{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RBR6AWCEZFECD2UPACJABLGT27","short_pith_number":"pith:RBR6AWCE","canonical_record":{"source":{"id":"1108.3995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-19T16:19:33Z","cross_cats_sorted":[],"title_canon_sha256":"7f35d69b8b569ded1eeb53afe312c09015d49e287bb147b18a695b71494caf71","abstract_canon_sha256":"5ebdef01f133be24263a96169f74014081ccdf37490402acb721f6f36367473f"},"schema_version":"1.0"},"canonical_sha256":"8863e05844c94821ea8f009200acd3d7cedb5e6e5958b16102b957804175f477","source":{"kind":"arxiv","id":"1108.3995","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3995","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3995v2","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3995","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"RBR6AWCEZFEC","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RBR6AWCEZFECD2UP","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RBR6AWCE","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RBR6AWCEZFECD2UPACJABLGT27","target":"record","payload":{"canonical_record":{"source":{"id":"1108.3995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-19T16:19:33Z","cross_cats_sorted":[],"title_canon_sha256":"7f35d69b8b569ded1eeb53afe312c09015d49e287bb147b18a695b71494caf71","abstract_canon_sha256":"5ebdef01f133be24263a96169f74014081ccdf37490402acb721f6f36367473f"},"schema_version":"1.0"},"canonical_sha256":"8863e05844c94821ea8f009200acd3d7cedb5e6e5958b16102b957804175f477","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:48.826073Z","signature_b64":"HEKzZy7fnJ0XWa53ziltH51UlG3chR5vtBepnuU0zITkjobDVP9lBxcOIHm1PVkY9N9AC4E8Sz2oGGkeCM+YCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8863e05844c94821ea8f009200acd3d7cedb5e6e5958b16102b957804175f477","last_reissued_at":"2026-05-18T03:51:48.825268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:48.825268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.3995","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":"2026-05-18T03:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qm+MGO5BT/8gYKrVr67MOh0N3wNsmvbnIbBoAC1nGjowhb6wvZpGS1J1/jsUBIcExpvWqo4EXgYhCKekqv2wCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:05:58.819996Z"},"content_sha256":"b93a6aaa6558e6ddabb79e2a1196daacd88e2716b7f761fa56d9cf0b41f26834","schema_version":"1.0","event_id":"sha256:b93a6aaa6558e6ddabb79e2a1196daacd88e2716b7f761fa56d9cf0b41f26834"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RBR6AWCEZFECD2UPACJABLGT27","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Dominique Deuschel, Noam Berger","submitted_at":"2011-08-19T16:19:33Z","abstract_excerpt":"We consider a random walk on Z^d in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from x to nearest neighbor x+e is the same as to nearest neighbor x-e. Assuming that the environment is genuinely d-dimensional and balanced we show a quenched invariance principle: for P almost every environment, the diffusive rescaled random walk converges to a Brownian motion with deterministic non-degenerate diffusion matrix. Within the i.i.d. setting, our result extend both Lawler's uniformly elliptic result and Guo and Zeitouni's elliptic result to the genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3995","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":"2026-05-18T03:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ta17nkYy6wDH1DxsEi3iPcc033A3Nl9aXz8gOOUC9Ezy5VfkUybU/47cHIsTLrJISO6g0ZNkcDN06rnRPsDJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:05:58.820639Z"},"content_sha256":"efd9c9443ec6b4b2a790e86aa3d799b12805ff4a5e3544c6a355a01aeafa4293","schema_version":"1.0","event_id":"sha256:efd9c9443ec6b4b2a790e86aa3d799b12805ff4a5e3544c6a355a01aeafa4293"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBR6AWCEZFECD2UPACJABLGT27/bundle.json","state_url":"https://pith.science/pith/RBR6AWCEZFECD2UPACJABLGT27/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBR6AWCEZFECD2UPACJABLGT27/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":"2026-06-04T03:05:58Z","links":{"resolver":"https://pith.science/pith/RBR6AWCEZFECD2UPACJABLGT27","bundle":"https://pith.science/pith/RBR6AWCEZFECD2UPACJABLGT27/bundle.json","state":"https://pith.science/pith/RBR6AWCEZFECD2UPACJABLGT27/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBR6AWCEZFECD2UPACJABLGT27/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RBR6AWCEZFECD2UPACJABLGT27","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":"5ebdef01f133be24263a96169f74014081ccdf37490402acb721f6f36367473f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-19T16:19:33Z","title_canon_sha256":"7f35d69b8b569ded1eeb53afe312c09015d49e287bb147b18a695b71494caf71"},"schema_version":"1.0","source":{"id":"1108.3995","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3995","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3995v2","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3995","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"RBR6AWCEZFEC","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RBR6AWCEZFECD2UP","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RBR6AWCE","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:efd9c9443ec6b4b2a790e86aa3d799b12805ff4a5e3544c6a355a01aeafa4293","target":"graph","created_at":"2026-05-18T03:51:48Z","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 Z^d in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from x to nearest neighbor x+e is the same as to nearest neighbor x-e. Assuming that the environment is genuinely d-dimensional and balanced we show a quenched invariance principle: for P almost every environment, the diffusive rescaled random walk converges to a Brownian motion with deterministic non-degenerate diffusion matrix. Within the i.i.d. setting, our result extend both Lawler's uniformly elliptic result and Guo and Zeitouni's elliptic result to the genera","authors_text":"Jean-Dominique Deuschel, Noam Berger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-19T16:19:33Z","title":"A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3995","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:b93a6aaa6558e6ddabb79e2a1196daacd88e2716b7f761fa56d9cf0b41f26834","target":"record","created_at":"2026-05-18T03:51:48Z","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":"5ebdef01f133be24263a96169f74014081ccdf37490402acb721f6f36367473f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-19T16:19:33Z","title_canon_sha256":"7f35d69b8b569ded1eeb53afe312c09015d49e287bb147b18a695b71494caf71"},"schema_version":"1.0","source":{"id":"1108.3995","kind":"arxiv","version":2}},"canonical_sha256":"8863e05844c94821ea8f009200acd3d7cedb5e6e5958b16102b957804175f477","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8863e05844c94821ea8f009200acd3d7cedb5e6e5958b16102b957804175f477","first_computed_at":"2026-05-18T03:51:48.825268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:48.825268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HEKzZy7fnJ0XWa53ziltH51UlG3chR5vtBepnuU0zITkjobDVP9lBxcOIHm1PVkY9N9AC4E8Sz2oGGkeCM+YCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:48.826073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3995","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b93a6aaa6558e6ddabb79e2a1196daacd88e2716b7f761fa56d9cf0b41f26834","sha256:efd9c9443ec6b4b2a790e86aa3d799b12805ff4a5e3544c6a355a01aeafa4293"],"state_sha256":"269c094adb9b435d9b48f7349a5d5972c02b15a8027abfc7159d1be505e8be68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rIQ9ioNQmb7LAetQizPi9Si/66gVB09PhOE0WDpLClrqdaWn9r5NiunNLsVpS1BEU2kXv+7wxx7Gtr+bla++Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:05:58.824032Z","bundle_sha256":"05c62d0db47f0ebb4cfb35bcef3171c554720207549edfcf0de50818704ed48a"}}