{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4T6NVMB2C5UII5TZBNU7XTQN26","short_pith_number":"pith:4T6NVMB2","canonical_record":{"source":{"id":"1706.08360","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-26T13:27:34Z","cross_cats_sorted":[],"title_canon_sha256":"ecc413d616fb9f65c41a7cd17ef469d7031d4d53b8d7cbe1fdd81bd9b6c3633f","abstract_canon_sha256":"04e113f81611ddb30164346a8a4338954982cbefe314befb80fbc12c4ef5eb30"},"schema_version":"1.0"},"canonical_sha256":"e4fcdab03a17688476790b69fbce0dd7a1a980471fdabbf142f52c42b72d1dfe","source":{"kind":"arxiv","id":"1706.08360","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08360","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08360v2","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08360","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"4T6NVMB2C5UI","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4T6NVMB2C5UII5TZ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4T6NVMB2","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4T6NVMB2C5UII5TZBNU7XTQN26","target":"record","payload":{"canonical_record":{"source":{"id":"1706.08360","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-26T13:27:34Z","cross_cats_sorted":[],"title_canon_sha256":"ecc413d616fb9f65c41a7cd17ef469d7031d4d53b8d7cbe1fdd81bd9b6c3633f","abstract_canon_sha256":"04e113f81611ddb30164346a8a4338954982cbefe314befb80fbc12c4ef5eb30"},"schema_version":"1.0"},"canonical_sha256":"e4fcdab03a17688476790b69fbce0dd7a1a980471fdabbf142f52c42b72d1dfe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:28.918199Z","signature_b64":"z0avrtmC/PrraRZ8553CbVb49A3WN2ES6Fuq7yp4PtCMGkmPnk9mMlE47hRf/YZNqC8ybQ+O6ygPmK8GVNxLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4fcdab03a17688476790b69fbce0dd7a1a980471fdabbf142f52c42b72d1dfe","last_reissued_at":"2026-05-18T00:14:28.917454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:28.917454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.08360","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WAi1HNQHT6EuDnj0aAnhTZGfvAdn1z+gPnL60ZphhGKb+8CJwx/uAJotmvH63kXFxWTwpbDIgJ0Ox6mVN6+cAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:21:59.317678Z"},"content_sha256":"771461af9c73ec5bcbd7fc867fe2d9b67a0b47183f390b50fbc14e311ff19170","schema_version":"1.0","event_id":"sha256:771461af9c73ec5bcbd7fc867fe2d9b67a0b47183f390b50fbc14e311ff19170"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4T6NVMB2C5UII5TZBNU7XTQN26","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremes of $L^p$-norm of Vector-valued Gaussian processes with Trend","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Long Bai","submitted_at":"2017-06-26T13:27:34Z","abstract_excerpt":"Let $\\boldsymbol{X}(t)=(X_1(t),\\ldots,X_d(t))$ be a Gaussian vector process and $g(t)$ be a continuous function. The asymptotics of distribution of $\\left\\|\\boldsymbol{X}(t)\\right\\|_p$, the $L^p$ norm for Gaussian finite-dimensional vector, have been investigated in numerous literatures. In this contribution we are concerned with the exact tail asymptotics of $\\left\\|\\boldsymbol{X}(t)\\right\\|^c_p,\\ c>0, $ with trend $g(t)$ over $[0,T]$. Both scenarios that $\\boldsymbol{X}(t)$ is locally stationary and non-stationary are considered. Important examples include $\\sum_{i=1}^d \\left|X_i(t)\\right|+g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08360","kind":"arxiv","version":2},"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":"2026-05-18T00:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8RIKQD2Tqi1+HjyP1TlAQLHP5i99eYW19XVNiM4uaP+xv6xpS9qffpi1zoc8ddfG/yQ1LIKS3awJkId2N1UTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:21:59.318011Z"},"content_sha256":"7a8bc51ac09e2621d83d5b395eb7dea519d6dfffd2dd330124efda4d35a6d98c","schema_version":"1.0","event_id":"sha256:7a8bc51ac09e2621d83d5b395eb7dea519d6dfffd2dd330124efda4d35a6d98c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4T6NVMB2C5UII5TZBNU7XTQN26/bundle.json","state_url":"https://pith.science/pith/4T6NVMB2C5UII5TZBNU7XTQN26/