{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7IC2BACXYCBR4LVV6PZL256KZD","short_pith_number":"pith:7IC2BACX","canonical_record":{"source":{"id":"1707.09637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-30T16:13:12Z","cross_cats_sorted":[],"title_canon_sha256":"9dece12063d044b06a7a4fe7d50eecc751412e63d5b0fe77db0a2cb89f478274","abstract_canon_sha256":"0d04690da0f49e9b16c71b3374155e6e0897cb2665349be0d6b14ef52569c7f4"},"schema_version":"1.0"},"canonical_sha256":"fa05a08057c0831e2eb5f3f2bd77cac8dcc2ce8c6213d8dbcfda7893aa0d4631","source":{"kind":"arxiv","id":"1707.09637","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09637","created_at":"2026-05-18T00:39:10Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09637v1","created_at":"2026-05-18T00:39:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09637","created_at":"2026-05-18T00:39:10Z"},{"alias_kind":"pith_short_12","alias_value":"7IC2BACXYCBR","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7IC2BACXYCBR4LVV","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7IC2BACX","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7IC2BACXYCBR4LVV6PZL256KZD","target":"record","payload":{"canonical_record":{"source":{"id":"1707.09637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-30T16:13:12Z","cross_cats_sorted":[],"title_canon_sha256":"9dece12063d044b06a7a4fe7d50eecc751412e63d5b0fe77db0a2cb89f478274","abstract_canon_sha256":"0d04690da0f49e9b16c71b3374155e6e0897cb2665349be0d6b14ef52569c7f4"},"schema_version":"1.0"},"canonical_sha256":"fa05a08057c0831e2eb5f3f2bd77cac8dcc2ce8c6213d8dbcfda7893aa0d4631","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:10.758215Z","signature_b64":"hlhBQTCNySxt6qaWEZGCxvOew1fmYeNfwGspF1DX6icwCSTQdtJJiIbWVfxl6157wTPD7GS/31uKQrNetzwaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa05a08057c0831e2eb5f3f2bd77cac8dcc2ce8c6213d8dbcfda7893aa0d4631","last_reissued_at":"2026-05-18T00:39:10.757513Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:10.757513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.09637","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2x8OI1utyc2f0GTsIakLE4EfYrV5AmNqsDUej7hUlUfGYlikIbQuMkb3GHdDD5hvS9/FcFh7FGW1ONh74B7BDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:44:52.974834Z"},"content_sha256":"76101245b7360f7d2a30792ac43094e95419c95d9d7ccc08e2e95903c45c32b8","schema_version":"1.0","event_id":"sha256:76101245b7360f7d2a30792ac43094e95419c95d9d7ccc08e2e95903c45c32b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7IC2BACXYCBR4LVV6PZL256KZD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rate of convergence for Hilbert space valued processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Moritz Jirak","submitted_at":"2017-07-30T16:13:12Z","abstract_excerpt":"Consider a stationary, linear Hilbert space valued process. We establish Berry-Essen type results with optimal convergence rates under sharp dependence conditions on the underlying coefficient sequence of the linear operators. The case of non-linear Bernoulli-shift sequences is also considered. If the sequence is $m$-dependent, the optimal rate $(n/m)^{1/2}$ is reached. If the sequence is weakly geometrically dependent, the rate $(n/\\log n)^{1/2}$ is obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09637","kind":"arxiv","version":1},"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":"2026-05-18T00:39:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SjZRJNwUFn5ubfp3V6Lfj5XQoe5fNluTr0zEdvUY7F++j0vXXa66saotWQ81p2o9/T+s+gkM8W3yjjDfBc5ICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:44:52.975168Z"},"content_sha256":"07e89ec1e87077e38f85613683eb76bf4e860b66eb247fdd2bb8c2f4ff8e7249","schema_version":"1.0","event_id":"sha256:07e89ec1e87077e38f85613683eb76bf4e860b66eb247fdd2bb8c2f4ff8e7249"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IC2BACXYCBR4LVV6PZL256KZD/bundle.json","state_url":"https://pith.science/pith/7IC2BACXYCBR4LVV6PZL256KZD