{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4FGGFZ7F7BY6O4V6VCJYNDFFIU","short_pith_number":"pith:4FGGFZ7F","canonical_record":{"source":{"id":"1609.00338","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-01T18:27:02Z","cross_cats_sorted":[],"title_canon_sha256":"44444b287f7ce23a423e8a880dbc1c7c039a169c220a24e03e18c57460465644","abstract_canon_sha256":"19ad69185bfad04949da6e5fac6a828b97d0fb45efc037499dcceced96f31226"},"schema_version":"1.0"},"canonical_sha256":"e14c62e7e5f871e772bea893868ca5450f48bc69687ed7df99f9760d0d2466f3","source":{"kind":"arxiv","id":"1609.00338","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00338","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00338v2","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00338","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"pith_short_12","alias_value":"4FGGFZ7F7BY6","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FGGFZ7F7BY6O4V6","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FGGFZ7F","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4FGGFZ7F7BY6O4V6VCJYNDFFIU","target":"record","payload":{"canonical_record":{"source":{"id":"1609.00338","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-01T18:27:02Z","cross_cats_sorted":[],"title_canon_sha256":"44444b287f7ce23a423e8a880dbc1c7c039a169c220a24e03e18c57460465644","abstract_canon_sha256":"19ad69185bfad04949da6e5fac6a828b97d0fb45efc037499dcceced96f31226"},"schema_version":"1.0"},"canonical_sha256":"e14c62e7e5f871e772bea893868ca5450f48bc69687ed7df99f9760d0d2466f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:59.659763Z","signature_b64":"P6OSTuO3+wqQdtR4ArsdE1s08f6tqJ4WK6/VQVFgj3GDFUQfD8A0Hr3R2gMy8YtwPCZq9QyvC5UFQRosxCfYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e14c62e7e5f871e772bea893868ca5450f48bc69687ed7df99f9760d0d2466f3","last_reissued_at":"2026-05-18T00:31:59.659368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:59.659368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.00338","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":"2026-05-18T00:31:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C+ulL4nDZAMaz3uH5D8alJmAzoOCqpl0KRJEf/t2tzorZ6dxalPTPzeyd8zmqiFN5my6h7mfCNB5wYQxKIGZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:21:09.756863Z"},"content_sha256":"1a8f20628762766e967c3edddfc4ff5de8feb1acfbb6f5038f524a45511968f0","schema_version":"1.0","event_id":"sha256:1a8f20628762766e967c3edddfc4ff5de8feb1acfbb6f5038f524a45511968f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4FGGFZ7F7BY6O4V6VCJYNDFFIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremes of $q$-Ornstein-Uhlenbeck processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yizao Wang","submitted_at":"2016-09-01T18:27:02Z","abstract_excerpt":"The $q$-Ornstein-Uhlenbeck processes, $q\\in(-1,1)$, are a family of stationary Markov processes that converge weakly to the standard Ornstein-Uhlenbeck process as $q$ tends to 1. It has been noticed recently that in terms of path properties, however, for each $q$ fixed the $q$-Ornstein-Uhlenbeck process behaves qualitatively different from their Gaussian counterpart in several aspects. Here, two limit theorems on the extremes of $q$-Ornstein-Uhlenbeck processes are established. Both results are based on the weak convergence of the tangent process at the lower boundary, a positive self-similar "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00338","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":"2026-05-18T00:31:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJfwLPNjDG07Jkv97RIjz4kUd0hQsCNGOrWaSsweASX2BAIL3heU8ofRCzvSkzRfAaLSULY6ecgU8JDgvGgSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:21:09.757207Z"},"content_sha256":"5d9ec8dae5ed09e516a7ea3ce0a10295302ad6e790d92f4509d8ffa27a20e4b9","schema_version":"1.0","event_id":"sha256:5d9ec8dae5ed09e516a7ea3ce0a10295302ad6e790d92f4509d8ffa27a20e4b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4FGGFZ7F7BY6O4V6VCJYNDFFIU/bundle.json","state_url":"https://pith.science/