{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:I3F4TBVHZRKIAXFQ26JOHAJ2HP","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":"6c9fea46399247b1847e2ddf00e03909540542382134c319edc7bf8fb7035221","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-20T10:11:27Z","title_canon_sha256":"6837535c42d370fec5390f7d18fccca8539566bef7aab784d606d67086880462"},"schema_version":"1.0","source":{"id":"1901.06652","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.06652","created_at":"2026-05-17T23:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"1901.06652v2","created_at":"2026-05-17T23:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.06652","created_at":"2026-05-17T23:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"I3F4TBVHZRKI","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I3F4TBVHZRKIAXFQ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I3F4TBVH","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:38fff1c47bd50813ecf92cf266f61dff2f3716f27ca7b3e0bb3f7ec7cd8bb00a","target":"graph","created_at":"2026-05-17T23:54:53Z","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":"Randomly distributed non-overlapping perfectly conducting spheres are embedded in a conducting matrix with the concentration of inclusions $f$. Jeffrey (1973) suggested an analytical formula valid up to $O(f^3)$ for macroscopically isotropic random composites. A conditionally convergent sum arose in the spatial averaging. In the present paper, we apply a method of functional equations to random composites and correct Jeffrey's formula. The main revision concerns the proper investigation of the conditionally convergent sum and correction the $f^2$-term. A new model of symbolic computations is d","authors_text":"Vladimir Mityushev, Wojciech Nawalaniec","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-20T10:11:27Z","title":"Effective conductivity of a random suspension of highly conducting spherical particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06652","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:f5c83c2009f2a0da0b41bb6c54b4372c3a03463b2e9c61c56c16bae3a283a2e6","target":"record","created_at":"2026-05-17T23:54:53Z","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":"6c9fea46399247b1847e2ddf00e03909540542382134c319edc7bf8fb7035221","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-20T10:11:27Z","title_canon_sha256":"6837535c42d370fec5390f7d18fccca8539566bef7aab784d606d67086880462"},"schema_version":"1.0","source":{"id":"1901.06652","kind":"arxiv","version":2}},"canonical_sha256":"46cbc986a7cc54805cb0d792e3813a3bd0ed15600788a1ec353b1424227d60ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46cbc986a7cc54805cb0d792e3813a3bd0ed15600788a1ec353b1424227d60ce","first_computed_at":"2026-05-17T23:54:53.116332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:53.116332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"praNRYew/Rx0pMrSyzwTDtIh3y6pUYNCZB6Cfha2IBgeqVw/465Rpue/Ln/10xinWtRfmC5qenHUoIsyAz6LCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:53.116882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.06652","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5c83c2009f2a0da0b41bb6c54b4372c3a03463b2e9c61c56c16bae3a283a2e6","sha256:38fff1c47bd50813ecf92cf266f61dff2f3716f27ca7b3e0bb3f7ec7cd8bb00a"],"state_sha256":"54e28996f44f692b4da11d67679d55bff94571c1a42f9f22f0c1bf8d82f235c1"}