{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:C3H5GCZI5ZG2AYFC4SNJIZC4X3","short_pith_number":"pith:C3H5GCZI","canonical_record":{"source":{"id":"1607.05167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-18T16:31:58Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"daa29aa92c54010b1628394af7a8ade1855077a269fa9ea29c22b74d8949d8ac","abstract_canon_sha256":"0268e45b2a8bcfa5d7b00a7d6b7a074996ab2740f61a30bb98a9923461b24c6d"},"schema_version":"1.0"},"canonical_sha256":"16cfd30b28ee4da060a2e49a94645cbedf123683faf3c8bc34e9f39401e97876","source":{"kind":"arxiv","id":"1607.05167","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05167","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05167v2","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05167","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"C3H5GCZI5ZG2","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C3H5GCZI5ZG2AYFC","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C3H5GCZI","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:C3H5GCZI5ZG2AYFC4SNJIZC4X3","target":"record","payload":{"canonical_record":{"source":{"id":"1607.05167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-18T16:31:58Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"daa29aa92c54010b1628394af7a8ade1855077a269fa9ea29c22b74d8949d8ac","abstract_canon_sha256":"0268e45b2a8bcfa5d7b00a7d6b7a074996ab2740f61a30bb98a9923461b24c6d"},"schema_version":"1.0"},"canonical_sha256":"16cfd30b28ee4da060a2e49a94645cbedf123683faf3c8bc34e9f39401e97876","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:13.918076Z","signature_b64":"CCHw70AVOeE9lthT0UXZFZU0e1GDsI6ioTrELT2JFTM/PLgS+ujKqqwhkV0cKSJEQB2clbcEIc5us/YLTLX2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16cfd30b28ee4da060a2e49a94645cbedf123683faf3c8bc34e9f39401e97876","last_reissued_at":"2026-05-18T00:38:13.917458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:13.917458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.05167","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":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+dRg8ZTctG0+w5RAJOa9OJwpJNfbly1Y/JwIVeh4oBf+RMr+SVZD84LzKWT+CB/N+eyHtzob91FtuGRxsUHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:12:47.947976Z"},"content_sha256":"77f1cbfa735218f38937f8ab7fc8d4fd58bc94069dfeb3130de82c798e1eb20e","schema_version":"1.0","event_id":"sha256:77f1cbfa735218f38937f8ab7fc8d4fd58bc94069dfeb3130de82c798e1eb20e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:C3H5GCZI5ZG2AYFC4SNJIZC4X3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-step wavelet-based estimation for mixed Gaussian fractional processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Gustavo Didier, Hui Li, Patrice Abry","submitted_at":"2016-07-18T16:31:58Z","abstract_excerpt":"A mixed Gaussian fractional process $\\{Y(t)\\}_{t \\in {\\Bbb R}} = \\{PX(t)\\}_{t \\in {\\Bbb R}}$ is a multivariate stochastic process obtained by pre-multiplying a vector of independent, Gaussian fractional process entries $X$ by a nonsingular matrix $P$. It is interpreted that $Y$ is observable, while $X$ is a hidden process occurring in an (unknown) system of coordinates $P$. Mixed processes naturally arise as approximations to solutions of physically relevant classes of multivariate fractional SDEs under aggregation. We propose a semiparametric two-step wavelet-based method for estimating both "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05167","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":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rogt2F09Z8vF512Qm36bc7ugjF6AZVaO9wG+dw0ozs+en51/UUN0D2xrRaPbj7BgAw48jQsY5Y9La6PWs94ODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:12:47.948623Z"},"content_sha256":"c3160a3fbbada8fe080263e95951d12af62245d3d8931a4e8e7da96fdc1bf9f6","schema_version":"1.0","event_id":"sha256:c3160a3fbbada8fe080263e95951d12af62245d3d8931a4e8e7da96fdc1bf9f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3H5GCZI5ZG2AYFC4SNJIZC4X3/bundle.json","state_url":"https://pith.science/pith/C3H5GCZI5ZG2AYFC4SNJIZC4X3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3H5GCZI5ZG2AYFC4SNJIZC4X3/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":"2026-05-28T23:12:47Z","links":{"resolver":"https://pith.science/pith/C3H5GCZI5ZG2AYFC4SNJIZC4X3","bundle":"https://pith.science/pith/C3H5GCZI5ZG2AYFC4SNJIZC4X3/bundle.json","state":"https://pith.science/pith/C3H5GCZI5ZG2AYFC4SNJIZC4X3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3H5GCZI5ZG2AYFC4SNJIZC4X3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C3H5GCZI5ZG2AYFC4SNJIZC4X3","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":"0268e45b2a8bcfa5d7b00a7d6b7a074996ab2740f61a30bb98a9923461b24c6d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-18T16:31:58Z","title_canon_sha256":"daa29aa92c54010b1628394af7a8ade1855077a269fa9ea29c22b74d8949d8ac"},"schema_version":"1.0","source":{"id":"1607.05167","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05167","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05167v2","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05167","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"C3H5GCZI5ZG2","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C3H5GCZI5ZG2AYFC","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C3H5GCZI","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:c3160a3fbbada8fe080263e95951d12af62245d3d8931a4e8e7da96fdc1bf9f6","target":"graph","created_at":"2026-05-18T00:38:13Z","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":"A mixed Gaussian fractional process $\\{Y(t)\\}_{t \\in {\\Bbb R}} = \\{PX(t)\\}_{t \\in {\\Bbb R}}$ is a multivariate stochastic process obtained by pre-multiplying a vector of independent, Gaussian fractional process entries $X$ by a nonsingular matrix $P$. It is interpreted that $Y$ is observable, while $X$ is a hidden process occurring in an (unknown) system of coordinates $P$. Mixed processes naturally arise as approximations to solutions of physically relevant classes of multivariate fractional SDEs under aggregation. We propose a semiparametric two-step wavelet-based method for estimating both ","authors_text":"Gustavo Didier, Hui Li, Patrice Abry","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-18T16:31:58Z","title":"Two-step wavelet-based estimation for mixed Gaussian fractional processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05167","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":"sha256:77f1cbfa735218f38937f8ab7fc8d4fd58bc94069dfeb3130de82c798e1eb20e","target":"record","created_at":"2026-05-18T00:38:13Z","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":"0268e45b2a8bcfa5d7b00a7d6b7a074996ab2740f61a30bb98a9923461b24c6d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-18T16:31:58Z","title_canon_sha256":"daa29aa92c54010b1628394af7a8ade1855077a269fa9ea29c22b74d8949d8ac"},"schema_version":"1.0","source":{"id":"1607.05167","kind":"arxiv","version":2}},"canonical_sha256":"16cfd30b28ee4da060a2e49a94645cbedf123683faf3c8bc34e9f39401e97876","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16cfd30b28ee4da060a2e49a94645cbedf123683faf3c8bc34e9f39401e97876","first_computed_at":"2026-05-18T00:38:13.917458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:13.917458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CCHw70AVOeE9lthT0UXZFZU0e1GDsI6ioTrELT2JFTM/PLgS+ujKqqwhkV0cKSJEQB2clbcEIc5us/YLTLX2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:13.918076Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.05167","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77f1cbfa735218f38937f8ab7fc8d4fd58bc94069dfeb3130de82c798e1eb20e","sha256:c3160a3fbbada8fe080263e95951d12af62245d3d8931a4e8e7da96fdc1bf9f6"],"state_sha256":"10c65def42b28b20adf0d9c22623735927c9a65805e0f3a70acd3661948dd651"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TqZsk3aVfHG2AIA1wCvhv7l88O/rvNTeCOJ5dnCUY/0oaVL/Khcc0MLRoLBatJOGsIQc0vWf+n8DSVDsxIUNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:12:47.952470Z","bundle_sha256":"3ee229082d4d4cfaef4cc85924b256a8ff6ef102399ca8a8bd61a6c93790a141"}}