{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:XYE7E52SDU4F4WUNZ6QOEE6PTY","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":"10209a34d0919ae6351395c8f3d3b2c6c3918350a54071c31f6f2013b0b93828","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"math.MG","submitted_at":"1998-02-05T00:00:00Z","title_canon_sha256":"1d37ee7b3821cc76dd38871752732ac0a87e92eda2a2a23fb47a789e8e4ba451"},"schema_version":"1.0","source":{"id":"math/9802128","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9802128","created_at":"2026-07-04T14:40:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/9802128v2","created_at":"2026-07-04T14:40:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9802128","created_at":"2026-07-04T14:40:27Z"},{"alias_kind":"pith_short_12","alias_value":"XYE7E52SDU4F","created_at":"2026-07-04T14:40:27Z"},{"alias_kind":"pith_short_16","alias_value":"XYE7E52SDU4F4WUN","created_at":"2026-07-04T14:40:27Z"},{"alias_kind":"pith_short_8","alias_value":"XYE7E52S","created_at":"2026-07-04T14:40:27Z"}],"graph_snapshots":[{"event_id":"sha256:efce8da3474f3ce00a9b9d868e0656645b5861b0e6481659e983b95929c29420","target":"graph","created_at":"2026-07-04T14:40:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/9802128/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A unified analytic solution to the Busemann-Petty problem was recently found by Gardner, Koldobsky and Schlumprecht. We give an elementary proof of their formulas for the inverse Radon transform.","authors_text":"Bernard Maurey, Franck Barthe, Matthieu Fradelizi","cross_cats":["math.FA"],"headline":"","license":"","primary_cat":"math.MG","submitted_at":"1998-02-05T00:00:00Z","title":"Elementary solution to the Busemann-Petty problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9802128","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:cb31e6fa9b81d859bc612619c7609f8a2925d28f6d3907e27cb4da5878bb6b0d","target":"record","created_at":"2026-07-04T14:40:27Z","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":"10209a34d0919ae6351395c8f3d3b2c6c3918350a54071c31f6f2013b0b93828","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"math.MG","submitted_at":"1998-02-05T00:00:00Z","title_canon_sha256":"1d37ee7b3821cc76dd38871752732ac0a87e92eda2a2a23fb47a789e8e4ba451"},"schema_version":"1.0","source":{"id":"math/9802128","kind":"arxiv","version":2}},"canonical_sha256":"be09f277521d385e5a8dcfa0e213cf9e222434cb1a5f051e7face52728a196cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be09f277521d385e5a8dcfa0e213cf9e222434cb1a5f051e7face52728a196cb","first_computed_at":"2026-07-04T14:40:27.994553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:40:27.994553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KBheGFHH8Y8Mhlf8qjhR8NSUkKRU+XPa+FqRwVbWw8lQDJyslqxFpa/o2kIYzjMl9CL/r97LGeXCDZYwRnoFBw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:40:27.994903Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9802128","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb31e6fa9b81d859bc612619c7609f8a2925d28f6d3907e27cb4da5878bb6b0d","sha256:efce8da3474f3ce00a9b9d868e0656645b5861b0e6481659e983b95929c29420"],"state_sha256":"0752579e9dd6779595300e377d891f2acad24c90439a953b3550855d19dbb3ca"}