{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GCW5MX2LFBTLP55YSHXRVZZMLP","short_pith_number":"pith:GCW5MX2L","canonical_record":{"source":{"id":"1110.4865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-21T18:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"62b92f9710aa2d01326a36d51df365b842328a620c83e3c9d0b7711b0a34d443","abstract_canon_sha256":"1813deb77e692e5308cfd55044e2ad89e3e694be4e417e6969fc8353409f6dc0"},"schema_version":"1.0"},"canonical_sha256":"30add65f4b2866b7f7b891ef1ae72c5bda5253c87d67d3947202059a71078131","source":{"kind":"arxiv","id":"1110.4865","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4865","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4865v2","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4865","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"GCW5MX2LFBTL","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GCW5MX2LFBTLP55Y","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GCW5MX2L","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GCW5MX2LFBTLP55YSHXRVZZMLP","target":"record","payload":{"canonical_record":{"source":{"id":"1110.4865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-21T18:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"62b92f9710aa2d01326a36d51df365b842328a620c83e3c9d0b7711b0a34d443","abstract_canon_sha256":"1813deb77e692e5308cfd55044e2ad89e3e694be4e417e6969fc8353409f6dc0"},"schema_version":"1.0"},"canonical_sha256":"30add65f4b2866b7f7b891ef1ae72c5bda5253c87d67d3947202059a71078131","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:03.323546Z","signature_b64":"T2xV6/q6pCNZoxqtmi4SGzDpTeAhmK3FnxrQjDKkXGNhBJbH5e8QuOcpWlCeIH0NrMwsfpIz6Y8NyWLvfyqQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30add65f4b2866b7f7b891ef1ae72c5bda5253c87d67d3947202059a71078131","last_reissued_at":"2026-05-18T03:40:03.323065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:03.323065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.4865","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":"2026-05-18T03:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5dDpahOPyWHqqd+jM2c92gAPIkVwZyOQcg11MenxxXkhN283rgyimCuDMcrTJTyfYecLaxry4nuugs7ybLhGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:20:51.067570Z"},"content_sha256":"4b73b8c817c851155da0e5ca78346b2e829e52afce0041488a7d323a3fc4bb5b","schema_version":"1.0","event_id":"sha256:4b73b8c817c851155da0e5ca78346b2e829e52afce0041488a7d323a3fc4bb5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GCW5MX2LFBTLP55YSHXRVZZMLP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random walk in random environment in a two-dimensional stratified medium with orientations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexis Devulder (LM-Versailles), Francoise Pene (LM)","submitted_at":"2011-10-21T18:47:05Z","abstract_excerpt":"We consider a model of random walk in ${\\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed orientations under general hypotheses. This contrasts with the model of Campanino and Petritis, in which probabilities to stay on these lines are all equal. We also establish a result of convergence in distribution for this walk with suitable normalizations under more precise assumptions. In particular, our model proves to be, in many cases, even more superdiffusi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4865","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":"2026-05-18T03:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Zskooq+4uRNwxYatTo1THajBY0FPnziEj1eXlkaZmd7Y+rl1/piTE8/hnBtg26eZ3W6REANpDSFz1Av96lcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:20:51.067922Z"},"content_sha256":"264278bed3a4aa7f1d6f81a1f98e592b63da6cec009f7be4c15d45178f688221","schema_version":"1.0","event_id":"sha256:264278bed3a4aa7f1d6f81a1f98e592b63da6cec009f7be4c15d45178f688221"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCW5MX2LFBTLP55YSHXRVZZMLP/bundle.json","state_url":"https://pith.science/pith/GCW5MX2LFBTLP55YSHXRVZZMLP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCW5MX2LFBTLP55YSHXRVZZMLP/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":"2026-06-27T06:20:51Z","links":{"resolver":"https://pith.science/pith/GCW5MX2LFBTLP55YSHXRVZZMLP","bundle":"https://pith.science/pith/GCW5MX2LFBTLP55YSHXRVZZMLP/bundle.json","state":"https://pith.science/pith/GCW5MX2LFBTLP55YSHXRVZZMLP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCW5MX2LFBTLP55YSHXRVZZMLP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GCW5MX2LFBTLP55YSHXRVZZMLP","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":"1813deb77e692e5308cfd55044e2ad89e3e694be4e417e6969fc8353409f6dc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-21T18:47:05Z","title_canon_sha256":"62b92f9710aa2d01326a36d51df365b842328a620c83e3c9d0b7711b0a34d443"},"schema_version":"1.0","source":{"id":"1110.4865","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4865","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4865v2","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4865","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"GCW5MX2LFBTL","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GCW5MX2LFBTLP55Y","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GCW5MX2L","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:264278bed3a4aa7f1d6f81a1f98e592b63da6cec009f7be4c15d45178f688221","target":"graph","created_at":"2026-05-18T03:40:03Z","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 model of random walk in ${\\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed orientations under general hypotheses. This contrasts with the model of Campanino and Petritis, in which probabilities to stay on these lines are all equal. We also establish a result of convergence in distribution for this walk with suitable normalizations under more precise assumptions. In particular, our model proves to be, in many cases, even more superdiffusi","authors_text":"Alexis Devulder (LM-Versailles), Francoise Pene (LM)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-21T18:47:05Z","title":"Random walk in random environment in a two-dimensional stratified medium with orientations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4865","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":"sha256:4b73b8c817c851155da0e5ca78346b2e829e52afce0041488a7d323a3fc4bb5b","target":"record","created_at":"2026-05-18T03:40:03Z","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":"1813deb77e692e5308cfd55044e2ad89e3e694be4e417e6969fc8353409f6dc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-21T18:47:05Z","title_canon_sha256":"62b92f9710aa2d01326a36d51df365b842328a620c83e3c9d0b7711b0a34d443"},"schema_version":"1.0","source":{"id":"1110.4865","kind":"arxiv","version":2}},"canonical_sha256":"30add65f4b2866b7f7b891ef1ae72c5bda5253c87d67d3947202059a71078131","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30add65f4b2866b7f7b891ef1ae72c5bda5253c87d67d3947202059a71078131","first_computed_at":"2026-05-18T03:40:03.323065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:03.323065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T2xV6/q6pCNZoxqtmi4SGzDpTeAhmK3FnxrQjDKkXGNhBJbH5e8QuOcpWlCeIH0NrMwsfpIz6Y8NyWLvfyqQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:03.323546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4865","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b73b8c817c851155da0e5ca78346b2e829e52afce0041488a7d323a3fc4bb5b","sha256:264278bed3a4aa7f1d6f81a1f98e592b63da6cec009f7be4c15d45178f688221"],"state_sha256":"657e50d615779d8f8a035f3dbef34ffb4c263c638abecd887e89aabedb78fda4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OEaeIunH6Piv7eH7QOMnl56nII1K6tXD23vnZTLvZGkZsyAgdpxI5LaGyUmVpuK7p68k8nihgSuerjzq7CDyAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T06:20:51.069777Z","bundle_sha256":"16f575c19bddb0b9e2f830248fa97170bf024b19b582d7c1801db657d72e4000"}}