{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:7MEPXDO46R5ATFO2JRAYXHEBMP","short_pith_number":"pith:7MEPXDO4","canonical_record":{"source":{"id":"0907.3680","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-21T15:13:42Z","cross_cats_sorted":[],"title_canon_sha256":"64e66bb960c318122221f1c473253d6d9ddc23c591c124a611b8ab5b49fcc09d","abstract_canon_sha256":"fe68c4d2016248fbcdba54d515913ffe83660b9e5d8ac96b9cd1e7846c25d619"},"schema_version":"1.0"},"canonical_sha256":"fb08fb8ddcf47a0995da4c418b9c8163c66fb0a1d2ccec52769ba09bbf38a941","source":{"kind":"arxiv","id":"0907.3680","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.3680","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"0907.3680v2","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.3680","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"7MEPXDO46R5A","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7MEPXDO46R5ATFO2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7MEPXDO4","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:7MEPXDO46R5ATFO2JRAYXHEBMP","target":"record","payload":{"canonical_record":{"source":{"id":"0907.3680","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-21T15:13:42Z","cross_cats_sorted":[],"title_canon_sha256":"64e66bb960c318122221f1c473253d6d9ddc23c591c124a611b8ab5b49fcc09d","abstract_canon_sha256":"fe68c4d2016248fbcdba54d515913ffe83660b9e5d8ac96b9cd1e7846c25d619"},"schema_version":"1.0"},"canonical_sha256":"fb08fb8ddcf47a0995da4c418b9c8163c66fb0a1d2ccec52769ba09bbf38a941","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:36.849135Z","signature_b64":"FTi5LDJ3y0iLHXwegwUmWzuKwt0QOarTpsz++DmZYsrD/bi6fQMKOOtmmy5VKtuvtuH7RokpDdxx3P+R7N5DBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb08fb8ddcf47a0995da4c418b9c8163c66fb0a1d2ccec52769ba09bbf38a941","last_reissued_at":"2026-05-18T01:12:36.848725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:36.848725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.3680","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":"2026-05-18T01:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wl/DunzPXBQDJ8ybBV0DsgrC8XBHQtEO3PmCq4rwGse0jTMNlWysLE2QzVnBZYEpJ1LXWDouy8IQ+5XJRh62Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:35:33.854577Z"},"content_sha256":"b2849fce199410cce21799c5b361fda6a569d28966f5f7b18d47b54fe0767d31","schema_version":"1.0","event_id":"sha256:b2849fce199410cce21799c5b361fda6a569d28966f5f7b18d47b54fe0767d31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:7MEPXDO46R5ATFO2JRAYXHEBMP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Systems of one-dimensional random walks in a common random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathon Peterson","submitted_at":"2009-07-21T15:13:42Z","abstract_excerpt":"We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at least one of the random walks started in the interval $[An, Bn]$ has traveled a distance of less than $(v_P - \\epsilon)n$. This leads to both a uniform law of large numbers and a hydrodynamic limit. We also identify a family of distributions on the configuration of particles (parameterized by particle density) which are stationary under the (quenched) dynamics o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.3680","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":"2026-05-18T01:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/gcddyyPZaUHVNOaaKmlJBp+QnFGD8UhtMRqoUZozhhEFzdRSKh5TXaizLbBhg4IKcMLxzM+/61qFtxWErQyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:35:33.854908Z"},"content_sha256":"2d4e60f6d35647a32d0c31276f40407de8aa9bc59a918f98b0c51bc19c9e055f","schema_version":"1.0","event_id":"sha256:2d4e60f6d35647a32d0c31276f40407de8aa9bc59a918f98b0c51bc19c9e055f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7MEPXDO46R5ATFO2JRAYXHEBMP/bundle.json","state_url":"https://pith.science/pith/7MEPXDO46R5ATFO2JRAYXHEBMP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7MEPXDO46R5ATFO2JRAYXHEBMP/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":"2026-06-20T07:35:33Z","links":{"resolver":"https://pith.science/pith/7MEPXDO46R5ATFO2JRAYXHEBMP","bundle":"https://pith.science/pith/7MEPXDO46R5ATFO2JRAYXHEBMP/bundle.json","state":"https://pith.science/pith/7MEPXDO46R5ATFO2JRAYXHEBMP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7MEPXDO46R5ATFO2JRAYXHEBMP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7MEPXDO46R5ATFO2JRAYXHEBMP","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":"fe68c4d2016248fbcdba54d515913ffe83660b9e5d8ac96b9cd1e7846c25d619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-21T15:13:42Z","title_canon_sha256":"64e66bb960c318122221f1c473253d6d9ddc23c591c124a611b8ab5b49fcc09d"},"schema_version":"1.0","source":{"id":"0907.3680","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.3680","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"0907.3680v2","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.3680","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"7MEPXDO46R5A","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7MEPXDO46R5ATFO2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7MEPXDO4","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:2d4e60f6d35647a32d0c31276f40407de8aa9bc59a918f98b0c51bc19c9e055f","target":"graph","created_at":"2026-05-18T01:12:36Z","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 consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at least one of the random walks started in the interval $[An, Bn]$ has traveled a distance of less than $(v_P - \\epsilon)n$. This leads to both a uniform law of large numbers and a hydrodynamic limit. We also identify a family of distributions on the configuration of particles (parameterized by particle density) which are stationary under the (quenched) dynamics o","authors_text":"Jonathon Peterson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-21T15:13:42Z","title":"Systems of one-dimensional random walks in a common random environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.3680","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:b2849fce199410cce21799c5b361fda6a569d28966f5f7b18d47b54fe0767d31","target":"record","created_at":"2026-05-18T01:12:36Z","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":"fe68c4d2016248fbcdba54d515913ffe83660b9e5d8ac96b9cd1e7846c25d619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-21T15:13:42Z","title_canon_sha256":"64e66bb960c318122221f1c473253d6d9ddc23c591c124a611b8ab5b49fcc09d"},"schema_version":"1.0","source":{"id":"0907.3680","kind":"arxiv","version":2}},"canonical_sha256":"fb08fb8ddcf47a0995da4c418b9c8163c66fb0a1d2ccec52769ba09bbf38a941","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb08fb8ddcf47a0995da4c418b9c8163c66fb0a1d2ccec52769ba09bbf38a941","first_computed_at":"2026-05-18T01:12:36.848725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:36.848725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FTi5LDJ3y0iLHXwegwUmWzuKwt0QOarTpsz++DmZYsrD/bi6fQMKOOtmmy5VKtuvtuH7RokpDdxx3P+R7N5DBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:36.849135Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.3680","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2849fce199410cce21799c5b361fda6a569d28966f5f7b18d47b54fe0767d31","sha256:2d4e60f6d35647a32d0c31276f40407de8aa9bc59a918f98b0c51bc19c9e055f"],"state_sha256":"c596350b3b4d70531c9d45413500443764c551b857d17947407e4c04e13d9c88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bk+iknykRkbRlwX9Sn7o9C9eDFaW9o/Rim/sEJAb2/mPajGwJjAqBROFCvcWInEQpvnOI2vCEplSMZ4amrjKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:35:33.856661Z","bundle_sha256":"aa7334e72edb980cb31443c6d9eaf3edb601f8965bd01e19cc2039a23d863456"}}