{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JIDYH7DQDJLR36SLHTQO6GNQJX","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":"118a99a891a831a8ad3671282cd65f4f07421f5d51df0454bbc42ef5f5fc071a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-13T13:28:31Z","title_canon_sha256":"16ca6c7dd351ce25c457b8bcf54390b88146467fa366f3dd26fe25349c7479b7"},"schema_version":"1.0","source":{"id":"1211.2987","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2987","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2987v1","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2987","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"JIDYH7DQDJLR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JIDYH7DQDJLR36SL","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JIDYH7DQ","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:97816f6130a5cecc16153992340c993df226855c82bfd7e9de3c20ae0056eb36","target":"graph","created_at":"2026-05-18T02:53:17Z","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 a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i) points endowed with probabilities drawn from a symmetric distribution with heavy tails at 0 and 1, and (ii) `fast points' with a fixed systematic drift. Without these fast points, the model is related to the diffusion in heavy-tailed (`stable') random potential studied by Schumacher and Singh; the fast points perturb that model. The two components compete to d","authors_text":"Andrew R. Wade, Mikhail V. Menshikov, Ostap Hryniv","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-13T13:28:31Z","title":"Random walk in mixed random environment without uniform ellipticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2987","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":"sha256:77f0680eeaaf0d75de20d83f59e306ad1ec87c08bedaeed92e549ac51b2cef42","target":"record","created_at":"2026-05-18T02:53:17Z","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":"118a99a891a831a8ad3671282cd65f4f07421f5d51df0454bbc42ef5f5fc071a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-13T13:28:31Z","title_canon_sha256":"16ca6c7dd351ce25c457b8bcf54390b88146467fa366f3dd26fe25349c7479b7"},"schema_version":"1.0","source":{"id":"1211.2987","kind":"arxiv","version":1}},"canonical_sha256":"4a0783fc701a571dfa4b3ce0ef19b04df8b26daa3feaf369a3ebeb786121c05c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a0783fc701a571dfa4b3ce0ef19b04df8b26daa3feaf369a3ebeb786121c05c","first_computed_at":"2026-05-18T02:53:17.727414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:17.727414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LQpAuCpo3jJp9AHROZWNcXIixbmZCNuG6EFBSuFB/KY2yDXJHnFB6j89xEi/i4RQKP3JIJBhgvXN4rsD0KrxCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:17.728203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2987","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77f0680eeaaf0d75de20d83f59e306ad1ec87c08bedaeed92e549ac51b2cef42","sha256:97816f6130a5cecc16153992340c993df226855c82bfd7e9de3c20ae0056eb36"],"state_sha256":"e2c7525e24dd7b855b7e40a1899b055c24f8ee14be8b6e5b83d3bd890588b41f"}