{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:F3KWTLDEIXKNTBVP575CZU7PWB","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":"176e941022b7c49417897f916d325ba808d5036dcd67d26fd658c5410eab518b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2026-05-20T07:29:36Z","title_canon_sha256":"2100a326a9708257be63dfa916163feeef2db946255b28a380eda9a462622ef0"},"schema_version":"1.0","source":{"id":"2605.20840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20840","created_at":"2026-05-21T01:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20840v1","created_at":"2026-05-21T01:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20840","created_at":"2026-05-21T01:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"F3KWTLDEIXKN","created_at":"2026-05-21T01:05:24Z"},{"alias_kind":"pith_short_16","alias_value":"F3KWTLDEIXKNTBVP","created_at":"2026-05-21T01:05:24Z"},{"alias_kind":"pith_short_8","alias_value":"F3KWTLDE","created_at":"2026-05-21T01:05:24Z"}],"graph_snapshots":[{"event_id":"sha256:2651f4968d68d21f35774f963a879913018cccccc8bff8c58ba0ee9c6f5899da","target":"graph","created_at":"2026-05-21T01:05:24Z","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/2605.20840/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a classical paper [20] in 2000, Lutwak-Yang-Zhang established the $L^p$ analog of the Petty projection inequality and the $L^p$ analog of the Busemann-Petty centroid inequality. In Section 7 of [20], Lutwak-Yang-Zhang proposed the important $L^p$ projection centroid conjecture. We give a positive solution to the $L^p$ projection centroid conjecture in this work.","authors_text":"Jin Dai, Tuo Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2026-05-20T07:29:36Z","title":"A positive solution to the $L^p$ projection centroid conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20840","kind":"arxiv","version":1},"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":"sha256:268643ab265f347a8c0fb5352e8b77a4706c69d2550d90bd3bd5c8c35299a578","target":"record","created_at":"2026-05-21T01:05:24Z","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":"176e941022b7c49417897f916d325ba808d5036dcd67d26fd658c5410eab518b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2026-05-20T07:29:36Z","title_canon_sha256":"2100a326a9708257be63dfa916163feeef2db946255b28a380eda9a462622ef0"},"schema_version":"1.0","source":{"id":"2605.20840","kind":"arxiv","version":1}},"canonical_sha256":"2ed569ac6445d4d986afeffa2cd3efb05a1dfbdca246012ee41d1a3c503d58b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ed569ac6445d4d986afeffa2cd3efb05a1dfbdca246012ee41d1a3c503d58b2","first_computed_at":"2026-05-21T01:05:24.065928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:24.065928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"35dki6UHdfIoxvRIPAv8sTNcQG/kdlx17lNUHtUHjMAAxPr54g+56k6A9EESqLGu7pW5Z2pyu1QXDYc4MqjfAA==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:24.066667Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:268643ab265f347a8c0fb5352e8b77a4706c69d2550d90bd3bd5c8c35299a578","sha256:2651f4968d68d21f35774f963a879913018cccccc8bff8c58ba0ee9c6f5899da"],"state_sha256":"11c25382579460b9018a3b94ea4050c3c02df843184ca9a342c909922d452226"}