{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BUIZUN7S6FUNIB5RMOU7YRAWP7","short_pith_number":"pith:BUIZUN7S","canonical_record":{"source":{"id":"1205.6174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-28T18:13:14Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"32636841b35fa225550430fff5f43ca3e9d63f63880663a5b1a2ab6387aa519b","abstract_canon_sha256":"a783e970d8e280b789aafc9a000221b5eeb16f6a4f92b5949f7412eac845e274"},"schema_version":"1.0"},"canonical_sha256":"0d119a37f2f168d407b163a9fc44167fd387fa03bb575ab86b938d6766ac175f","source":{"kind":"arxiv","id":"1205.6174","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6174","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6174v1","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6174","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"BUIZUN7S6FUN","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BUIZUN7S6FUNIB5R","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BUIZUN7S","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BUIZUN7S6FUNIB5RMOU7YRAWP7","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-28T18:13:14Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"32636841b35fa225550430fff5f43ca3e9d63f63880663a5b1a2ab6387aa519b","abstract_canon_sha256":"a783e970d8e280b789aafc9a000221b5eeb16f6a4f92b5949f7412eac845e274"},"schema_version":"1.0"},"canonical_sha256":"0d119a37f2f168d407b163a9fc44167fd387fa03bb575ab86b938d6766ac175f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:48.198137Z","signature_b64":"w9KpZRsB9hEgKaMukwVbnS3PlWyXWAYgO9yR6XJ2dxlPsRteIg4JiX99wCak97rOeYaPCVrSGfQ53WyFPMkaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d119a37f2f168d407b163a9fc44167fd387fa03bb575ab86b938d6766ac175f","last_reissued_at":"2026-05-18T03:54:48.197520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:48.197520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6174","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":"2026-05-18T03:54:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"986FQacUXZTUknlfeURCOcktDqImUzvVAvy9hjxpKxb4AgyFcKVCXS7z/i1tJ5u6LueKZqtWofEDsJyUGjoVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:37:34.470488Z"},"content_sha256":"27a24c3619ccfa2939d3f1134e7f05c947d51aea27b31cc133582b0fb6d03744","schema_version":"1.0","event_id":"sha256:27a24c3619ccfa2939d3f1134e7f05c947d51aea27b31cc133582b0fb6d03744"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BUIZUN7S6FUNIB5RMOU7YRAWP7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Gaussian behavior of marginals and the mean width of random polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"David Alonso-Gutierrez, Joscha Prochno","submitted_at":"2012-05-28T18:13:14Z","abstract_excerpt":"We show that the expected value of the mean width of a random polytope generated by $N$ random vectors ($n\\leq N\\leq e^{\\sqrt n}$) uniformly distributed in an isotropic convex body in $\\R^n$ is of the order $\\sqrt{\\log N} L_K$. This completes a result of Dafnis, Giannopoulos and Tsolomitis. We also prove some results in connection with the 1-dimensional marginals of the uniform probability measure on an isotropic convex body, extending the interval in which the average of the distribution functions of those marginals behaves in a sub- or supergaussian way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6174","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":""},"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":"2026-05-18T03:54:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QJf8cFziP1R8mDnF17vdYqp1/kobhilHgKYJn13yC8XnanBAC8Pawrj8Q6xaHXK81WZEE3UcDeu0MoLQgwRuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:37:34.471109Z"},"content_sha256":"d2fbc3e8d77858bbe6b46bab54f7da643f3ccd0f66c2cbfec8ed21b801e3b58e","schema_version":"1.0","event_id":"sha256:d2fbc3e8d77858bbe6b46bab54f7da643f3ccd0f66c2cbfec8ed21b801e3b58e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BUIZUN7S6FUNIB5RMOU7YRAWP7/bundle.json","state_url":"https://pith.science/pith/BUIZUN7S6FUNIB5RMOU7YRAWP7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BUIZUN7S6FUNIB5RMOU7YRAWP7/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":"2026-05-30T15:37:34Z","links":{"resolver":"https://pith.science/pith/BUIZUN7S6FUNIB5RMOU7YRAWP7","bundle":"https://pith.science/pith/BUIZUN7S6FUNIB5RMOU7YRAWP7/bundle.json","state":"https://pith.science/pith/BUIZUN7S6FUNIB5RMOU7YRAWP7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BUIZUN7S6FUNIB5RMOU7YRAWP7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BUIZUN7S6FUNIB5RMOU7YRAWP7","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":"a783e970d8e280b789aafc9a000221b5eeb16f6a4f92b5949f7412eac845e274","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-28T18:13:14Z","title_canon_sha256":"32636841b35fa225550430fff5f43ca3e9d63f63880663a5b1a2ab6387aa519b"},"schema_version":"1.0","source":{"id":"1205.6174","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6174","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6174v1","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6174","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"BUIZUN7S6FUN","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BUIZUN7S6FUNIB5R","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BUIZUN7S","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:d2fbc3e8d77858bbe6b46bab54f7da643f3ccd0f66c2cbfec8ed21b801e3b58e","target":"graph","created_at":"2026-05-18T03:54:48Z","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":"We show that the expected value of the mean width of a random polytope generated by $N$ random vectors ($n\\leq N\\leq e^{\\sqrt n}$) uniformly distributed in an isotropic convex body in $\\R^n$ is of the order $\\sqrt{\\log N} L_K$. This completes a result of Dafnis, Giannopoulos and Tsolomitis. We also prove some results in connection with the 1-dimensional marginals of the uniform probability measure on an isotropic convex body, extending the interval in which the average of the distribution functions of those marginals behaves in a sub- or supergaussian way.","authors_text":"David Alonso-Gutierrez, Joscha Prochno","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-28T18:13:14Z","title":"On the Gaussian behavior of marginals and the mean width of random polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6174","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":"sha256:27a24c3619ccfa2939d3f1134e7f05c947d51aea27b31cc133582b0fb6d03744","target":"record","created_at":"2026-05-18T03:54:48Z","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":"a783e970d8e280b789aafc9a000221b5eeb16f6a4f92b5949f7412eac845e274","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-28T18:13:14Z","title_canon_sha256":"32636841b35fa225550430fff5f43ca3e9d63f63880663a5b1a2ab6387aa519b"},"schema_version":"1.0","source":{"id":"1205.6174","kind":"arxiv","version":1}},"canonical_sha256":"0d119a37f2f168d407b163a9fc44167fd387fa03bb575ab86b938d6766ac175f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d119a37f2f168d407b163a9fc44167fd387fa03bb575ab86b938d6766ac175f","first_computed_at":"2026-05-18T03:54:48.197520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:48.197520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w9KpZRsB9hEgKaMukwVbnS3PlWyXWAYgO9yR6XJ2dxlPsRteIg4JiX99wCak97rOeYaPCVrSGfQ53WyFPMkaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:48.198137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6174","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27a24c3619ccfa2939d3f1134e7f05c947d51aea27b31cc133582b0fb6d03744","sha256:d2fbc3e8d77858bbe6b46bab54f7da643f3ccd0f66c2cbfec8ed21b801e3b58e"],"state_sha256":"0269159ecad8e3f532edaa0a87a53a423fd03a343ba5aa8b27cebdf078bfd08f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9crnNlH099YSZlC4Z3HxGlZu9hCYv1MChkUkarYI4PFAspbBK4Mmn7KR6tG58ICbfr6DNtEdrgg8b9V0w2gAAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:37:34.475092Z","bundle_sha256":"ec1719d80da883c820aa93566f144934f3360f34d7746d9c531ca4c72306e6a0"}}