{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YQOXC5YT2MJV2USYYZNOJTCFJ7","short_pith_number":"pith:YQOXC5YT","canonical_record":{"source":{"id":"1709.00934","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-04T13:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"58062bf3e3c0cbc709bee3285fdf73ee4c872eb4abaaba9e1ee550a5f73d4e38","abstract_canon_sha256":"d9fc19395d064e04c97d096fe730e6f8e9de557b6fc712aa4045e3e67d34fa3c"},"schema_version":"1.0"},"canonical_sha256":"c41d717713d3135d5258c65ae4cc454fdcab284628de4484e06ee00bd2901c67","source":{"kind":"arxiv","id":"1709.00934","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00934","created_at":"2026-05-18T00:23:53Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00934v2","created_at":"2026-05-18T00:23:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00934","created_at":"2026-05-18T00:23:53Z"},{"alias_kind":"pith_short_12","alias_value":"YQOXC5YT2MJV","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YQOXC5YT2MJV2USY","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YQOXC5YT","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YQOXC5YT2MJV2USYYZNOJTCFJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1709.00934","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-04T13:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"58062bf3e3c0cbc709bee3285fdf73ee4c872eb4abaaba9e1ee550a5f73d4e38","abstract_canon_sha256":"d9fc19395d064e04c97d096fe730e6f8e9de557b6fc712aa4045e3e67d34fa3c"},"schema_version":"1.0"},"canonical_sha256":"c41d717713d3135d5258c65ae4cc454fdcab284628de4484e06ee00bd2901c67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:53.090975Z","signature_b64":"yT+gudz0KOnFPwsDxKo/yhXADZmCFbRQViHvZHh0AqyL6UgbnlV5pfne8nlYFmMJN78ToVdYeffcViuXl9jADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c41d717713d3135d5258c65ae4cc454fdcab284628de4484e06ee00bd2901c67","last_reissued_at":"2026-05-18T00:23:53.090411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:53.090411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.00934","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":"2026-05-18T00:23:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HaNkUpIzQ4ahECkMuffHmnxAF9mflaFoaIVuSZH4vHj1rejni+TDVlGYulUfalh3m/BEFMA85O6WXEEHXGkaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:19:55.651330Z"},"content_sha256":"87bcbb6a19503a47a7f6dcc62c602ee9b567941a02977ccd9ea35186861d745a","schema_version":"1.0","event_id":"sha256:87bcbb6a19503a47a7f6dcc62c602ee9b567941a02977ccd9ea35186861d745a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YQOXC5YT2MJV2USYYZNOJTCFJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From random partitions to fractional Brownian sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Olivier Durieu, Yizao Wang","submitted_at":"2017-09-04T13:07:27Z","abstract_excerpt":"We propose discrete random-field models that are based on random partitions of $\\mathbb{N}^2$. The covariance structure of each random field is determined by the underlying random partition. Functional central limit theorems are established for the proposed models, and fractional Brownian sheets, with full range of Hurst indices, arise in the limit. Our models could be viewed as discrete analogues of fractional Brownian sheets, in the same spirit that the simple random walk is the discrete analogue of the Brownian motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00934","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":"2026-05-18T00:23:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BRlU4FWCg3hLMo2+QjJHdq/bYg/geqQDtMMRiNcd4mGHcv8pnuvG1OpM6ZajOJvb/+LZ602KhiQwdjiPzZpeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:19:55.651696Z"},"content_sha256":"2b9a11ee6e823a1d990d35055a2da5b61126154a12eace6ad84fb33a3d87ec91","schema_version":"1.0","event_id":"sha256:2b9a11ee6e823a1d990d35055a2da5b61126154a12eace6ad84fb33a3d87ec91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YQOXC5YT2MJV2USYYZNOJTCFJ7/bundle.json","state_url":"https://pith.science/pith/YQOXC5YT2MJV2USYYZNOJTCFJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YQOXC5YT2MJV2USYYZNOJTCFJ7/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":"2026-05-31T04:19:55Z","links":{"resolver":"https://pith.science/pith/YQOXC5YT2MJV2USYYZNOJTCFJ7","bundle":"https://pith.science/pith/YQOXC5YT2MJV2USYYZNOJTCFJ7/bundle.json","state":"https://pith.science/pith/YQOXC5YT2MJV2USYYZNOJTCFJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YQOXC5YT2MJV2USYYZNOJTCFJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YQOXC5YT2MJV2USYYZNOJTCFJ7","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":"d9fc19395d064e04c97d096fe730e6f8e9de557b6fc712aa4045e3e67d34fa3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-04T13:07:27Z","title_canon_sha256":"58062bf3e3c0cbc709bee3285fdf73ee4c872eb4abaaba9e1ee550a5f73d4e38"},"schema_version":"1.0","source":{"id":"1709.00934","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00934","created_at":"2026-05-18T00:23:53Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00934v2","created_at":"2026-05-18T00:23:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00934","created_at":"2026-05-18T00:23:53Z"},{"alias_kind":"pith_short_12","alias_value":"YQOXC5YT2MJV","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YQOXC5YT2MJV2USY","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YQOXC5YT","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:2b9a11ee6e823a1d990d35055a2da5b61126154a12eace6ad84fb33a3d87ec91","target":"graph","created_at":"2026-05-18T00:23:53Z","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":"We propose discrete random-field models that are based on random partitions of $\\mathbb{N}^2$. The covariance structure of each random field is determined by the underlying random partition. Functional central limit theorems are established for the proposed models, and fractional Brownian sheets, with full range of Hurst indices, arise in the limit. Our models could be viewed as discrete analogues of fractional Brownian sheets, in the same spirit that the simple random walk is the discrete analogue of the Brownian motion.","authors_text":"Olivier Durieu, Yizao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-04T13:07:27Z","title":"From random partitions to fractional Brownian sheets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00934","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":"sha256:87bcbb6a19503a47a7f6dcc62c602ee9b567941a02977ccd9ea35186861d745a","target":"record","created_at":"2026-05-18T00:23:53Z","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":"d9fc19395d064e04c97d096fe730e6f8e9de557b6fc712aa4045e3e67d34fa3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-04T13:07:27Z","title_canon_sha256":"58062bf3e3c0cbc709bee3285fdf73ee4c872eb4abaaba9e1ee550a5f73d4e38"},"schema_version":"1.0","source":{"id":"1709.00934","kind":"arxiv","version":2}},"canonical_sha256":"c41d717713d3135d5258c65ae4cc454fdcab284628de4484e06ee00bd2901c67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c41d717713d3135d5258c65ae4cc454fdcab284628de4484e06ee00bd2901c67","first_computed_at":"2026-05-18T00:23:53.090411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:53.090411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yT+gudz0KOnFPwsDxKo/yhXADZmCFbRQViHvZHh0AqyL6UgbnlV5pfne8nlYFmMJN78ToVdYeffcViuXl9jADg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:53.090975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00934","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87bcbb6a19503a47a7f6dcc62c602ee9b567941a02977ccd9ea35186861d745a","sha256:2b9a11ee6e823a1d990d35055a2da5b61126154a12eace6ad84fb33a3d87ec91"],"state_sha256":"ba1dce37948bb718c7eb90c14fa2e2fe6f7fc8e005069631331dba056b7775ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qli8YCkABVwVA/3JCxWRXTvWgv9Pw5YNS4tDlb7g8NIJnOBh2phY50CXTllvRdYwtr7V1SNHw2kegCDxDlNPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:19:55.654353Z","bundle_sha256":"dc9f9e054a8140934d13f2d2c44f90548cf7bd4b09ea5cd2f45e149c700d9c68"}}