{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OZLCWIO3KFFIUSYFLLLCVR254N","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":"3c2b1c8f25a5094f3756afbdc6e55a5a96a9e87031abb2bffd917b0461f3dcec","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-26T18:35:47Z","title_canon_sha256":"676af2ff15c148030929401ab747b047c9c07c039f0e1b2ac9f94bc5df77ea68"},"schema_version":"1.0","source":{"id":"1602.08428","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08428","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08428v2","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08428","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"OZLCWIO3KFFI","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OZLCWIO3KFFIUSYF","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OZLCWIO3","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:e9e8c30c08e3e7c42fc03aea34bab8fa01921ff24fdb4657d3d9960ab543aac0","target":"graph","created_at":"2026-05-18T00:25:27Z","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 stationary and ergodic random field $\\{\\omega(e) : e \\in E_d\\}$ that is parameterized by the edge set of the Euclidean lattice $\\mathbb{Z}^d$, $d \\geq 2$. The random variable $\\omega(e)$, taking values in $[0, \\infty)$ and satisfying certain moment bounds, is thought of as the conductance of the edge $e$. Assuming that the set of edges with positive conductances give rise to a unique infinite cluster $\\mathcal{C}_{\\infty}(\\omega)$, we prove a quenched invariance principle for the continuous-time random walk among random conductances under relatively mild conditions on the structu","authors_text":"Jean-Dominique Deuschel, Martin Slowik, Tuan Anh Nguyen","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-26T18:35:47Z","title":"Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08428","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":"sha256:62134d9c6a8a1b79860f3b009f2cad2fe952553851018d44728633b3d1d35fad","target":"record","created_at":"2026-05-18T00:25:27Z","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":"3c2b1c8f25a5094f3756afbdc6e55a5a96a9e87031abb2bffd917b0461f3dcec","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-26T18:35:47Z","title_canon_sha256":"676af2ff15c148030929401ab747b047c9c07c039f0e1b2ac9f94bc5df77ea68"},"schema_version":"1.0","source":{"id":"1602.08428","kind":"arxiv","version":2}},"canonical_sha256":"76562b21db514a8a4b055ad62ac75de3590a36accc0daf4700e1f08c5cfefbdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76562b21db514a8a4b055ad62ac75de3590a36accc0daf4700e1f08c5cfefbdd","first_computed_at":"2026-05-18T00:25:27.303348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:27.303348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"53wndaxnUKub23RTL1YThFn3yGNcTD1zHZs5ijTNaHo8iRDqmOqdn4kuZpBqsK7IAxA8MasPRTiyCY/WSKWjAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:27.304046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08428","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62134d9c6a8a1b79860f3b009f2cad2fe952553851018d44728633b3d1d35fad","sha256:e9e8c30c08e3e7c42fc03aea34bab8fa01921ff24fdb4657d3d9960ab543aac0"],"state_sha256":"b6708a3711fd20c90c8f882273b537731c228e39273f422da5cc8646b85958c8"}