{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UXOUEBD2IMPYNVDBGUSMOC2P3O","short_pith_number":"pith:UXOUEBD2","canonical_record":{"source":{"id":"2411.19163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-28T14:06:00Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"aa8eee6e370227842b14a725a4ab5415fc13ea02bcaaeaf063101bf68d2eff0f","abstract_canon_sha256":"acd299ebe8a945079461c74a2297ed5887572a21e190b0b5fe72b6d950084ef5"},"schema_version":"1.0"},"canonical_sha256":"a5dd42047a431f86d4613524c70b4fdb8802e693d67361377a97ba72e712c795","source":{"kind":"arxiv","id":"2411.19163","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.19163","created_at":"2026-07-05T09:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"2411.19163v1","created_at":"2026-07-05T09:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19163","created_at":"2026-07-05T09:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"UXOUEBD2IMPY","created_at":"2026-07-05T09:41:58Z"},{"alias_kind":"pith_short_16","alias_value":"UXOUEBD2IMPYNVDB","created_at":"2026-07-05T09:41:58Z"},{"alias_kind":"pith_short_8","alias_value":"UXOUEBD2","created_at":"2026-07-05T09:41:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UXOUEBD2IMPYNVDBGUSMOC2P3O","target":"record","payload":{"canonical_record":{"source":{"id":"2411.19163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-28T14:06:00Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"aa8eee6e370227842b14a725a4ab5415fc13ea02bcaaeaf063101bf68d2eff0f","abstract_canon_sha256":"acd299ebe8a945079461c74a2297ed5887572a21e190b0b5fe72b6d950084ef5"},"schema_version":"1.0"},"canonical_sha256":"a5dd42047a431f86d4613524c70b4fdb8802e693d67361377a97ba72e712c795","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:41:58.074264Z","signature_b64":"wdVq32HS0V5u4dgtwasFicWd8dRYPf6msz9WuiRolguXCoxUqYh2Nsvf71bk2TYatNZkfex54NXGVNi34n1LDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5dd42047a431f86d4613524c70b4fdb8802e693d67361377a97ba72e712c795","last_reissued_at":"2026-07-05T09:41:58.073776Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:41:58.073776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.19163","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UYa4dXgV5RAZ+qXg96rEGVslHrN2ID0rrcLsdNBKjH/ehaDR+76K05aY/rG8Q9e6e7cwUd2Fdpctdk4pC6SzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T12:46:26.797803Z"},"content_sha256":"ec975537cf8120a26b772c016ce756b7011d7252a5cec15ea59e1a386ff0e4b9","schema_version":"1.0","event_id":"sha256:ec975537cf8120a26b772c016ce756b7011d7252a5cec15ea59e1a386ff0e4b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UXOUEBD2IMPYNVDBGUSMOC2P3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random polytopes in convex bodies: Bridging the gap between extremal containers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Anna Gusakova, Christoph Th\\\"ale, Florian Besau","submitted_at":"2024-11-28T14:06:00Z","abstract_excerpt":"We investigate the asymptotic properties of random polytopes arising as convex hulls of $n$ independent random points sampled from a family of block-beta distributions. Notably, this family includes the uniform distribution on a product of Euclidean balls of varying dimensions as a key example. As $n\\to\\infty$, we establish explicit growth rates for the expected number of facets, which depend in a subtle way on the the underlying model parameters. For the case of the uniform distribution, we further examine the expected number of faces of arbitrary dimensions as well as the volume difference. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19163","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/2411.19163/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pEc7AO/A5EOW6TwORAfATWzngvi8Z5NQYs8gFk5S+z2ArPLOwC9TnucJJ0iVu7U8q8TbeDqLL5dRrETPGauoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T12:46:26.799156Z"},"content_sha256":"6e8bb9e6e6ce38eae3f80aca0de094ab96eb8b578a553d4039523d5c242b040e","schema_version":"1.0","event_id":"sha256:6e8bb9e6e6ce38eae3f80aca0de094ab96eb8b578a553d4039523d5c242b040e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXOUEBD2IMPYNVDBGUSMOC2P3O/bundle.json","state_url":"https://pith.science/pith/UXOUEBD2IMPYNVDBGUSMOC2P3