{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:L7YGPDRRTVEEJBACXCIQC7J7IT","short_pith_number":"pith:L7YGPDRR","schema_version":"1.0","canonical_sha256":"5ff0678e319d48448402b891017d3f44c2e092948f7eab78d162aae959989073","source":{"kind":"arxiv","id":"1210.2371","version":3},"attestation_state":"computed","paper":{"title":"A central limit theorem for the effective conductance: Linear boundary data and small ellipticity contrasts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NA"],"primary_cat":"math.PR","authors_text":"Marek Biskup, Michele Salvi, Tilman Wolff","submitted_at":"2012-10-08T18:27:22Z","abstract_excerpt":"Given a resistor network on $\\mathbb Z^d$ with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central limit theorem holds. The "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.2371","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-08T18:27:22Z","cross_cats_sorted":["math-ph","math.MP","math.NA"],"title_canon_sha256":"b7bdc3f71c2cf630b39a9bf16c2360ddebb4160cf0dfe13a2a4f1416e599c8a5","abstract_canon_sha256":"ae8e8975cc7992526a6e1e1c762ff6feb41459ff16a848b01853a2c458288174"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:17.357185Z","signature_b64":"NjzyRbq9tW32fcpvwkUhV4+z26+5Hq8X7vDbgmhKo52uYuCm8P+c+ahOBS3hPiGNwRUtLDPrIc0gn2yuzwCOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ff0678e319d48448402b891017d3f44c2e092948f7eab78d162aae959989073","last_reissued_at":"2026-05-18T02:39:17.356655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:17.356655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A central limit theorem for the effective conductance: Linear boundary data and small ellipticity contrasts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NA"],"primary_cat":"math.PR","authors_text":"Marek Biskup, Michele Salvi, Tilman Wolff","submitted_at":"2012-10-08T18:27:22Z","abstract_excerpt":"Given a resistor network on $\\mathbb Z^d$ with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central limit theorem holds. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2371","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.2371","created_at":"2026-05-18T02:39:17.356749+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.2371v3","created_at":"2026-05-18T02:39:17.356749+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2371","created_at":"2026-05-18T02:39:17.356749+00:00"},{"alias_kind":"pith_short_12","alias_value":"L7YGPDRRTVEE","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"L7YGPDRRTVEEJBAC","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"L7YGPDRR","created_at":"2026-05-18T12:27:14.488303+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L7YGPDRRTVEEJBACXCIQC7J7IT","json":"https://pith.science/pith/L7YGPDRRTVEEJBACXCIQC7J7IT.json","graph_json":"https://pith.science/api/pith-number/L7YGPDRRTVEEJBACXCIQC7J7IT/graph.json","events_json":"https://pith.science/api/pith-number/L7YGPDRRTVEEJBACXCIQC7J7IT/events.json","paper":"https://pith.science/paper/L7YGPDRR"},"agent_actions":{"view_html":"https://pith.science/pith/L7YGPDRRTVEEJBACXCIQC7J7IT","download_json":"https://pith.science/pith/L7YGPDRRTVEEJBACXCIQC7J7IT.json","view_paper":"https://pith.science/paper/L7YGPDRR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.2371&json=true","fetch_graph":"https://pith.science/api/pith-number/L7YGPDRRTVEEJBACXCIQC7J7IT/graph.json","fetch_events":"https://pith.science/api/pith-number/L7YGPDRRTVEEJBACXCIQC7J7IT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L7YGPDRRTVEEJBACXCIQC7J7IT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L7YGPDRRTVEEJBACXCIQC7J7IT/action/storage_attestation","attest_author":"https://pith.science/pith/L7YGPDRRTVEEJBACXCIQC7J7IT/action/author_attestation","sign_citation":"https://pith.science/pith/L7YGPDRRTVEEJBACXCIQC7J7IT/action/citation_signature","submit_replication":"https://pith.science/pith/L7YGPDRRTVEEJBACXCIQC7J7IT/action/replication_record"}},"created_at":"2026-05-18T02:39:17.356749+00:00","updated_at":"2026-05-18T02:39:17.356749+00:00"}