{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6XBXXPSMZV6IWXDWWEWXIDOA4B","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":"9c2be75a05dd037ab882de619e1439f69bc76d97957bedc9a33d75f1b6dab871","cross_cats_sorted":["math-ph","math.AP","math.MP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-01-06T14:06:15Z","title_canon_sha256":"2cfd4c612d18a1b0b9795fa38ba3449d0df335a066cab5efd0982e7bdbecf922"},"schema_version":"1.0","source":{"id":"1201.1419","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1419","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1419v2","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1419","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"6XBXXPSMZV6I","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6XBXXPSMZV6IWXDW","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6XBXXPSM","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:aaff5f31ac2d92d5bfa1df3d743027c7a0581e66069dc9528941d7b5d213d915","target":"graph","created_at":"2026-05-17T23:44:48Z","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 determine the effective conductivity of a two-dimensional composite consisting of a doubly periodic array of identical circular cylinders within a homogeneous matrix. We obtain an exact analytic expression for the effective conductivity tensor as well as its expansion in terms of volume fraction of the cylinders. Results are illustrated by examples.","authors_text":"Yuri A. Godin","cross_cats":["math-ph","math.AP","math.MP","physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-01-06T14:06:15Z","title":"The effective conductivity of a periodic lattice of circular inclusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1419","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":"sha256:1a1ca837b15636b58af0a3e10a04931fb984ac0bf49eff9ecc478471204d2305","target":"record","created_at":"2026-05-17T23:44:48Z","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":"9c2be75a05dd037ab882de619e1439f69bc76d97957bedc9a33d75f1b6dab871","cross_cats_sorted":["math-ph","math.AP","math.MP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-01-06T14:06:15Z","title_canon_sha256":"2cfd4c612d18a1b0b9795fa38ba3449d0df335a066cab5efd0982e7bdbecf922"},"schema_version":"1.0","source":{"id":"1201.1419","kind":"arxiv","version":2}},"canonical_sha256":"f5c37bbe4ccd7c8b5c76b12d740dc0e06e1ec6de1d00b801abb7c5b568aa6a5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5c37bbe4ccd7c8b5c76b12d740dc0e06e1ec6de1d00b801abb7c5b568aa6a5f","first_computed_at":"2026-05-17T23:44:48.779980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:48.779980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E4icj87SXGtqTXJ+LVtqZOcp9/TjGnwsD33Z72yUYs+wmaGZu3YBqw2zYRrgo6uB7LL8YCIL5Gcsij+GDXVxDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:48.780644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1419","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a1ca837b15636b58af0a3e10a04931fb984ac0bf49eff9ecc478471204d2305","sha256:aaff5f31ac2d92d5bfa1df3d743027c7a0581e66069dc9528941d7b5d213d915"],"state_sha256":"e586ac549987d07601a0c34297a1a6db34a22a7f5ceafe7a259e73ae8f47f70f"}