{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EHCN456WOATU3CNG6AI6ZJLTPM","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":"0d0ac8f73b4d6540dac5e12a95c55152633d605f8afebd4956768ef979f7bd50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-04T16:08:13Z","title_canon_sha256":"ae9a2d472fdc78e6f1194123e4e4acca9fe1fcfa46745d8540bdc2fdac86de0c"},"schema_version":"1.0","source":{"id":"1011.1196","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1196","created_at":"2026-05-18T03:44:05Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1196v2","created_at":"2026-05-18T03:44:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1196","created_at":"2026-05-18T03:44:05Z"},{"alias_kind":"pith_short_12","alias_value":"EHCN456WOATU","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EHCN456WOATU3CNG","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EHCN456W","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:f8abc476cc61ac9d0b21f0fc710fea4910c616b2d5deb7844c934ddfba493132","target":"graph","created_at":"2026-05-18T03:44:05Z","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 one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) we prove a quenched \\textit{conditional} invariance principle for the random walk, under the condition that it remains positive until time $n$. As a corollary of this result, we study the effect of conditioning the random walk to exceed level $n$ before returning to 0 as $n\\to \\infty$. One of the main tools for proving these conditional limit la","authors_text":"Christophe Gallesco, Serguei Popov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-04T16:08:13Z","title":"Conditional and uniform quenched CLTs for one-dimensional random walks among random conductances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1196","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":"sha256:3b8083aa02af8169805de4dd44389b28fd2462cbe607af7ff9da34cbc5017cb4","target":"record","created_at":"2026-05-18T03:44:05Z","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":"0d0ac8f73b4d6540dac5e12a95c55152633d605f8afebd4956768ef979f7bd50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-04T16:08:13Z","title_canon_sha256":"ae9a2d472fdc78e6f1194123e4e4acca9fe1fcfa46745d8540bdc2fdac86de0c"},"schema_version":"1.0","source":{"id":"1011.1196","kind":"arxiv","version":2}},"canonical_sha256":"21c4de77d670274d89a6f011eca5737b1c85ec1320b0aeafabbb854a493095a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21c4de77d670274d89a6f011eca5737b1c85ec1320b0aeafabbb854a493095a3","first_computed_at":"2026-05-18T03:44:05.227677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:05.227677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fWhL5zBMLF1c7yxU4jQItDGUeoYxJ1WpcO7l1P2buQVGufhJLPb36XUqQBLXkpwzN6/PMRWg+S2msLJB/Wu7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:05.228373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1196","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b8083aa02af8169805de4dd44389b28fd2462cbe607af7ff9da34cbc5017cb4","sha256:f8abc476cc61ac9d0b21f0fc710fea4910c616b2d5deb7844c934ddfba493132"],"state_sha256":"1bb0097cbfca5736bcb1d9fe93a9b87402302fdae0b5c01c4bb1f15d467e46b8"}