{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4D6S53OQB3HFT7UVWHCBHAFYI5","short_pith_number":"pith:4D6S53OQ","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"},"canonical_sha256":"e0fd2eedd00ece59fe95b1c41380b84761f04b7e34b86a13edaab48ecc04314b","source":{"kind":"arxiv","id":"1801.09113","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09113","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09113v2","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09113","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"pith_short_12","alias_value":"4D6S53OQB3HF","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4D6S53OQB3HFT7UV","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4D6S53OQ","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4D6S53OQB3HFT7UVWHCBHAFYI5","target":"record","payload":{"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"},"canonical_sha256":"e0fd2eedd00ece59fe95b1c41380b84761f04b7e34b86a13edaab48ecc04314b","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"},"source_kind":"arxiv","source_id":"1801.09113","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aBylDqmPF24TsCVGYeuPwmF2TMYEAgIi2nHS2hp8JI82wfHiMH+h11EOzUWcRk1iF04ER/7p29x+YfwPXH/eCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:59:07.645251Z"},"content_sha256":"87ab5b68ac057d96f52c58fae7402bbb03be1ae1d987e8ab7bc3ce0993789f9c","schema_version":"1.0","event_id":"sha256:87ab5b68ac057d96f52c58fae7402bbb03be1ae1d987e8ab7bc3ce0993789f9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4D6S53OQB3HFT7UVWHCBHAFYI5","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/XuyOHEw2bSsbAy+BuG9IaDvuM2dfovjKdNY+Q6+Sou7XLYXPZoUGe29JMG7ENvbW5ij3wNkqx/d/S7ho8lBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:59:07.645643Z"},"content_sha256":"5566cb4a10c6cad0fe05ddb0577810c1f02e62cb8f82a6f0b498f03e5b8c7b0b","schema_version":"1.0","event_id":"sha256:5566cb4a10c6cad0fe05ddb0577810c1f02e62cb8f82a6f0b498f03e5b8c7b0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/bundle.json","state_url":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T14:59:07Z","links":{"resolver":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5","bundle":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/bundle.json","state":"https://pith.science/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4D6S53OQB3HFT7UVWHCBHAFYI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4D6S53OQB3HFT7UVWHCBHAFYI5","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":"48aff35fb0b889e028ff4b1f3ef4919cc3aa3343e95045578d51a080f7482247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-01-27T17:05:34Z","title_canon_sha256":"d02b125fe558e5a85088533de71aacd41687a900e530ad3e76d5799e456a9b1f"},"schema_version":"1.0","source":{"id":"1801.09113","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09113","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09113v2","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09113","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"pith_short_12","alias_value":"4D6S53OQB3HF","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4D6S53OQB3HFT7UV","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4D6S53OQ","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:5566cb4a10c6cad0fe05ddb0577810c1f02e62cb8f82a6f0b498f03e5b8c7b0b","target":"graph","created_at":"2026-05-18T00:00:08Z","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":"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.","authors_text":"Boris Rubin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-01-27T17:05:34Z","title":"On the Blaschke-Petkantschin Formula and Drury's Identity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09113","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":"sha256:87ab5b68ac057d96f52c58fae7402bbb03be1ae1d987e8ab7bc3ce0993789f9c","target":"record","created_at":"2026-05-18T00:00:08Z","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":"48aff35fb0b889e028ff4b1f3ef4919cc3aa3343e95045578d51a080f7482247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-01-27T17:05:34Z","title_canon_sha256":"d02b125fe558e5a85088533de71aacd41687a900e530ad3e76d5799e456a9b1f"},"schema_version":"1.0","source":{"id":"1801.09113","kind":"arxiv","version":2}},"canonical_sha256":"e0fd2eedd00ece59fe95b1c41380b84761f04b7e34b86a13edaab48ecc04314b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0fd2eedd00ece59fe95b1c41380b84761f04b7e34b86a13edaab48ecc04314b","first_computed_at":"2026-05-18T00:00:08.811996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:08.811996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BZHu/iXYYymi6OZYdyzL9+31EsYe84ut6bImbaBF6zu+HS3RoCljl5dImqGcYpsZFtTU1qV0TbfsDV/v5ZF5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:08.812523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09113","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87ab5b68ac057d96f52c58fae7402bbb03be1ae1d987e8ab7bc3ce0993789f9c","sha256:5566cb4a10c6cad0fe05ddb0577810c1f02e62cb8f82a6f0b498f03e5b8c7b0b"],"state_sha256":"e9d485c0dae97dace2d1dc3819599aa0359da4f264473b455399c55a79c20f44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1M+SYJkJcFLdpKlNrsqRAcoN2DsS7xQ3ETv5ci2v6N8vC8iNUB07uLSaXed3pGUsV+r2jQIu36YWrRn0uEfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:59:07.647611Z","bundle_sha256":"07b412c29efdb213a044980cc25bcc109f7bc946066b661221be1c1e1065e5d2"}}