{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ELO6GFQZIS7E3TTQCHZ5EJANMP","short_pith_number":"pith:ELO6GFQZ","canonical_record":{"source":{"id":"1508.02542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-11T09:58:00Z","cross_cats_sorted":[],"title_canon_sha256":"14c88e2342faf24f86d666b1db6de1f9fdd9286d3bfa77e1ed63d664bc8ad2bf","abstract_canon_sha256":"a5db2ac8810d2d55449ab13dde5c1c5cc765ca3e4c49ffa51394bf478ca4a619"},"schema_version":"1.0"},"canonical_sha256":"22dde3161944be4dce7011f3d2240d63e607bd4f97fae80e35527336bd35f5f1","source":{"kind":"arxiv","id":"1508.02542","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02542","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02542v1","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02542","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"pith_short_12","alias_value":"ELO6GFQZIS7E","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ELO6GFQZIS7E3TTQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ELO6GFQZ","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ELO6GFQZIS7E3TTQCHZ5EJANMP","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-11T09:58:00Z","cross_cats_sorted":[],"title_canon_sha256":"14c88e2342faf24f86d666b1db6de1f9fdd9286d3bfa77e1ed63d664bc8ad2bf","abstract_canon_sha256":"a5db2ac8810d2d55449ab13dde5c1c5cc765ca3e4c49ffa51394bf478ca4a619"},"schema_version":"1.0"},"canonical_sha256":"22dde3161944be4dce7011f3d2240d63e607bd4f97fae80e35527336bd35f5f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:28.895412Z","signature_b64":"0jyHIvPMYyr4U7qKqaPiLRB+jQH1nrT3KCKehaLTLEzo2RZisgTOyONaQPr8TxZq8iSh4AwJg7z+bJ8gdmVyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22dde3161944be4dce7011f3d2240d63e607bd4f97fae80e35527336bd35f5f1","last_reissued_at":"2026-05-18T01:35:28.894829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:28.894829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02542","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":"2026-05-18T01:35:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ME6banTVVO8HRvKfvPW9jNozvJR7w+efk02W/O6YY0PipUglfRPW3WO4y71ssm9DY0EVKX/PTrLRxWdbuo5SDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:29:47.357824Z"},"content_sha256":"fb9f79f50aa5cd4e9972fc0589b41eeb4a7df6b4979a3d00a5581db9e08f9acb","schema_version":"1.0","event_id":"sha256:fb9f79f50aa5cd4e9972fc0589b41eeb4a7df6b4979a3d00a5581db9e08f9acb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ELO6GFQZIS7E3TTQCHZ5EJANMP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the range of the Campanino and P\\'etritis random walk","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":"2015-08-11T09:58:00Z","abstract_excerpt":"We are interested in the behaviour of the range of the Campanino and P\\'etritis random walk, namely a simple random walk on the lattice $\\mathbb Z^2$ with random orientations of the horizontal layers. We also study the range of random walks in random scenery, from which the asymptotic behaviour of the range of the first coordinate of the Campanino and P\\'etritis random walk can be deduced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02542","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":"2026-05-18T01:35:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"az7eUukDDlSCslvcLyiYCAeKM+gDjgaStp1zN0QVGW7mxnfhPxTWNirWNpfRGBY8fIpDFeqNIZT5cDmCu8arCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:29:47.358161Z"},"content_sha256":"f24d81edaff58bedde746ff58707e319ba0559f3d00094a0bb77e3f128178d6b","schema_version":"1.0","event_id":"sha256:f24d81edaff58bedde746ff58707e319ba0559f3d00094a0bb77e3f128178d6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELO6GFQZIS7E3TTQCHZ5EJANMP/bundle.json","state_url":"https://pith.science/pith/ELO6GFQZIS7E3TTQCHZ5EJANMP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELO6GFQZIS7E3TTQCHZ5EJANMP/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":"2026-06-24T02:29:47Z","links":{"resolver":"https://pith.science/pith/ELO6GFQZIS7E3TTQCHZ5EJANMP","bundle":"https://pith.science/pith/ELO6GFQZIS7E3TTQCHZ5EJANMP/bundle.json","state":"https://pith.science/pith/ELO6GFQZIS7E3TTQCHZ5EJANMP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELO6GFQZIS7E3TTQCHZ5EJANMP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ELO6GFQZIS7E3TTQCHZ5EJANMP","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":"a5db2ac8810d2d55449ab13dde5c1c5cc765ca3e4c49ffa51394bf478ca4a619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-11T09:58:00Z","title_canon_sha256":"14c88e2342faf24f86d666b1db6de1f9fdd9286d3bfa77e1ed63d664bc8ad2bf"},"schema_version":"1.0","source":{"id":"1508.02542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02542","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02542v1","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02542","created_at":"2026-05-18T01:35:28Z"},{"alias_kind":"pith_short_12","alias_value":"ELO6GFQZIS7E","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ELO6GFQZIS7E3TTQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ELO6GFQZ","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:f24d81edaff58bedde746ff58707e319ba0559f3d00094a0bb77e3f128178d6b","target":"graph","created_at":"2026-05-18T01:35:28Z","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 are interested in the behaviour of the range of the Campanino and P\\'etritis random walk, namely a simple random walk on the lattice $\\mathbb Z^2$ with random orientations of the horizontal layers. We also study the range of random walks in random scenery, from which the asymptotic behaviour of the range of the first coordinate of the Campanino and P\\'etritis random walk can be deduced.","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":"2015-08-11T09:58:00Z","title":"On the range of the Campanino and P\\'etritis random walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02542","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:fb9f79f50aa5cd4e9972fc0589b41eeb4a7df6b4979a3d00a5581db9e08f9acb","target":"record","created_at":"2026-05-18T01:35:28Z","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":"a5db2ac8810d2d55449ab13dde5c1c5cc765ca3e4c49ffa51394bf478ca4a619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-11T09:58:00Z","title_canon_sha256":"14c88e2342faf24f86d666b1db6de1f9fdd9286d3bfa77e1ed63d664bc8ad2bf"},"schema_version":"1.0","source":{"id":"1508.02542","kind":"arxiv","version":1}},"canonical_sha256":"22dde3161944be4dce7011f3d2240d63e607bd4f97fae80e35527336bd35f5f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22dde3161944be4dce7011f3d2240d63e607bd4f97fae80e35527336bd35f5f1","first_computed_at":"2026-05-18T01:35:28.894829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:28.894829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0jyHIvPMYyr4U7qKqaPiLRB+jQH1nrT3KCKehaLTLEzo2RZisgTOyONaQPr8TxZq8iSh4AwJg7z+bJ8gdmVyDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:28.895412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb9f79f50aa5cd4e9972fc0589b41eeb4a7df6b4979a3d00a5581db9e08f9acb","sha256:f24d81edaff58bedde746ff58707e319ba0559f3d00094a0bb77e3f128178d6b"],"state_sha256":"cfe850520afe06d672aac5f14f4bdd352074eacc41843616affe70efac4f6d66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"60sj5vpLjHfehc4N8tAeI0fzj/9n3Ov5ena6WRsEVa0Z2l/ilv9kFudi+aLfozvaAxk/I7Z+hgv3892e90wFAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T02:29:47.360074Z","bundle_sha256":"fbd8573c74a07556abeda18051b04165d9bd24f3e8af0fed117218ad5cb562f3"}}