{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TZUD6WTKOW346L5YTD5XOQTUSV","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":"d20f056373b8c76351c5574a8b60301447e1b107fe474d4e8ef65a226200c68e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-28T20:29:08Z","title_canon_sha256":"55fb4337a7668bf0a664004740241e9cc2897328a858d9e3c0f387c1b885364f"},"schema_version":"1.0","source":{"id":"1403.7535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7535","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7535v1","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7535","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"pith_short_12","alias_value":"TZUD6WTKOW34","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TZUD6WTKOW346L5Y","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TZUD6WTK","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:720bc04c22a83a08b7ce7b9203450fbd3ac38908394cec3dae9fccfb6a7394db","target":"graph","created_at":"2026-05-18T02:55:19Z","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 apply the techniques developed in Comets and Popov (2003) to present a new proof to Sinai's theorem (Sinai, 1982) on one-dimensional random walk in random environment (RWRE), working in a scale-free way to avoid rescaling arguments and splitting the proof in two independent parts: a quenched one, related to the measure $P_\\omega$ conditioned on a fixed, typical realization $\\omega$ of the environment, and an annealed one, related to the product measure $\\mathbb{P}$ of the environment $\\omega$. The quenched part still holds even if we use another measure (possibly dependent) for the environm","authors_text":"Marcelo Ventura Freire","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-28T20:29:08Z","title":"Application of moderate deviation techniques to prove Sinai's Theorem on RWRE"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7535","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":"sha256:1c6c3ad3fc70e65e5de8ee9d9c5aaa43f17d2dc77af349f2eacf791b2876a12c","target":"record","created_at":"2026-05-18T02:55:19Z","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":"d20f056373b8c76351c5574a8b60301447e1b107fe474d4e8ef65a226200c68e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-28T20:29:08Z","title_canon_sha256":"55fb4337a7668bf0a664004740241e9cc2897328a858d9e3c0f387c1b885364f"},"schema_version":"1.0","source":{"id":"1403.7535","kind":"arxiv","version":1}},"canonical_sha256":"9e683f5a6a75b7cf2fb898fb7742749573347a747a0382d750d589cc2a761775","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e683f5a6a75b7cf2fb898fb7742749573347a747a0382d750d589cc2a761775","first_computed_at":"2026-05-18T02:55:19.151099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:19.151099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x34cZ+cp3rAfkmVpiRkHM3BcIXQ6te3jrn2MaLssIwRF3qGEM3o2zoECZ/J/QgtigLcJJ+lDyKKtSl4ccXjmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:19.151566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c6c3ad3fc70e65e5de8ee9d9c5aaa43f17d2dc77af349f2eacf791b2876a12c","sha256:720bc04c22a83a08b7ce7b9203450fbd3ac38908394cec3dae9fccfb6a7394db"],"state_sha256":"15bdef2cacb6362fcbe07ea6612299c05c937546906304f7a215d5578e190eb3"}