{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DWFHKYWYZBZVPXYAL3DZXBO22V","short_pith_number":"pith:DWFHKYWY","canonical_record":{"source":{"id":"1110.2842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-13T04:56:17Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"67e4336476bb3a6eb03371804f8d40dc8eed9d82cf5c32ae6476fa8dd153bb8c","abstract_canon_sha256":"9f5f1a61efe7ddfa74a65fcd310495c6771e8036b40f3dde961fb92cbcb962fb"},"schema_version":"1.0"},"canonical_sha256":"1d8a7562d8c87357df005ec79b85dad57a363b74636388efd596e2bd8c0aa7cb","source":{"kind":"arxiv","id":"1110.2842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2842","created_at":"2026-05-18T04:11:06Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2842v1","created_at":"2026-05-18T04:11:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2842","created_at":"2026-05-18T04:11:06Z"},{"alias_kind":"pith_short_12","alias_value":"DWFHKYWYZBZV","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DWFHKYWYZBZVPXYA","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DWFHKYWY","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DWFHKYWYZBZVPXYAL3DZXBO22V","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-13T04:56:17Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"67e4336476bb3a6eb03371804f8d40dc8eed9d82cf5c32ae6476fa8dd153bb8c","abstract_canon_sha256":"9f5f1a61efe7ddfa74a65fcd310495c6771e8036b40f3dde961fb92cbcb962fb"},"schema_version":"1.0"},"canonical_sha256":"1d8a7562d8c87357df005ec79b85dad57a363b74636388efd596e2bd8c0aa7cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:06.860373Z","signature_b64":"o1eaGbwu5tvkyZxe7XsTEcjtsc1ATUmkXw2LfRusUzgsBSH61d90jDQLFNB4/O/BED1fUHb2Bnp3Spvzz3vQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d8a7562d8c87357df005ec79b85dad57a363b74636388efd596e2bd8c0aa7cb","last_reissued_at":"2026-05-18T04:11:06.859816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:06.859816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2842","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":"2026-05-18T04:11:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"St/XksCEGJ0taLicSxazQMzjXPEXH9UypFfbs/lBqdnt+2JJXJ1S9OmZbyGYNvyQRr9wPmJYWiG0jNoBkYwmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:43:01.312391Z"},"content_sha256":"9c1ec152046143838a6c1f7f5e53f1c26d6005be9712cd2fe1a679849a55f01b","schema_version":"1.0","event_id":"sha256:9c1ec152046143838a6c1f7f5e53f1c26d6005be9712cd2fe1a679849a55f01b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DWFHKYWYZBZVPXYAL3DZXBO22V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A tail inequality for quadratic forms of subgaussian random vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.PR","authors_text":"Daniel Hsu, Sham M. Kakade, Tong Zhang","submitted_at":"2011-10-13T04:56:17Z","abstract_excerpt":"We prove an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2842","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":"2026-05-18T04:11:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hiIflkE0F3eUGb+67Zzfu7PIkNa1kqdJV4qv3oNufiJpl7n3lSR0DKHTYgvWI1gEBkKLs1tHBsCz0On+ckjDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:43:01.313095Z"},"content_sha256":"225baaca641e5a1fe87eef5104868aa18a2376d2b92836bb19f68d335f55aceb","schema_version":"1.0","event_id":"sha256:225baaca641e5a1fe87eef5104868aa18a2376d2b92836bb19f68d335f55aceb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DWFHKYWYZBZVPXYAL3DZXBO22V/bundle.json","state_url":"https://pith.science/pith/DWFHKYWYZBZVPXYAL3DZXBO22V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DWFHKYWYZBZVPXYAL3DZXBO22V/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":"2026-05-25T13:43:01Z","links":{"resolver":"https://pith.science/pith/DWFHKYWYZBZVPXYAL3DZXBO22V","bundle":"https://pith.science/pith/DWFHKYWYZBZVPXYAL3DZXBO22V/bundle.json","state":"https://pith.science/pith/DWFHKYWYZBZVPXYAL3DZXBO22V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DWFHKYWYZBZVPXYAL3DZXBO22V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DWFHKYWYZBZVPXYAL3DZXBO22V","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":"9f5f1a61efe7ddfa74a65fcd310495c6771e8036b40f3dde961fb92cbcb962fb","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-13T04:56:17Z","title_canon_sha256":"67e4336476bb3a6eb03371804f8d40dc8eed9d82cf5c32ae6476fa8dd153bb8c"},"schema_version":"1.0","source":{"id":"1110.2842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2842","created_at":"2026-05-18T04:11:06Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2842v1","created_at":"2026-05-18T04:11:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2842","created_at":"2026-05-18T04:11:06Z"},{"alias_kind":"pith_short_12","alias_value":"DWFHKYWYZBZV","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DWFHKYWYZBZVPXYA","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DWFHKYWY","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:225baaca641e5a1fe87eef5104868aa18a2376d2b92836bb19f68d335f55aceb","target":"graph","created_at":"2026-05-18T04:11:06Z","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 prove an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries.","authors_text":"Daniel Hsu, Sham M. Kakade, Tong Zhang","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-13T04:56:17Z","title":"A tail inequality for quadratic forms of subgaussian random vectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2842","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":"sha256:9c1ec152046143838a6c1f7f5e53f1c26d6005be9712cd2fe1a679849a55f01b","target":"record","created_at":"2026-05-18T04:11:06Z","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":"9f5f1a61efe7ddfa74a65fcd310495c6771e8036b40f3dde961fb92cbcb962fb","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-13T04:56:17Z","title_canon_sha256":"67e4336476bb3a6eb03371804f8d40dc8eed9d82cf5c32ae6476fa8dd153bb8c"},"schema_version":"1.0","source":{"id":"1110.2842","kind":"arxiv","version":1}},"canonical_sha256":"1d8a7562d8c87357df005ec79b85dad57a363b74636388efd596e2bd8c0aa7cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d8a7562d8c87357df005ec79b85dad57a363b74636388efd596e2bd8c0aa7cb","first_computed_at":"2026-05-18T04:11:06.859816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:06.859816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o1eaGbwu5tvkyZxe7XsTEcjtsc1ATUmkXw2LfRusUzgsBSH61d90jDQLFNB4/O/BED1fUHb2Bnp3Spvzz3vQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:06.860373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c1ec152046143838a6c1f7f5e53f1c26d6005be9712cd2fe1a679849a55f01b","sha256:225baaca641e5a1fe87eef5104868aa18a2376d2b92836bb19f68d335f55aceb"],"state_sha256":"16ff0a1e49a2e1dbd3293b7bea90224191bce11443c5aacf4d34a99d7a8aee34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4OcapyM3fvLkJET7GV+X6Lo/xAgwnSV+yi6XkWx4C5bJ2P+E9kdhCC7Q/tCXnDjBo97mm7P92EoUrI0rNkHBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T13:43:01.317148Z","bundle_sha256":"36806b5ff72bb07ba8552f03b17e0fd637d7bd1688c8fade8ca8377c13f36576"}}