pith/4FGGFZ7F7BY6O4V6VCJYNDFFIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4FGGFZ7F7BY6O4V6VCJYNDFFIU/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":"2026-06-03T13:21:09Z","links":{"resolver":"https://pith.science/pith/4FGGFZ7F7BY6O4V6VCJYNDFFIU","bundle":"https://pith.science/pith/4FGGFZ7F7BY6O4V6VCJYNDFFIU/bundle.json","state":"https://pith.science/pith/4FGGFZ7F7BY6O4V6VCJYNDFFIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4FGGFZ7F7BY6O4V6VCJYNDFFIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4FGGFZ7F7BY6O4V6VCJYNDFFIU","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":"19ad69185bfad04949da6e5fac6a828b97d0fb45efc037499dcceced96f31226","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-01T18:27:02Z","title_canon_sha256":"44444b287f7ce23a423e8a880dbc1c7c039a169c220a24e03e18c57460465644"},"schema_version":"1.0","source":{"id":"1609.00338","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00338","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00338v2","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00338","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"pith_short_12","alias_value":"4FGGFZ7F7BY6","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FGGFZ7F7BY6O4V6","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FGGFZ7F","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:5d9ec8dae5ed09e516a7ea3ce0a10295302ad6e790d92f4509d8ffa27a20e4b9","target":"graph","created_at":"2026-05-18T00:31:59Z","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":"The $q$-Ornstein-Uhlenbeck processes, $q\\in(-1,1)$, are a family of stationary Markov processes that converge weakly to the standard Ornstein-Uhlenbeck process as $q$ tends to 1. It has been noticed recently that in terms of path properties, however, for each $q$ fixed the $q$-Ornstein-Uhlenbeck process behaves qualitatively different from their Gaussian counterpart in several aspects. Here, two limit theorems on the extremes of $q$-Ornstein-Uhlenbeck processes are established. Both results are based on the weak convergence of the tangent process at the lower boundary, a positive self-similar ","authors_text":"Yizao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-01T18:27:02Z","title":"Extremes of $q$-Ornstein-Uhlenbeck processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00338","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":"sha256:1a8f20628762766e967c3edddfc4ff5de8feb1acfbb6f5038f524a45511968f0","target":"record","created_at":"2026-05-18T00:31:59Z","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":"19ad69185bfad04949da6e5fac6a828b97d0fb45efc037499dcceced96f31226","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-01T18:27:02Z","title_canon_sha256":"44444b287f7ce23a423e8a880dbc1c7c039a169c220a24e03e18c57460465644"},"schema_version":"1.0","source":{"id":"1609.00338","kind":"arxiv","version":2}},"canonical_sha256":"e14c62e7e5f871e772bea893868ca5450f48bc69687ed7df99f9760d0d2466f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e14c62e7e5f871e772bea893868ca5450f48bc69687ed7df99f9760d0d2466f3","first_computed_at":"2026-05-18T00:31:59.659368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:59.659368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P6OSTuO3+wqQdtR4ArsdE1s08f6tqJ4WK6/VQVFgj3GDFUQfD8A0Hr3R2gMy8YtwPCZq9QyvC5UFQRosxCfYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:59.659763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00338","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a8f20628762766e967c3edddfc4ff5de8feb1acfbb6f5038f524a45511968f0","sha256:5d9ec8dae5ed09e516a7ea3ce0a10295302ad6e790d92f4509d8ffa27a20e4b9"],"state_sha256":"966cb3baef0ebb00a40bcedbf8b80d80b22ebd2a1fc7cee21eef97f82337bdad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zp8O+Bh1zmUYgMx0So/jY1iIpLrNuYfMQmVJLj1Cz+1uQ2LigE2N450mGy7D84QaH4cRvnDJsxCsOq2kclGvBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:21:09.759220Z","bundle_sha256":"15e8ab3f774fe1c31cdc133c26be74cb7d887882b7b72c1e00b0cac10e3c55c0"}}