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4T6NVMB2C5UII5TZBNU7XTQN26/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":"2026-06-03T01:21:59Z","links":{"resolver":"https://pith.science/pith/4T6NVMB2C5UII5TZBNU7XTQN26","bundle":"https://pith.science/pith/4T6NVMB2C5UII5TZBNU7XTQN26/bundle.json","state":"https://pith.science/pith/4T6NVMB2C5UII5TZBNU7XTQN26/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4T6NVMB2C5UII5TZBNU7XTQN26/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4T6NVMB2C5UII5TZBNU7XTQN26","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":"04e113f81611ddb30164346a8a4338954982cbefe314befb80fbc12c4ef5eb30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-26T13:27:34Z","title_canon_sha256":"ecc413d616fb9f65c41a7cd17ef469d7031d4d53b8d7cbe1fdd81bd9b6c3633f"},"schema_version":"1.0","source":{"id":"1706.08360","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08360","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08360v2","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08360","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"4T6NVMB2C5UI","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4T6NVMB2C5UII5TZ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4T6NVMB2","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:7a8bc51ac09e2621d83d5b395eb7dea519d6dfffd2dd330124efda4d35a6d98c","target":"graph","created_at":"2026-05-18T00:14:28Z","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":"Let $\\boldsymbol{X}(t)=(X_1(t),\\ldots,X_d(t))$ be a Gaussian vector process and $g(t)$ be a continuous function. The asymptotics of distribution of $\\left\\|\\boldsymbol{X}(t)\\right\\|_p$, the $L^p$ norm for Gaussian finite-dimensional vector, have been investigated in numerous literatures. In this contribution we are concerned with the exact tail asymptotics of $\\left\\|\\boldsymbol{X}(t)\\right\\|^c_p,\\ c>0, $ with trend $g(t)$ over $[0,T]$. Both scenarios that $\\boldsymbol{X}(t)$ is locally stationary and non-stationary are considered. Important examples include $\\sum_{i=1}^d \\left|X_i(t)\\right|+g","authors_text":"Long Bai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-26T13:27:34Z","title":"Extremes of $L^p$-norm of Vector-valued Gaussian processes with Trend"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08360","kind":"arxiv","version":2},"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":"sha256:771461af9c73ec5bcbd7fc867fe2d9b67a0b47183f390b50fbc14e311ff19170","target":"record","created_at":"2026-05-18T00:14:28Z","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":"04e113f81611ddb30164346a8a4338954982cbefe314befb80fbc12c4ef5eb30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-26T13:27:34Z","title_canon_sha256":"ecc413d616fb9f65c41a7cd17ef469d7031d4d53b8d7cbe1fdd81bd9b6c3633f"},"schema_version":"1.0","source":{"id":"1706.08360","kind":"arxiv","version":2}},"canonical_sha256":"e4fcdab03a17688476790b69fbce0dd7a1a980471fdabbf142f52c42b72d1dfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4fcdab03a17688476790b69fbce0dd7a1a980471fdabbf142f52c42b72d1dfe","first_computed_at":"2026-05-18T00:14:28.917454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:28.917454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z0avrtmC/PrraRZ8553CbVb49A3WN2ES6Fuq7yp4PtCMGkmPnk9mMlE47hRf/YZNqC8ybQ+O6ygPmK8GVNxLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:28.918199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08360","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:771461af9c73ec5bcbd7fc867fe2d9b67a0b47183f390b50fbc14e311ff19170","sha256:7a8bc51ac09e2621d83d5b395eb7dea519d6dfffd2dd330124efda4d35a6d98c"],"state_sha256":"885497c304e32ab9da8dc1922fad834215444d51d049446aa77d3f42f49c777f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZR4pB7PXPpBgoY4GAQ96zrID3YX1wC67BH4w6H20B3JKjl+U1DuFEp9r0A8PuPmhZkIrUwafCjQBR2DpYmEAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:21:59.319780Z","bundle_sha256":"d7a15cb39efa5905785a05693d66815b546e6bf5b0f4ef52146892573994c308"}}