{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2WRKTBQYC4ICL6J26YHSO7MAHW","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":"4a5b07e8b8c9e69cfbb9c7d2d76d6cdb5bb2f823a9e5d143a88d7965b03d29c1","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-12-18T21:29:21Z","title_canon_sha256":"d10c1aa48de050d6f3ee927013a1da1aeb3463e4a92bb1e9909ee09d0524df81"},"schema_version":"1.0","source":{"id":"2412.14346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.14346","created_at":"2026-07-05T09:51:45Z"},{"alias_kind":"arxiv_version","alias_value":"2412.14346v1","created_at":"2026-07-05T09:51:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.14346","created_at":"2026-07-05T09:51:45Z"},{"alias_kind":"pith_short_12","alias_value":"2WRKTBQYC4IC","created_at":"2026-07-05T09:51:45Z"},{"alias_kind":"pith_short_16","alias_value":"2WRKTBQYC4ICL6J2","created_at":"2026-07-05T09:51:45Z"},{"alias_kind":"pith_short_8","alias_value":"2WRKTBQY","created_at":"2026-07-05T09:51:45Z"}],"graph_snapshots":[{"event_id":"sha256:0233dc3f81685c466fc9c84124334566b55fadc7787380fec897897bb0da2c67","target":"graph","created_at":"2026-07-05T09:51:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.14346/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where the approximating object is not constant, but a sequence as well. We extend Gaussian approximation results for the partial sum process by allowing each summand to be multiplied by a data-dependent matrix. The results allow for serial dependence of the data, and for high-dimensionality of both the data and the multipliers. In the finite-dimensional and locall","authors_text":"Fabian Mies","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-12-18T21:29:21Z","title":"Strong Gaussian approximations with random multipliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14346","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":"sha256:9a6490b1c8489c616dc2143ce7b6c800b8588836473bf9fbb920cbcbd64681ea","target":"record","created_at":"2026-07-05T09:51:45Z","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":"4a5b07e8b8c9e69cfbb9c7d2d76d6cdb5bb2f823a9e5d143a88d7965b03d29c1","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-12-18T21:29:21Z","title_canon_sha256":"d10c1aa48de050d6f3ee927013a1da1aeb3463e4a92bb1e9909ee09d0524df81"},"schema_version":"1.0","source":{"id":"2412.14346","kind":"arxiv","version":1}},"canonical_sha256":"d5a2a98618171025f93af60f277d803da1b06ebb5a423152657822654e8e0b67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5a2a98618171025f93af60f277d803da1b06ebb5a423152657822654e8e0b67","first_computed_at":"2026-07-05T09:51:45.981080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:51:45.981080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R5ApZS0JzNmI1KOdSEUELEBNmid09rkFUrR35U0Oteu5kbx7NAvPTNbWxbpOZWkt7AAjEh2xqUCZJdzUX1cwDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:51:45.981496Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.14346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a6490b1c8489c616dc2143ce7b6c800b8588836473bf9fbb920cbcbd64681ea","sha256:0233dc3f81685c466fc9c84124334566b55fadc7787380fec897897bb0da2c67"],"state_sha256":"39d774afaf31d42ca51aafa866fad998e690f860f2f5991afc6efee3455a6c3b"}