{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:YIZUIH77L5QO4WE5TIL4B5GELL","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":"4a548a2500e9361b57c1ea3bd294b169f8029f116197a412073e289966a235e1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-09-28T20:34:18Z","title_canon_sha256":"caa8caed91bda98c8641cbbeb7cfefec9c6f4d73dc84bb6a9108efdabcd34581"},"schema_version":"1.0","source":{"id":"0809.4867","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.4867","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"arxiv_version","alias_value":"0809.4867v3","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4867","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"pith_short_12","alias_value":"YIZUIH77L5QO","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"YIZUIH77L5QO4WE5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"YIZUIH77","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:d981eeb258b62d95adfd1eb391246897c8fbea0f3fdfcf47e23e1f408e0367fe","target":"graph","created_at":"2026-05-18T04:24:44Z","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 the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions, and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s =1, our result is\n  R_{NxN} = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).","authors_text":"F. Y. Wu, J. W. Essam","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-09-28T20:34:18Z","title":"The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4867","kind":"arxiv","version":3},"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":"sha256:81f0c94ec277e36aaae797e261448392a80e992155dbdf79ed52d592106c05a8","target":"record","created_at":"2026-05-18T04:24:44Z","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":"4a548a2500e9361b57c1ea3bd294b169f8029f116197a412073e289966a235e1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-09-28T20:34:18Z","title_canon_sha256":"caa8caed91bda98c8641cbbeb7cfefec9c6f4d73dc84bb6a9108efdabcd34581"},"schema_version":"1.0","source":{"id":"0809.4867","kind":"arxiv","version":3}},"canonical_sha256":"c233441fff5f60ee589d9a17c0f4c45acaba2b6bf26feec2827ee0f0afe5c458","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c233441fff5f60ee589d9a17c0f4c45acaba2b6bf26feec2827ee0f0afe5c458","first_computed_at":"2026-05-18T04:24:44.102542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:44.102542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/FwvIltvMLNW35XNTmtliwXYdzxNkUyXEZZ3W1DHzpdUtWnDEnm04ui4e8nmQ0WN70XhDAtNyTuIf+sfHQd6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:44.102950Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.4867","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81f0c94ec277e36aaae797e261448392a80e992155dbdf79ed52d592106c05a8","sha256:d981eeb258b62d95adfd1eb391246897c8fbea0f3fdfcf47e23e1f408e0367fe"],"state_sha256":"e6b92c11a593def19bcbfc87748a636cedee7f770544a3b169da3a42fa2c9796"}