{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JEQFH7P6D6CHYX6CKLO5YBERWI","short_pith_number":"pith:JEQFH7P6","canonical_record":{"source":{"id":"1601.05715","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-21T17:17:06Z","cross_cats_sorted":[],"title_canon_sha256":"2a1e9405292967d00d744a37ebc4c7ca0273d16bf1544bf73ed3a0c08098d2d4","abstract_canon_sha256":"a9f4ad50ec28ac9d72df67b50717903a075e0c3a19d35b2c6276296f173ee82b"},"schema_version":"1.0"},"canonical_sha256":"492053fdfe1f847c5fc252dddc0491b207208a6802954d590d983df9a06fefca","source":{"kind":"arxiv","id":"1601.05715","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05715","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05715v6","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05715","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"pith_short_12","alias_value":"JEQFH7P6D6CH","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JEQFH7P6D6CHYX6C","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JEQFH7P6","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JEQFH7P6D6CHYX6CKLO5YBERWI","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05715","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-21T17:17:06Z","cross_cats_sorted":[],"title_canon_sha256":"2a1e9405292967d00d744a37ebc4c7ca0273d16bf1544bf73ed3a0c08098d2d4","abstract_canon_sha256":"a9f4ad50ec28ac9d72df67b50717903a075e0c3a19d35b2c6276296f173ee82b"},"schema_version":"1.0"},"canonical_sha256":"492053fdfe1f847c5fc252dddc0491b207208a6802954d590d983df9a06fefca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:31.245906Z","signature_b64":"J6sBbGYp7LEp/y8cb5Caev9fW5WgrL/0AdQ946pHo0eD/YsxR03fpHhzbUJvRLmoUim7vJtEIQxgnZKEVW9tBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"492053fdfe1f847c5fc252dddc0491b207208a6802954d590d983df9a06fefca","last_reissued_at":"2026-05-18T00:15:31.245237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:31.245237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05715","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c1M+PbDgmO341hENe5felF4TAlasImu1kAMjHqz99fLNu5esD61KzxFjX3ygqK/wzSvM+hfzgtTkUXlvuTuYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:59:54.758105Z"},"content_sha256":"edde059a6fed546962d96729e874069bd3f2a549e40f6c982f35242fe9689987","schema_version":"1.0","event_id":"sha256:edde059a6fed546962d96729e874069bd3f2a549e40f6c982f35242fe9689987"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JEQFH7P6D6CHYX6CKLO5YBERWI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact asymptotics in eigenproblems for fractional Brownian covariance operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marina Kleptsyna, Pavel Chigansky","submitted_at":"2016-01-21T17:17:06Z","abstract_excerpt":"Many results in the theory of Gaussian processes rely on the eigenstructure of the covariance operator. However, eigenproblems are notoriously hard to solve explicitly and closed form solutions are known only in a limited number of cases. In this paper we set up a framework for the spectral analysis of the fractional type covariance operators, corresponding to an important family of processes, which includes the fractional Brownian motion and its noise. We obtain accurate asymptotic approximations for the eigenvalues and the eigenfunctions. Our results provide a key to several problems, whose "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05715","kind":"arxiv","version":6},"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":"2026-05-18T00:15:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avg0wkjwVc3iqkJYqs16jfJ9PPpRyxWrJWI1qFdRAHc7ivSnI9nl1oQZlCv4nYoF7+xra2e5Q1F7d8WB4Jl8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:59:54.758464Z"},"content_sha256":"009daf3d21afd6c45e7fb6c6ea8216d4dacd9e48157884a32b27956942042825","schema_version":"1.0","event_id":"sha256:009daf3d21afd6c45e7fb6c6ea8216d4dacd9e48157884a32b27956942042825"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEQFH7P6D6CHYX6CKLO5YBERWI/bundle.json","state_url":"https://pith.science/pith/JEQFH7P6D6CHYX6CKLO5YBERWI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEQFH7P6D6CHYX6CKLO5YBERWI/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":"2026-06-23T19:59:54Z","links":{"resolver":"https://pith.science/pith/JEQFH7P6D6CHYX6CKLO5YBERWI","bundle":"https://pith.science/pith/JEQFH7P6D6CHYX6CKLO5YBERWI/bundle.json","state":"https://pith.science/pith/JEQFH7P6D6CHYX6CKLO5YBERWI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEQFH7P6D6CHYX6CKLO5YBERWI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JEQFH7P6D6CHYX6CKLO5YBERWI","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":"a9f4ad50ec28ac9d72df67b50717903a075e0c3a19d35b2c6276296f173ee82b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-21T17:17:06Z","title_canon_sha256":"2a1e9405292967d00d744a37ebc4c7ca0273d16bf1544bf73ed3a0c08098d2d4"},"schema_version":"1.0","source":{"id":"1601.05715","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05715","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05715v6","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05715","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"pith_short_12","alias_value":"JEQFH7P6D6CH","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JEQFH7P6D6CHYX6C","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JEQFH7P6","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:009daf3d21afd6c45e7fb6c6ea8216d4dacd9e48157884a32b27956942042825","target":"graph","created_at":"2026-05-18T00:15:31Z","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":"Many results in the theory of Gaussian processes rely on the eigenstructure of the covariance operator. However, eigenproblems are notoriously hard to solve explicitly and closed form solutions are known only in a limited number of cases. In this paper we set up a framework for the spectral analysis of the fractional type covariance operators, corresponding to an important family of processes, which includes the fractional Brownian motion and its noise. We obtain accurate asymptotic approximations for the eigenvalues and the eigenfunctions. Our results provide a key to several problems, whose ","authors_text":"Marina Kleptsyna, Pavel Chigansky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-21T17:17:06Z","title":"Exact asymptotics in eigenproblems for fractional Brownian covariance operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05715","kind":"arxiv","version":6},"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:edde059a6fed546962d96729e874069bd3f2a549e40f6c982f35242fe9689987","target":"record","created_at":"2026-05-18T00:15:31Z","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":"a9f4ad50ec28ac9d72df67b50717903a075e0c3a19d35b2c6276296f173ee82b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-21T17:17:06Z","title_canon_sha256":"2a1e9405292967d00d744a37ebc4c7ca0273d16bf1544bf73ed3a0c08098d2d4"},"schema_version":"1.0","source":{"id":"1601.05715","kind":"arxiv","version":6}},"canonical_sha256":"492053fdfe1f847c5fc252dddc0491b207208a6802954d590d983df9a06fefca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"492053fdfe1f847c5fc252dddc0491b207208a6802954d590d983df9a06fefca","first_computed_at":"2026-05-18T00:15:31.245237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:31.245237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J6sBbGYp7LEp/y8cb5Caev9fW5WgrL/0AdQ946pHo0eD/YsxR03fpHhzbUJvRLmoUim7vJtEIQxgnZKEVW9tBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:31.245906Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05715","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edde059a6fed546962d96729e874069bd3f2a549e40f6c982f35242fe9689987","sha256:009daf3d21afd6c45e7fb6c6ea8216d4dacd9e48157884a32b27956942042825"],"state_sha256":"ae955929f20bddc5a2af8fc7cfaa6edfd9672d20d87a57ae0f411bf62b200be7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"24sGq7MiXoTxx6zijmtspplgjPiJH8sotqKnBoDPZCfP07vfbGOX5mM4lzqXBkU7KbkuNWJ0yE0xbXohWlVKCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:59:54.760608Z","bundle_sha256":"64e7f247dc72689cbab89a8a34ac8032513440381d8514447d5111bc679dc455"}}