{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:4D34GK36JGYBQVJQPRTLAZFQTB","short_pith_number":"pith:4D34GK36","schema_version":"1.0","canonical_sha256":"e0f7c32b7e49b01855307c66b064b098463de99d8698e342014b2956d85b7f4a","source":{"kind":"arxiv","id":"math/0406406","version":1},"attestation_state":"computed","paper":{"title":"The Busemann-Petty problem for arbitrary measures","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Artem Zvavitch","submitted_at":"2004-06-21T15:44:31Z","abstract_excerpt":"The aim of this paper is to study properties of sections of convex bodies with respect to different types of measures. We present a formula connecting the Minkowski functional of a convex symmetric body K with the measure of its sections. We apply this formula to study properties of general measures most of which were known before only in the case of the standard Lebesgue measure. We solve an analog of the Busemann-Petty problem for the case of general measures. In addition, we show that there are measures, for which the answer to the generalized Busemann-Petty problem is affirmative in all di"},"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":"math/0406406","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.MG","submitted_at":"2004-06-21T15:44:31Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"209a7a44e2d6c87cd183f001d3d62d89267e888cf7317e5ae5f704e529e37834","abstract_canon_sha256":"23dff478a0cc29ba6acdca2d64126364c1946d5654e797b1b5ccb270ad8679f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:44.069475Z","signature_b64":"Dtl4zP/CHKEj058GstX8B4u7PzKyaiGik2M+WahEgouV7HAwp+E1J1rKtuutLyWjCLbn7RlQZk+SaOCTi+XIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0f7c32b7e49b01855307c66b064b098463de99d8698e342014b2956d85b7f4a","last_reissued_at":"2026-07-04T14:38:44.069058Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:44.069058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Busemann-Petty problem for arbitrary measures","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Artem Zvavitch","submitted_at":"2004-06-21T15:44:31Z","abstract_excerpt":"The aim of this paper is to study properties of sections of convex bodies with respect to different types of measures. We present a formula connecting the Minkowski functional of a convex symmetric body K with the measure of its sections. We apply this formula to study properties of general measures most of which were known before only in the case of the standard Lebesgue measure. We solve an analog of the Busemann-Petty problem for the case of general measures. In addition, we show that there are measures, for which the answer to the generalized Busemann-Petty problem is affirmative in all di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406406","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/math/0406406/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":"math/0406406","created_at":"2026-07-04T14:38:44.069120+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0406406v1","created_at":"2026-07-04T14:38:44.069120+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0406406","created_at":"2026-07-04T14:38:44.069120+00:00"},{"alias_kind":"pith_short_12","alias_value":"4D34GK36JGYB","created_at":"2026-07-04T14:38:44.069120+00:00"},{"alias_kind":"pith_short_16","alias_value":"4D34GK36JGYBQVJQ","created_at":"2026-07-04T14:38:44.069120+00:00"},{"alias_kind":"pith_short_8","alias_value":"4D34GK36","created_at":"2026-07-04T14:38:44.069120+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/4D34GK36JGYBQVJQPRTLAZFQTB","json":"https://pith.science/pith/4D34GK36JGYBQVJQPRTLAZFQTB.json","graph_json":"https://pith.science/api/pith-number/4D34GK36JGYBQVJQPRTLAZFQTB/graph.json","events_json":"https://pith.science/api/pith-number/4D34GK36JGYBQVJQPRTLAZFQTB/events.json","paper":"https://pith.science/paper/4D34GK36"},"agent_actions":{"view_html":"https://pith.science/pith/4D34GK36JGYBQVJQPRTLAZFQTB","download_json":"https://pith.science/pith/4D34GK36JGYBQVJQPRTLAZFQTB.json","view_paper":"https://pith.science/paper/4D34GK36","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0406406&json=true","fetch_graph":"https://pith.science/api/pith-number/4D34GK36JGYBQVJQPRTLAZFQTB/graph.json","fetch_events":"https://pith.science/api/pith-number/4D34GK36JGYBQVJQPRTLAZFQTB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4D34GK36JGYBQVJQPRTLAZFQTB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4D34GK36JGYBQVJQPRTLAZFQTB/action/storage_attestation","attest_author":"https://pith.science/pith/4D34GK36JGYBQVJQPRTLAZFQTB/action/author_attestation","sign_citation":"https://pith.science/pith/4D34GK36JGYBQVJQPRTLAZFQTB/action/citation_signature","submit_replication":"https://pith.science/pith/4D34GK36JGYBQVJQPRTLAZFQTB/action/replication_record"}},"created_at":"2026-07-04T14:38:44.069120+00:00","updated_at":"2026-07-04T14:38:44.069120+00:00"}