $1$-level set of a positively homogeneous function $\\nu$ and arbitrary positive radial random variable $r$. Prominent subclasses of $\\nu$-spherical distributions are spherically symmetric distributions ($\\nu(\\x)=\\|\\x\\|_2$) which have been further gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0740","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1008.0740","created_at":"2026-05-18T04:42:35.729541+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.0740v1","created_at":"2026-05-18T04:42:35.729541+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0740","created_at":"2026-05-18T04:42:35.729541+00:00"},{"alias_kind":"pith_short_12","alias_value":"IJI4TMZQR4D6","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IJI4TMZQR4D6EMQZ","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IJI4TMZQ","created_at":"2026-05-18T12:26:09.077623+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/IJI4TMZQR4D6EMQZNKBNEOUVDD","json":"https://pith.science/pith/IJI4TMZQR4D6EMQZNKBNEOUVDD.json","graph_json":"https://pith.science/api/pith-number/IJI4TMZQR4D6EMQZNKBNEOUVDD/graph.json","events_json":"https://pith.science/api/pith-number/IJI4TMZQR4D6EMQZNKBNEOUVDD/events.json","paper":"https://pith.science/paper/IJI4TMZQ"},"agent_actions":{"view_html":"https://pith.science/pith/IJI4TMZQR4D6EMQZNKBNEOUVDD","download_json":"https://pith.science/pith/IJI4TMZQR4D6EMQZNKBNEOUVDD.json","view_paper":"https://pith.science/paper/IJI4TMZQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.0740&json=true","fetch_graph":"https://pith.science/api/pith-number/IJI4TMZQR4D6EMQZNKBNEOUVDD/graph.json","fetch_events":"https://pith.science/api/pith-number/IJI4TMZQR4D6EMQZNKBNEOUVDD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IJI4TMZQR4D6EMQZNKBNEOUVDD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IJI4TMZQR4D6EMQZNKBNEOUVDD/action/storage_attestation","attest_author":"https://pith.science/pith/IJI4TMZQR4D6EMQZNKBNEOUVDD/action/author_attestation","sign_citation":"https://pith.science/pith/IJI4TMZQR4D6EMQZNKBNEOUVDD/action/citation_signature","submit_replication":"https://pith.science/pith/IJI4TMZQR4D6EMQZNKBNEOUVDD/action/replication_record"}},"created_at":"2026-05-18T04:42:35.729541+00:00","updated_at":"2026-05-18T04:42:35.729541+00:00"}