{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3WYSWB5ON4E3JMUPQAGH7VPBSN","short_pith_number":"pith:3WYSWB5O","canonical_record":{"source":{"id":"1704.06072","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-20T10:06:40Z","cross_cats_sorted":[],"title_canon_sha256":"c3fdf4e3009a5ecd9e59f9587d7fc0178eb0d970f7e31373aacd9f93566f1cfc","abstract_canon_sha256":"ed4ec7367ed27acfbd562b768ed0a32370c6c380929d7675cbe0b1a75045d345"},"schema_version":"1.0"},"canonical_sha256":"ddb12b07ae6f09b4b28f800c7fd5e193614abb9ba4cd7768052135511329aeec","source":{"kind":"arxiv","id":"1704.06072","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06072","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06072v3","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06072","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"3WYSWB5ON4E3","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3WYSWB5ON4E3JMUP","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3WYSWB5O","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3WYSWB5ON4E3JMUPQAGH7VPBSN","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06072","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-20T10:06:40Z","cross_cats_sorted":[],"title_canon_sha256":"c3fdf4e3009a5ecd9e59f9587d7fc0178eb0d970f7e31373aacd9f93566f1cfc","abstract_canon_sha256":"ed4ec7367ed27acfbd562b768ed0a32370c6c380929d7675cbe0b1a75045d345"},"schema_version":"1.0"},"canonical_sha256":"ddb12b07ae6f09b4b28f800c7fd5e193614abb9ba4cd7768052135511329aeec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:59.189016Z","signature_b64":"ZogOSjZD5H64/EHCx75uY4nE67eNBK0yUxzVUzxcJRvNo5nM8YcVwfeHDKdjnd/IxiqLE0Upzkmi4wgDPno7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddb12b07ae6f09b4b28f800c7fd5e193614abb9ba4cd7768052135511329aeec","last_reissued_at":"2026-05-18T00:33:59.188416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:59.188416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06072","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0S64U7Tb/vlprsGx2VP6YXvP/HmVM6p8BZPzYZchhTFgjEvLoXvidi5tuF4DeypM1Uxrw4dhDcZAfxUwmEXPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:29:04.429373Z"},"content_sha256":"532e37593588a5385f02a60a69c079956facc446c24a6a0ae7160de2c665a907","schema_version":"1.0","event_id":"sha256:532e37593588a5385f02a60a69c079956facc446c24a6a0ae7160de2c665a907"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3WYSWB5ON4E3JMUPQAGH7VPBSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quenched Central Limit Theorem for Random Walks in Doubly Stochastic Random Environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"B\\'alint T\\'oth","submitted_at":"2017-04-20T10:06:40Z","abstract_excerpt":"We prove the quenched version of the central limit theorem for the displacement of a random walk in doubly stochastic random environment, under the $H_{-1}$-condition, with slightly stronger, $L^{2+\\varepsilon}$ (rather than $L^2$) integrability condition on the stream tensor. On the way we extend Nash's moment bound to the non-reversible, divergence-free drift case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06072","kind":"arxiv","version":3},"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":"2026-05-18T00:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"flzotJcGpbAGW61jkg0mgksgKbSb1799xghjr+JP0v1oEks6UEVKcqkrTaoTQWqQvgEO3lFS+9qFgQ+opXwVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:29:04.429720Z"},"content_sha256":"f6cdbf36d211ad7dbc258158b1ac0694ae4b323810ab875e4387e48e5fd88b18","schema_version":"1.0","event_id":"sha256:f6cdbf36d211ad7dbc258158b1ac0694ae4b323810ab875e4387e48e5fd88b18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WYSWB5ON4E3JMUPQAGH7VPBSN/bundle.json","state_url":"https://pith.science/pith/3WYSWB5ON4E3JMUPQAGH7VPBSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WYSWB5ON4E3JMUPQAGH7VPBSN/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":"2026-05-28T10:29:04Z","links":{"resolver":"https://pith.science/pith/3WYSWB5ON4E3JMUPQAGH7VPBSN","bundle":"https://pith.science/pith/3WYSWB5ON4E3JMUPQAGH7VPBSN/bundle.json","state":"https://pith.science/pith/3WYSWB5ON4E3JMUPQAGH7VPBSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WYSWB5ON4E3JMUPQAGH7VPBSN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3WYSWB5ON4E3JMUPQAGH7VPBSN","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":"ed4ec7367ed27acfbd562b768ed0a32370c6c380929d7675cbe0b1a75045d345","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-20T10:06:40Z","title_canon_sha256":"c3fdf4e3009a5ecd9e59f9587d7fc0178eb0d970f7e31373aacd9f93566f1cfc"},"schema_version":"1.0","source":{"id":"1704.06072","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06072","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06072v3","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06072","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"3WYSWB5ON4E3","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3WYSWB5ON4E3JMUP","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3WYSWB5O","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:f6cdbf36d211ad7dbc258158b1ac0694ae4b323810ab875e4387e48e5fd88b18","target":"graph","created_at":"2026-05-18T00:33:59Z","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 prove the quenched version of the central limit theorem for the displacement of a random walk in doubly stochastic random environment, under the $H_{-1}$-condition, with slightly stronger, $L^{2+\\varepsilon}$ (rather than $L^2$) integrability condition on the stream tensor. On the way we extend Nash's moment bound to the non-reversible, divergence-free drift case.","authors_text":"B\\'alint T\\'oth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-20T10:06:40Z","title":"Quenched Central Limit Theorem for Random Walks in Doubly Stochastic Random Environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06072","kind":"arxiv","version":3},"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":"sha256:532e37593588a5385f02a60a69c079956facc446c24a6a0ae7160de2c665a907","target":"record","created_at":"2026-05-18T00:33:59Z","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":"ed4ec7367ed27acfbd562b768ed0a32370c6c380929d7675cbe0b1a75045d345","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-20T10:06:40Z","title_canon_sha256":"c3fdf4e3009a5ecd9e59f9587d7fc0178eb0d970f7e31373aacd9f93566f1cfc"},"schema_version":"1.0","source":{"id":"1704.06072","kind":"arxiv","version":3}},"canonical_sha256":"ddb12b07ae6f09b4b28f800c7fd5e193614abb9ba4cd7768052135511329aeec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddb12b07ae6f09b4b28f800c7fd5e193614abb9ba4cd7768052135511329aeec","first_computed_at":"2026-05-18T00:33:59.188416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:59.188416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZogOSjZD5H64/EHCx75uY4nE67eNBK0yUxzVUzxcJRvNo5nM8YcVwfeHDKdjnd/IxiqLE0Upzkmi4wgDPno7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:59.189016Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06072","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:532e37593588a5385f02a60a69c079956facc446c24a6a0ae7160de2c665a907","sha256:f6cdbf36d211ad7dbc258158b1ac0694ae4b323810ab875e4387e48e5fd88b18"],"state_sha256":"d3de51bffcd1c7219c755bedadb704a2cd8e87074b2f348a8e4c4f1717f68ed3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UPr/6S56/C1dwpTqFGOHq6rKPI0d9rw2ya89RIdi8HT5+iEQv3kkzuKIxhkFGEPQRgpRSE/+Lna5Mj0ogwmuCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:29:04.431621Z","bundle_sha256":"eb7386ee393ed8ee9b04a68401761db016af35d318fafb0cda7593d6d4b0128e"}}