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXOUEBD2IMPYNVDBGUSMOC2P3O/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":"2026-08-21T12:46:26Z","links":{"resolver":"https://pith.science/pith/UXOUEBD2IMPYNVDBGUSMOC2P3O","bundle":"https://pith.science/pith/UXOUEBD2IMPYNVDBGUSMOC2P3O/bundle.json","state":"https://pith.science/pith/UXOUEBD2IMPYNVDBGUSMOC2P3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXOUEBD2IMPYNVDBGUSMOC2P3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UXOUEBD2IMPYNVDBGUSMOC2P3O","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":"acd299ebe8a945079461c74a2297ed5887572a21e190b0b5fe72b6d950084ef5","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-28T14:06:00Z","title_canon_sha256":"aa8eee6e370227842b14a725a4ab5415fc13ea02bcaaeaf063101bf68d2eff0f"},"schema_version":"1.0","source":{"id":"2411.19163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.19163","created_at":"2026-07-05T09:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"2411.19163v1","created_at":"2026-07-05T09:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19163","created_at":"2026-07-05T09:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"UXOUEBD2IMPY","created_at":"2026-07-05T09:41:58Z"},{"alias_kind":"pith_short_16","alias_value":"UXOUEBD2IMPYNVDB","created_at":"2026-07-05T09:41:58Z"},{"alias_kind":"pith_short_8","alias_value":"UXOUEBD2","created_at":"2026-07-05T09:41:58Z"}],"graph_snapshots":[{"event_id":"sha256:6e8bb9e6e6ce38eae3f80aca0de094ab96eb8b578a553d4039523d5c242b040e","target":"graph","created_at":"2026-07-05T09:41:58Z","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/2411.19163/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the asymptotic properties of random polytopes arising as convex hulls of $n$ independent random points sampled from a family of block-beta distributions. Notably, this family includes the uniform distribution on a product of Euclidean balls of varying dimensions as a key example. As $n\\to\\infty$, we establish explicit growth rates for the expected number of facets, which depend in a subtle way on the the underlying model parameters. For the case of the uniform distribution, we further examine the expected number of faces of arbitrary dimensions as well as the volume difference. ","authors_text":"Anna Gusakova, Christoph Th\\\"ale, Florian Besau","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-28T14:06:00Z","title":"Random polytopes in convex bodies: Bridging the gap between extremal containers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19163","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:ec975537cf8120a26b772c016ce756b7011d7252a5cec15ea59e1a386ff0e4b9","target":"record","created_at":"2026-07-05T09:41:58Z","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":"acd299ebe8a945079461c74a2297ed5887572a21e190b0b5fe72b6d950084ef5","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-28T14:06:00Z","title_canon_sha256":"aa8eee6e370227842b14a725a4ab5415fc13ea02bcaaeaf063101bf68d2eff0f"},"schema_version":"1.0","source":{"id":"2411.19163","kind":"arxiv","version":1}},"canonical_sha256":"a5dd42047a431f86d4613524c70b4fdb8802e693d67361377a97ba72e712c795","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5dd42047a431f86d4613524c70b4fdb8802e693d67361377a97ba72e712c795","first_computed_at":"2026-07-05T09:41:58.073776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:58.073776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wdVq32HS0V5u4dgtwasFicWd8dRYPf6msz9WuiRolguXCoxUqYh2Nsvf71bk2TYatNZkfex54NXGVNi34n1LDA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:58.074264Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.19163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec975537cf8120a26b772c016ce756b7011d7252a5cec15ea59e1a386ff0e4b9","sha256:6e8bb9e6e6ce38eae3f80aca0de094ab96eb8b578a553d4039523d5c242b040e"],"state_sha256":"bcbb0cbabb1112cacd0d9fc555a443f2aff148893bdf25979c8a8ab0f84693cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4kmSbu/Qma1QxWKXMCpu4rSoR3Hbq887U7X3TzF66ZZROp1q6ow2w9GTQNVl31aOg6rNkk+zWNGTos9FTGKRDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T12:46:26.811881Z","bundle_sha256":"bf7cb69a5c6d3eeb928d7cf99244176eac40eb985260ca54a55b686d50da0238"}}