{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2UMJDQHGR5VDNALGLI7I7MPW7N","short_pith_number":"pith:2UMJDQHG","canonical_record":{"source":{"id":"1403.5928","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-03-24T12:10:23Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"72442e1d3716e204eb3251e678f8352591e0ac71c2c2b498d675538c09c3b4f0","abstract_canon_sha256":"4f7eb9be4e418e8178da370a20c97a4a3a00f14869782d19d6c2e0a44e3ed3a6"},"schema_version":"1.0"},"canonical_sha256":"d51891c0e68f6a3681665a3e8fb1f6fb7e560e8c7cfe9fdbbdb70219b9106f22","source":{"kind":"arxiv","id":"1403.5928","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5928","created_at":"2026-05-18T02:55:03Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5928v3","created_at":"2026-05-18T02:55:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5928","created_at":"2026-05-18T02:55:03Z"},{"alias_kind":"pith_short_12","alias_value":"2UMJDQHGR5VD","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2UMJDQHGR5VDNALG","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2UMJDQHG","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2UMJDQHGR5VDNALGLI7I7MPW7N","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5928","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-03-24T12:10:23Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"72442e1d3716e204eb3251e678f8352591e0ac71c2c2b498d675538c09c3b4f0","abstract_canon_sha256":"4f7eb9be4e418e8178da370a20c97a4a3a00f14869782d19d6c2e0a44e3ed3a6"},"schema_version":"1.0"},"canonical_sha256":"d51891c0e68f6a3681665a3e8fb1f6fb7e560e8c7cfe9fdbbdb70219b9106f22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:03.563029Z","signature_b64":"6ZqXO27CPddJIffK/dDU2HS6DXkKh4LuQA/hBKRQ3gedhbMBMSRx7vitIBwSA058fQ5CwCX8yMQQBcr8MFoqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d51891c0e68f6a3681665a3e8fb1f6fb7e560e8c7cfe9fdbbdb70219b9106f22","last_reissued_at":"2026-05-18T02:55:03.561865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:03.561865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5928","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:55:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4aS98WbvFBpXZIqAhzD0W6fImNa/ppNm2T6JiSGp6U+B81YjdCw0QhUHvrh2QAHGkzhgI2AR+uJgs5JhRhoSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:24:33.758057Z"},"content_sha256":"057e73f1cb593fce0bef5e765a032932cc46f1afad166ef5ec279c044b69cb5a","schema_version":"1.0","event_id":"sha256:057e73f1cb593fce0bef5e765a032932cc46f1afad166ef5ec279c044b69cb5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2UMJDQHGR5VDNALGLI7I7MPW7N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Viewing the Welch bound inequality from the kernel trick viewpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Liang Dai","submitted_at":"2014-03-24T12:10:23Z","abstract_excerpt":"This brief note views to the Welch bound inequality using the idea of the kernel trick from the machine learning research area. From this angle, some novel insights of the inequality are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5928","kind":"arxiv","version":3},"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":"2026-05-18T02:55:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"POI7sPU4qQTCaaYXPYeHrhQRq62cZpW+ChcdE/h/F2jjoz2DSQ8PV7bs+rhd2yJsbbCwVcVn1dxS10Y5plj8Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:24:33.758411Z"},"content_sha256":"387775b810e4a8d72150078ba3e3bfc4bc9169279eeaadfe9daa4cddc0e7af20","schema_version":"1.0","event_id":"sha256:387775b810e4a8d72150078ba3e3bfc4bc9169279eeaadfe9daa4cddc0e7af20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2UMJDQHGR5VDNALGLI7I7MPW7N/bundle.json","state_url":"https://pith.science/pith/2UMJDQHGR5VDNALGLI7I7MPW7N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2UMJDQHGR5VDNALGLI7I7MPW7N/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":"2026-05-28T10:24:33Z","links":{"resolver":"https://pith.science/pith/2UMJDQHGR5VDNALGLI7I7MPW7N","bundle":"https://pith.science/pith/2UMJDQHGR5VDNALGLI7I7MPW7N/bundle.json","state":"https://pith.science/pith/2UMJDQHGR5VDNALGLI7I7MPW7N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2UMJDQHGR5VDNALGLI7I7MPW7N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2UMJDQHGR5VDNALGLI7I7MPW7N","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":"4f7eb9be4e418e8178da370a20c97a4a3a00f14869782d19d6c2e0a44e3ed3a6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-03-24T12:10:23Z","title_canon_sha256":"72442e1d3716e204eb3251e678f8352591e0ac71c2c2b498d675538c09c3b4f0"},"schema_version":"1.0","source":{"id":"1403.5928","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5928","created_at":"2026-05-18T02:55:03Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5928v3","created_at":"2026-05-18T02:55:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5928","created_at":"2026-05-18T02:55:03Z"},{"alias_kind":"pith_short_12","alias_value":"2UMJDQHGR5VD","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2UMJDQHGR5VDNALG","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2UMJDQHG","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:387775b810e4a8d72150078ba3e3bfc4bc9169279eeaadfe9daa4cddc0e7af20","target":"graph","created_at":"2026-05-18T02:55:03Z","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":"This brief note views to the Welch bound inequality using the idea of the kernel trick from the machine learning research area. From this angle, some novel insights of the inequality are obtained.","authors_text":"Liang Dai","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-03-24T12:10:23Z","title":"Viewing the Welch bound inequality from the kernel trick viewpoint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5928","kind":"arxiv","version":3},"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":"sha256:057e73f1cb593fce0bef5e765a032932cc46f1afad166ef5ec279c044b69cb5a","target":"record","created_at":"2026-05-18T02:55:03Z","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":"4f7eb9be4e418e8178da370a20c97a4a3a00f14869782d19d6c2e0a44e3ed3a6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-03-24T12:10:23Z","title_canon_sha256":"72442e1d3716e204eb3251e678f8352591e0ac71c2c2b498d675538c09c3b4f0"},"schema_version":"1.0","source":{"id":"1403.5928","kind":"arxiv","version":3}},"canonical_sha256":"d51891c0e68f6a3681665a3e8fb1f6fb7e560e8c7cfe9fdbbdb70219b9106f22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d51891c0e68f6a3681665a3e8fb1f6fb7e560e8c7cfe9fdbbdb70219b9106f22","first_computed_at":"2026-05-18T02:55:03.561865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:03.561865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6ZqXO27CPddJIffK/dDU2HS6DXkKh4LuQA/hBKRQ3gedhbMBMSRx7vitIBwSA058fQ5CwCX8yMQQBcr8MFoqAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:03.563029Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5928","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:057e73f1cb593fce0bef5e765a032932cc46f1afad166ef5ec279c044b69cb5a","sha256:387775b810e4a8d72150078ba3e3bfc4bc9169279eeaadfe9daa4cddc0e7af20"],"state_sha256":"579cc0226eb4ae023b304d3819f788ed6d0ebd522e2dc0f51dd0c12f020f9f9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBVhu4/qJ97ixH7pdMHsrzIIM1dSMv5adaQz9SPq+vZWjCkUNix2eDXdmJcTZ8A172SD2GyMacIP1Fv4U0veDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:24:33.760384Z","bundle_sha256":"e2d423b1c6fef4131cca824c2da8bc83fdf58aae891fb788a0fc4903e1a05a5c"}}