{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:X2BHYZFH7TCJVDDDPEQVCVF6XP","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":"8f1ce965655d0fd0ff47d152b53681d9f435d5f76e82e371a3fb2faa839139c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-06T18:28:23Z","title_canon_sha256":"088f0646cff7daad8826404dc91d222d55c62ef99df20567aeb5a654f3ea2a61"},"schema_version":"1.0","source":{"id":"1004.0920","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0920","created_at":"2026-05-18T04:33:29Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0920v2","created_at":"2026-05-18T04:33:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0920","created_at":"2026-05-18T04:33:29Z"},{"alias_kind":"pith_short_12","alias_value":"X2BHYZFH7TCJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"X2BHYZFH7TCJVDDD","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"X2BHYZFH","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:f43bd60ae28320567ed84c2e7e48804064e7cdfaafb38659e7bbadc0884be37b","target":"graph","created_at":"2026-05-18T04:33:29Z","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 consider a random walk on $\\R^d$ in a polynomially mixing random environment that is refreshed at each time step. We use a martingale approach to give a necessary and sufficient condition for the almost-sure functional central limit theorem to hold.","authors_text":"Firas Rassoul-Agha, Mathew Joseph","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-06T18:28:23Z","title":"Almost Sure Invariance Principle for Continuous-Space Random Walk in Dynamic Random Environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0920","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":"sha256:09250fc7cacac754d738ad6f9c1c84e33ad45c09ba083050d4130b7a5a18122f","target":"record","created_at":"2026-05-18T04:33:29Z","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":"8f1ce965655d0fd0ff47d152b53681d9f435d5f76e82e371a3fb2faa839139c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-06T18:28:23Z","title_canon_sha256":"088f0646cff7daad8826404dc91d222d55c62ef99df20567aeb5a654f3ea2a61"},"schema_version":"1.0","source":{"id":"1004.0920","kind":"arxiv","version":2}},"canonical_sha256":"be827c64a7fcc49a8c6379215154bebbc7600d7ecd1f396635598b637e152f80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be827c64a7fcc49a8c6379215154bebbc7600d7ecd1f396635598b637e152f80","first_computed_at":"2026-05-18T04:33:29.331696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:29.331696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JclX4IiwBx9uu0jPHmgzphoGUC+wdjDNvhRBs/t6DtRW3w1ANQ9K3slop8y781/dZJHhFYnOn+r2mro52DhsBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:29.332358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0920","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09250fc7cacac754d738ad6f9c1c84e33ad45c09ba083050d4130b7a5a18122f","sha256:f43bd60ae28320567ed84c2e7e48804064e7cdfaafb38659e7bbadc0884be37b"],"state_sha256":"211b0fcbada7f5663153ab0d4cce9a83a8a7089841985ff56a288a19367e9dd4"}