{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NDKJVROHS4PUID76C7QP7IPYNY","short_pith_number":"pith:NDKJVROH","canonical_record":{"source":{"id":"1508.07144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-28T09:31:17Z","cross_cats_sorted":[],"title_canon_sha256":"07a8ffd24323d6fb39c274eb72969142fe091406ce3ab2643da6357f35ecb293","abstract_canon_sha256":"ac3122b33631fb89906d0ea811dfceced13f3a167d38ef417789bf4dc4df07e3"},"schema_version":"1.0"},"canonical_sha256":"68d49ac5c7971f440ffe17e0ffa1f86e38eac32357ed1f3a89e9138920832493","source":{"kind":"arxiv","id":"1508.07144","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07144","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07144v1","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07144","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"NDKJVROHS4PU","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NDKJVROHS4PUID76","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NDKJVROH","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NDKJVROHS4PUID76C7QP7IPYNY","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-28T09:31:17Z","cross_cats_sorted":[],"title_canon_sha256":"07a8ffd24323d6fb39c274eb72969142fe091406ce3ab2643da6357f35ecb293","abstract_canon_sha256":"ac3122b33631fb89906d0ea811dfceced13f3a167d38ef417789bf4dc4df07e3"},"schema_version":"1.0"},"canonical_sha256":"68d49ac5c7971f440ffe17e0ffa1f86e38eac32357ed1f3a89e9138920832493","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:36.788525Z","signature_b64":"Y4Hyokb1c13aIR9gAT7R7DsxmUTBGB519BPMG//DISJCWG03dhnhsq4IfBNSCvrPgZGVMcv+pYq9PXoFSkg3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68d49ac5c7971f440ffe17e0ffa1f86e38eac32357ed1f3a89e9138920832493","last_reissued_at":"2026-05-18T01:34:36.787859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:36.787859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07144","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DfIwoqJyN/R1SM/Yfxz7ksROfC0WF2VTo4JCQXRxhxGsyeYSghfv6JFHpR0rX4RBpajrHzB7lMJRTGH/nQ+DBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:26:32.718867Z"},"content_sha256":"47d5d47873e051f309ee511b62e13b75a47b4a93793ace812e626151ab2755ca","schema_version":"1.0","event_id":"sha256:47d5d47873e051f309ee511b62e13b75a47b4a93793ace812e626151ab2755ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NDKJVROHS4PUID76C7QP7IPYNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Persistence exponent for random walk on directed versions of $Z^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fran\\c{c}oise P\\`ene, Nadine Guillotin-Plantard","submitted_at":"2015-08-28T09:31:17Z","abstract_excerpt":"We study the persistence exponent for random walks in random sceneries (RWRS) with integer values and for some special random walks in random environment in $\\mathbb Z^2$ including random walks in $\\mathbb Z^2$ with random orientations of the horizontal layers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07144","kind":"arxiv","version":1},"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":"2026-05-18T01:34:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8C6QgKwPJMft/HazB2Ffp9e66HY96moTBcy3hECgCeLDmKytVg2eESrqYkOkDm2yi49/NmWuBO4qD4hXRZvMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:26:32.719208Z"},"content_sha256":"312b8cc6ac3c8a187810980b62e455908e4740facf0447e9deb98c1a4fb9da5a","schema_version":"1.0","event_id":"sha256:312b8cc6ac3c8a187810980b62e455908e4740facf0447e9deb98c1a4fb9da5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NDKJVROHS4PUID76C7QP7IPYNY/bundle.json","state_url":"https://pith.science/pith/NDKJVROHS4PUID76C7QP7IPYNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NDKJVROHS4PUID76C7QP7IPYNY/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":"2026-06-24T02:26:32Z","links":{"resolver":"https://pith.science/pith/NDKJVROHS4PUID76C7QP7IPYNY","bundle":"https://pith.science/pith/NDKJVROHS4PUID76C7QP7IPYNY/bundle.json","state":"https://pith.science/pith/NDKJVROHS4PUID76C7QP7IPYNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NDKJVROHS4PUID76C7QP7IPYNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NDKJVROHS4PUID76C7QP7IPYNY","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":"ac3122b33631fb89906d0ea811dfceced13f3a167d38ef417789bf4dc4df07e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-28T09:31:17Z","title_canon_sha256":"07a8ffd24323d6fb39c274eb72969142fe091406ce3ab2643da6357f35ecb293"},"schema_version":"1.0","source":{"id":"1508.07144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07144","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07144v1","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07144","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"NDKJVROHS4PU","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NDKJVROHS4PUID76","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NDKJVROH","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:312b8cc6ac3c8a187810980b62e455908e4740facf0447e9deb98c1a4fb9da5a","target":"graph","created_at":"2026-05-18T01:34:36Z","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 study the persistence exponent for random walks in random sceneries (RWRS) with integer values and for some special random walks in random environment in $\\mathbb Z^2$ including random walks in $\\mathbb Z^2$ with random orientations of the horizontal layers.","authors_text":"Fran\\c{c}oise P\\`ene, Nadine Guillotin-Plantard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-28T09:31:17Z","title":"Persistence exponent for random walk on directed versions of $Z^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07144","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":"sha256:47d5d47873e051f309ee511b62e13b75a47b4a93793ace812e626151ab2755ca","target":"record","created_at":"2026-05-18T01:34:36Z","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":"ac3122b33631fb89906d0ea811dfceced13f3a167d38ef417789bf4dc4df07e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-28T09:31:17Z","title_canon_sha256":"07a8ffd24323d6fb39c274eb72969142fe091406ce3ab2643da6357f35ecb293"},"schema_version":"1.0","source":{"id":"1508.07144","kind":"arxiv","version":1}},"canonical_sha256":"68d49ac5c7971f440ffe17e0ffa1f86e38eac32357ed1f3a89e9138920832493","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68d49ac5c7971f440ffe17e0ffa1f86e38eac32357ed1f3a89e9138920832493","first_computed_at":"2026-05-18T01:34:36.787859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:36.787859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y4Hyokb1c13aIR9gAT7R7DsxmUTBGB519BPMG//DISJCWG03dhnhsq4IfBNSCvrPgZGVMcv+pYq9PXoFSkg3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:36.788525Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47d5d47873e051f309ee511b62e13b75a47b4a93793ace812e626151ab2755ca","sha256:312b8cc6ac3c8a187810980b62e455908e4740facf0447e9deb98c1a4fb9da5a"],"state_sha256":"826249619ca1648aade2d3506d11cd6c50e0fc99c2af13afaaa86380e06b3883"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"da5PVB3Iu+arLeEP2R+/qiG/RTV6v7fRNHfdjs/oRGd/ois7efbF+7F4MZgmB+65xduhSWYWN3KN2wp2h3jdDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T02:26:32.721140Z","bundle_sha256":"1fb4e05b3fe7b370d8747cba8be4840f722c471dd3537c76b0119c69c6026c2b"}}