{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:A434U3QUUULRE2KNAYBVP4I3MN","short_pith_number":"pith:A434U3QU","schema_version":"1.0","canonical_sha256":"0737ca6e14a51712694d060357f11b6353f0adda977b03d0142f9df81b6a1c86","source":{"kind":"arxiv","id":"1707.07143","version":2},"attestation_state":"computed","paper":{"title":"A relation on the effective conductivity of composites","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Vladimir Mityushev","submitted_at":"2017-07-22T11:55:55Z","abstract_excerpt":"Consider a 2D composites with non-overlapping equal inclusions imbedded in a host material of the normalized unit conductivity. The conductivity of inclusions takes two values $\\sigma_1$ and $\\sigma_2$ with the probabilities $p$ and $1-p$, respectively. We prove that the effective conductivity tensor of the considered three-phase random composite is equal to the effective conductivity tensor of the two-phase deterministic composite with the same inclusions of the conductivity $\\sigma=[p(\\sigma_1~-~\\sigma_2)+~\\sigma_2+\\sigma_1\\sigma_2] [1+\\sigma_1-p(\\sigma_1-\\sigma_2)]^{-1}$."},"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":"1707.07143","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-07-22T11:55:55Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"02da877e5656d9f89abc71e18e9e628148c8faf6463e37d6a9f9bac1e6db76de","abstract_canon_sha256":"04c880783197ec945a5923cdb013565b70931111eeca79d53fe1e899a1a4c610"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:57.162433Z","signature_b64":"OwOxrCKuUOdhp3GzHc8NvO95j1aZiSgcm1qtBbonJWKyFJtc75Ev/QSSfEzvOO5SLd/e09ceJC014LxYdtYMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0737ca6e14a51712694d060357f11b6353f0adda977b03d0142f9df81b6a1c86","last_reissued_at":"2026-05-18T00:27:57.161625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:57.161625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A relation on the effective conductivity of composites","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Vladimir Mityushev","submitted_at":"2017-07-22T11:55:55Z","abstract_excerpt":"Consider a 2D composites with non-overlapping equal inclusions imbedded in a host material of the normalized unit conductivity. The conductivity of inclusions takes two values $\\sigma_1$ and $\\sigma_2$ with the probabilities $p$ and $1-p$, respectively. We prove that the effective conductivity tensor of the considered three-phase random composite is equal to the effective conductivity tensor of the two-phase deterministic composite with the same inclusions of the conductivity $\\sigma=[p(\\sigma_1~-~\\sigma_2)+~\\sigma_2+\\sigma_1\\sigma_2] [1+\\sigma_1-p(\\sigma_1-\\sigma_2)]^{-1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07143","kind":"arxiv","version":2},"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":"1707.07143","created_at":"2026-05-18T00:27:57.161750+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07143v2","created_at":"2026-05-18T00:27:57.161750+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07143","created_at":"2026-05-18T00:27:57.161750+00:00"},{"alias_kind":"pith_short_12","alias_value":"A434U3QUUULR","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"A434U3QUUULRE2KN","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"A434U3QU","created_at":"2026-05-18T12:31:05.417338+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/A434U3QUUULRE2KNAYBVP4I3MN","json":"https://pith.science/pith/A434U3QUUULRE2KNAYBVP4I3MN.json","graph_json":"https://pith.science/api/pith-number/A434U3QUUULRE2KNAYBVP4I3MN/graph.json","events_json":"https://pith.science/api/pith-number/A434U3QUUULRE2KNAYBVP4I3MN/events.json","paper":"https://pith.science/paper/A434U3QU"},"agent_actions":{"view_html":"https://pith.science/pith/A434U3QUUULRE2KNAYBVP4I3MN","download_json":"https://pith.science/pith/A434U3QUUULRE2KNAYBVP4I3MN.json","view_paper":"https://pith.science/paper/A434U3QU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07143&json=true","fetch_graph":"https://pith.science/api/pith-number/A434U3QUUULRE2KNAYBVP4I3MN/graph.json","fetch_events":"https://pith.science/api/pith-number/A434U3QUUULRE2KNAYBVP4I3MN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A434U3QUUULRE2KNAYBVP4I3MN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A434U3QUUULRE2KNAYBVP4I3MN/action/storage_attestation","attest_author":"https://pith.science/pith/A434U3QUUULRE2KNAYBVP4I3MN/action/author_attestation","sign_citation":"https://pith.science/pith/A434U3QUUULRE2KNAYBVP4I3MN/action/citation_signature","submit_replication":"https://pith.science/pith/A434U3QUUULRE2KNAYBVP4I3MN/action/replication_record"}},"created_at":"2026-05-18T00:27:57.161750+00:00","updated_at":"2026-05-18T00:27:57.161750+00:00"}