{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4D6S53OQB3HFT7UVWHCBHAFYI5","short_pith_number":"pith:4D6S53OQ","schema_version":"1.0","canonical_sha256":"e0fd2eedd00ece59fe95b1c41380b84761f04b7e34b86a13edaab48ecc04314b","source":{"kind":"arxiv","id":"1801.09113","version":2},"attestation_state":"computed","paper":{"title":"On the Blaschke-Petkantschin Formula and Drury's Identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Boris Rubin","submitted_at":"2018-01-27T17:05:34Z","abstract_excerpt":"The Blaschke-Petkantschin formula is a variant of the polar decomposition of the $k$-fold Lebesgue measure on $\\mathbb {R}^n$ in terms of the corresponding measures on $k$-dimensional linear subspaces of $\\mathbb {R}^n$. We suggest a new elementary proof of this formula and discuss its connection with the celebrated Drury's identity that plays a key role in the study of mapping properties of the Radon-John $k$-plane transforms. We give a new derivation of this identity and provide it with precise information about constant factors and the class of admissible functions."},"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":"1801.09113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-01-27T17:05:34Z","cross_cats_sorted":[],"title_canon_sha256":"d02b125fe558e5a85088533de71aacd41687a900e530ad3e76d5799e456a9b1f","abstract_canon_sha256":"48aff35fb0b889e028ff4b1f3ef4919cc3aa3343e95045578d51a080f7482247"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:08.812523Z","signature_b64":"BZHu/iXYYymi6OZYdyzL9+31EsYe84ut6bImbaBF6zu+HS3RoCljl5dImqGcYpsZFtTU1qV0TbfsDV/v5ZF5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0fd2eedd00ece59fe95b1c41380b84761f04b7e34b86a13edaab48ecc04314b","last_reissued_at":"2026-05-18T00:00:08.811996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:08.811996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Blaschke-Petkantschin Formula and Drury's Identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Boris Rubin","submitted_at":"2018-01-27T17:05:34Z","abstract_excerpt":"The Blaschke-Petkantschin formula is a variant of the polar decomposition of the $k$-fold Lebesgue measure on $\\mathbb {R}^n$ in terms of the corresponding measures on $k$-dimensional linear subspaces of $\\mathbb {R}^n$. We suggest a new elementary proof of this formula and discuss its connection with the celebrated Drury's identity that plays a key role in the study of mapping properties of the Radon-John $k$-plane transforms. We give a new derivation of this identity and provide it with precise information about constant factors and the class of admissible functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09113","kind":"arxiv","version":2},"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":"1801.09113","created_at":"2026-05-18T00:00:08.812092+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.09113v2","created_at":"2026-05-18T00:00:08.812092+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09113","created_at":"2026-05-18T00:00:08.812092+00:00"},{"alias_kind":"pith_short_12","alias_value":"4D6S53OQB3HF","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4D6S53OQB3HFT7UV","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4D6S53OQ","created_at":"2026-05-18T12:32:05.422762+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/4D6S53OQB3HFT7UVWHCBHAFYI5","json":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5.json","graph_json":"https://pith.science/api/pith-number/4D6S53OQB3HFT7UVWHCBHAFYI5/graph.json","events_json":"https://pith.science/api/pith-number/4D6S53OQB3HFT7UVWHCBHAFYI5/events.json","paper":"https://pith.science/paper/4D6S53OQ"},"agent_actions":{"view_html":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5","download_json":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5.json","view_paper":"https://pith.science/paper/4D6S53OQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.09113&json=true","fetch_graph":"https://pith.science/api/pith-number/4D6S53OQB3HFT7UVWHCBHAFYI5/graph.json","fetch_events":"https://pith.science/api/pith-number/4D6S53OQB3HFT7UVWHCBHAFYI5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/action/storage_attestation","attest_author":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/action/author_attestation","sign_citation":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/action/citation_signature","submit_replication":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/action/replication_record"}},"created_at":"2026-05-18T00:00:08.812092+00:00","updated_at":"2026-05-18T00:00:08.812092+00:00"}