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IC2BACXYCBR4LVV6PZL256KZD/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":"2026-06-25T19:44:52Z","links":{"resolver":"https://pith.science/pith/7IC2BACXYCBR4LVV6PZL256KZD","bundle":"https://pith.science/pith/7IC2BACXYCBR4LVV6PZL256KZD/bundle.json","state":"https://pith.science/pith/7IC2BACXYCBR4LVV6PZL256KZD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IC2BACXYCBR4LVV6PZL256KZD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7IC2BACXYCBR4LVV6PZL256KZD","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":"0d04690da0f49e9b16c71b3374155e6e0897cb2665349be0d6b14ef52569c7f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-30T16:13:12Z","title_canon_sha256":"9dece12063d044b06a7a4fe7d50eecc751412e63d5b0fe77db0a2cb89f478274"},"schema_version":"1.0","source":{"id":"1707.09637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09637","created_at":"2026-05-18T00:39:10Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09637v1","created_at":"2026-05-18T00:39:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09637","created_at":"2026-05-18T00:39:10Z"},{"alias_kind":"pith_short_12","alias_value":"7IC2BACXYCBR","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7IC2BACXYCBR4LVV","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7IC2BACX","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:07e89ec1e87077e38f85613683eb76bf4e860b66eb247fdd2bb8c2f4ff8e7249","target":"graph","created_at":"2026-05-18T00:39:10Z","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":"Consider a stationary, linear Hilbert space valued process. We establish Berry-Essen type results with optimal convergence rates under sharp dependence conditions on the underlying coefficient sequence of the linear operators. The case of non-linear Bernoulli-shift sequences is also considered. If the sequence is $m$-dependent, the optimal rate $(n/m)^{1/2}$ is reached. If the sequence is weakly geometrically dependent, the rate $(n/\\log n)^{1/2}$ is obtained.","authors_text":"Moritz Jirak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-30T16:13:12Z","title":"Rate of convergence for Hilbert space valued processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09637","kind":"arxiv","version":1},"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":"sha256:76101245b7360f7d2a30792ac43094e95419c95d9d7ccc08e2e95903c45c32b8","target":"record","created_at":"2026-05-18T00:39:10Z","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":"0d04690da0f49e9b16c71b3374155e6e0897cb2665349be0d6b14ef52569c7f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-30T16:13:12Z","title_canon_sha256":"9dece12063d044b06a7a4fe7d50eecc751412e63d5b0fe77db0a2cb89f478274"},"schema_version":"1.0","source":{"id":"1707.09637","kind":"arxiv","version":1}},"canonical_sha256":"fa05a08057c0831e2eb5f3f2bd77cac8dcc2ce8c6213d8dbcfda7893aa0d4631","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa05a08057c0831e2eb5f3f2bd77cac8dcc2ce8c6213d8dbcfda7893aa0d4631","first_computed_at":"2026-05-18T00:39:10.757513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:10.757513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hlhBQTCNySxt6qaWEZGCxvOew1fmYeNfwGspF1DX6icwCSTQdtJJiIbWVfxl6157wTPD7GS/31uKQrNetzwaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:10.758215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.09637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76101245b7360f7d2a30792ac43094e95419c95d9d7ccc08e2e95903c45c32b8","sha256:07e89ec1e87077e38f85613683eb76bf4e860b66eb247fdd2bb8c2f4ff8e7249"],"state_sha256":"27dd0371cb3954803095b0bdb0286c4c3d5fc3368b6de8f4bc39d7fe5f9045f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bI0fiAGgIuImvFlTmiMLDK45VXSnIJlMfmwN7tqGPYntQNoui56QCo5iBC1mpI3kfCRcb2lHGCDSwXZoDIjMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:44:52.978434Z","bundle_sha256":"b3eda0a743943b5de8620f126deb5c24a586aef75df035022c1af9a981a0cea0"}}