{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:FHNOPWU56YR6X6UYCSI7E5TVB6","short_pith_number":"pith:FHNOPWU5","canonical_record":{"source":{"id":"math/0410001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2004-09-30T20:14:50Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"6ea2efdc068cc961c07ee37a6096c171acd53235585e482aa0a07576da4c964b","abstract_canon_sha256":"4ac34d37d13d579ec3b5228cd62091cf352500e95c40aa25523cc53e145e7d8b"},"schema_version":"1.0"},"canonical_sha256":"29dae7da9df623ebfa981491f276750f8bbcbf6722418ed6179f52615e09b24a","source":{"kind":"arxiv","id":"math/0410001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0410001","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0410001v1","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0410001","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"FHNOPWU56YR6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"FHNOPWU56YR6X6UY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"FHNOPWU5","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:FHNOPWU56YR6X6UYCSI7E5TVB6","target":"record","payload":{"canonical_record":{"source":{"id":"math/0410001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2004-09-30T20:14:50Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"6ea2efdc068cc961c07ee37a6096c171acd53235585e482aa0a07576da4c964b","abstract_canon_sha256":"4ac34d37d13d579ec3b5228cd62091cf352500e95c40aa25523cc53e145e7d8b"},"schema_version":"1.0"},"canonical_sha256":"29dae7da9df623ebfa981491f276750f8bbcbf6722418ed6179f52615e09b24a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:09.281136Z","signature_b64":"BkZK3Jym+c7k8YoXpz3NdjFsAXPrILVtOhfR46R5WIs4PQUjIrk1FCRDJyK+5KTGnmVw/NN5U3VKTJ2H3gIWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29dae7da9df623ebfa981491f276750f8bbcbf6722418ed6179f52615e09b24a","last_reissued_at":"2026-05-18T00:54:09.280604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:09.280604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0410001","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":"2026-05-18T00:54:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U3NG0+bTnvWA3n7jw/jnw390ehAvoGoFShpjoqGyegC8NhZaUx67dIWgMODSEyL4248Ti/tMn8IUQC3a5tNRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:52:20.760173Z"},"content_sha256":"483888be6e91493b55a6d8d1af80efc352a1f7bf57bb5a3b2c1f5ec52fc3c5e4","schema_version":"1.0","event_id":"sha256:483888be6e91493b55a6d8d1af80efc352a1f7bf57bb5a3b2c1f5ec52fc3c5e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:FHNOPWU56YR6X6UYCSI7E5TVB6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small ball probability and Dvoretzky theorem","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Bo'az Klartag, Roman Vershynin","submitted_at":"2004-09-30T20:14:50Z","abstract_excerpt":"Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, contrary to small deviationresults. In this note we present a novel application of a smalldeviations inequality to a problem related to the diameters of random sections of high dimensional convex bodies. Our results imply an unexpected distinction between the lower and the upper inclusions in Dvoretzky Theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410001","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":"2026-05-18T00:54:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2I8uGmz6XVYwGUPZQZz4LHYPQ+gztJvCsHqGxLWjCiq3ei0VDK3/ZvlTiPDCCrzpFFEoP0G0vYrf25kHJZ8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:52:20.760554Z"},"content_sha256":"b81700131845950c13e7c432a6f3596732af0df65f2c737a5f6d065c4dbc55d0","schema_version":"1.0","event_id":"sha256:b81700131845950c13e7c432a6f3596732af0df65f2c737a5f6d065c4dbc55d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHNOPWU56YR6X6UYCSI7E5TVB6/bundle.json","state_url":"https://pith.science/pith/FHNOPWU56YR6X6UYCSI7E5TVB6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHNOPWU56YR6X6UYCSI7E5TVB6/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":"2026-06-03T02:52:20Z","links":{"resolver":"https://pith.science/pith/FHNOPWU56YR6X6UYCSI7E5TVB6","bundle":"https://pith.science/pith/FHNOPWU56YR6X6UYCSI7E5TVB6/bundle.json","state":"https://pith.science/pith/FHNOPWU56YR6X6UYCSI7E5TVB6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHNOPWU56YR6X6UYCSI7E5TVB6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:FHNOPWU56YR6X6UYCSI7E5TVB6","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":"4ac34d37d13d579ec3b5228cd62091cf352500e95c40aa25523cc53e145e7d8b","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.FA","submitted_at":"2004-09-30T20:14:50Z","title_canon_sha256":"6ea2efdc068cc961c07ee37a6096c171acd53235585e482aa0a07576da4c964b"},"schema_version":"1.0","source":{"id":"math/0410001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0410001","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0410001v1","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0410001","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"FHNOPWU56YR6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"FHNOPWU56YR6X6UY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"FHNOPWU5","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:b81700131845950c13e7c432a6f3596732af0df65f2c737a5f6d065c4dbc55d0","target":"graph","created_at":"2026-05-18T00:54:09Z","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":"Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, contrary to small deviationresults. In this note we present a novel application of a smalldeviations inequality to a problem related to the diameters of random sections of high dimensional convex bodies. Our results imply an unexpected distinction between the lower and the upper inclusions in Dvoretzky Theorem.","authors_text":"Bo'az Klartag, Roman Vershynin","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2004-09-30T20:14:50Z","title":"Small ball probability and Dvoretzky theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410001","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":"sha256:483888be6e91493b55a6d8d1af80efc352a1f7bf57bb5a3b2c1f5ec52fc3c5e4","target":"record","created_at":"2026-05-18T00:54:09Z","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":"4ac34d37d13d579ec3b5228cd62091cf352500e95c40aa25523cc53e145e7d8b","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.FA","submitted_at":"2004-09-30T20:14:50Z","title_canon_sha256":"6ea2efdc068cc961c07ee37a6096c171acd53235585e482aa0a07576da4c964b"},"schema_version":"1.0","source":{"id":"math/0410001","kind":"arxiv","version":1}},"canonical_sha256":"29dae7da9df623ebfa981491f276750f8bbcbf6722418ed6179f52615e09b24a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29dae7da9df623ebfa981491f276750f8bbcbf6722418ed6179f52615e09b24a","first_computed_at":"2026-05-18T00:54:09.280604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:09.280604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BkZK3Jym+c7k8YoXpz3NdjFsAXPrILVtOhfR46R5WIs4PQUjIrk1FCRDJyK+5KTGnmVw/NN5U3VKTJ2H3gIWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:09.281136Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0410001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:483888be6e91493b55a6d8d1af80efc352a1f7bf57bb5a3b2c1f5ec52fc3c5e4","sha256:b81700131845950c13e7c432a6f3596732af0df65f2c737a5f6d065c4dbc55d0"],"state_sha256":"2360af35a7d0e5cea0d6a98fb36ace405d2c3822ff48c88a19e7d681a0ba2932"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B9q32Ax5L6RCA6z3vHAkj4SKblPqsBINJzscTlZrK5GXBgYpBq/8RkXSJqFW04ukNDo3TBj0a2JJUZ39BbyQDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:52:20.762465Z","bundle_sha256":"ea1324b97d0ac8ca34ba25ce23aa48007b20e183bfc1bce2ab7304c77aad2b96"}}