{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:D2WIWUPTRLOTXPWPCKNK2ML7F4","short_pith_number":"pith:D2WIWUPT","canonical_record":{"source":{"id":"1206.0857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-06-05T09:38:05Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"7a14a061d94cd9b94ea7c7b7775a5d197afc598697b909d7a3638a7500ed55f0","abstract_canon_sha256":"494b5eb40f08d0ff84250509192850fbbbca84d5efd40fc6b3d943631103ba80"},"schema_version":"1.0"},"canonical_sha256":"1eac8b51f38add3bbecf129aad317f2f315d54ca1ce028b65f1582fd09e4971e","source":{"kind":"arxiv","id":"1206.0857","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0857","created_at":"2026-05-18T03:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0857v1","created_at":"2026-05-18T03:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0857","created_at":"2026-05-18T03:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"D2WIWUPTRLOT","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D2WIWUPTRLOTXPWP","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D2WIWUPT","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:D2WIWUPTRLOTXPWPCKNK2ML7F4","target":"record","payload":{"canonical_record":{"source":{"id":"1206.0857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-06-05T09:38:05Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"7a14a061d94cd9b94ea7c7b7775a5d197afc598697b909d7a3638a7500ed55f0","abstract_canon_sha256":"494b5eb40f08d0ff84250509192850fbbbca84d5efd40fc6b3d943631103ba80"},"schema_version":"1.0"},"canonical_sha256":"1eac8b51f38add3bbecf129aad317f2f315d54ca1ce028b65f1582fd09e4971e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:16.138781Z","signature_b64":"qXprf+b7AvSr03CgNHXnliSzJbMNHOtWWdHYG96MfZzopuKYxynT+b1mJ/CJb2ykjcg+mbRLmpLxu/R7xCWlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1eac8b51f38add3bbecf129aad317f2f315d54ca1ce028b65f1582fd09e4971e","last_reissued_at":"2026-05-18T03:54:16.138020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:16.138020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.0857","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1/++MX2Vlw0E3NThu3HHcwK3gDwSP+YSwOPXlwUabEJXCsH5SFNmyYd7rdXTjlfx1sCMJqehEBUIN7iwYnr/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:42:51.818231Z"},"content_sha256":"7effa00011320a344e0e577baf8c4a8310288d64cc0dab20a8a5e98d7e5fa5b4","schema_version":"1.0","event_id":"sha256:7effa00011320a344e0e577baf8c4a8310288d64cc0dab20a8a5e98d7e5fa5b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:D2WIWUPTRLOTXPWPCKNK2ML7F4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized two-body self-consistent theory of random linear dielectric composites: an effective-medium approach to clustering in highly-disordered media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.dis-nn","authors_text":"Fran\\c{c}ois Willot, Yves-Patrick Pellegrini","submitted_at":"2012-06-05T09:38:05Z","abstract_excerpt":"Effects of two-body dipolar interactions on the effective permittivity/conductivity of a binary, symmetric, random dielectric composite are investigated in a self-consistent framework. By arbitrarily splitting the singularity of the Green tensor of the electric field, we introduce an additional degree of freedom into the problem, in the form of an unknown \"inner\" depolarization constant. Two coupled self-consistent equations determine the latter and the permittivity in terms of the dielectric contrast and the volume fractions. One of them generalizes the usual Coherent Potential condition to m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0857","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y5KGoLzYR+kRMELKwGgBNUAKg2K2mriMj3U8VY9fEE1PmFubkO85lBcyEFMWE+USNf9nkKAWGnTrQCZMYjLPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:42:51.818715Z"},"content_sha256":"ee14358f9fca56604217cdacd5d52c79f6636f91a3143eb18e3c361d45a63010","schema_version":"1.0","event_id":"sha256:ee14358f9fca56604217cdacd5d52c79f6636f91a3143eb18e3c361d45a63010"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2WIWUPTRLOTXPWPCKNK2ML7F4/bundle.json","state_url":"https://pith.science/pith/D2WIWUPTRLOTXPWPCKNK2ML7F4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2WIWUPTRLOTXPWPCKNK2ML7F4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T20:42:51Z","links":{"resolver":"https://pith.science/pith/D2WIWUPTRLOTXPWPCKNK2ML7F4","bundle":"https://pith.science/pith/D2WIWUPTRLOTXPWPCKNK2ML7F4/bundle.json","state":"https://pith.science/pith/D2WIWUPTRLOTXPWPCKNK2ML7F4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2WIWUPTRLOTXPWPCKNK2ML7F4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:D2WIWUPTRLOTXPWPCKNK2ML7F4","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":"494b5eb40f08d0ff84250509192850fbbbca84d5efd40fc6b3d943631103ba80","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-06-05T09:38:05Z","title_canon_sha256":"7a14a061d94cd9b94ea7c7b7775a5d197afc598697b909d7a3638a7500ed55f0"},"schema_version":"1.0","source":{"id":"1206.0857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0857","created_at":"2026-05-18T03:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0857v1","created_at":"2026-05-18T03:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0857","created_at":"2026-05-18T03:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"D2WIWUPTRLOT","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D2WIWUPTRLOTXPWP","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D2WIWUPT","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:ee14358f9fca56604217cdacd5d52c79f6636f91a3143eb18e3c361d45a63010","target":"graph","created_at":"2026-05-18T03:54:16Z","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":"Effects of two-body dipolar interactions on the effective permittivity/conductivity of a binary, symmetric, random dielectric composite are investigated in a self-consistent framework. By arbitrarily splitting the singularity of the Green tensor of the electric field, we introduce an additional degree of freedom into the problem, in the form of an unknown \"inner\" depolarization constant. Two coupled self-consistent equations determine the latter and the permittivity in terms of the dielectric contrast and the volume fractions. One of them generalizes the usual Coherent Potential condition to m","authors_text":"Fran\\c{c}ois Willot, Yves-Patrick Pellegrini","cross_cats":["cond-mat.mtrl-sci"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-06-05T09:38:05Z","title":"Generalized two-body self-consistent theory of random linear dielectric composites: an effective-medium approach to clustering in highly-disordered media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0857","kind":"arxiv","version":1},"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":"sha256:7effa00011320a344e0e577baf8c4a8310288d64cc0dab20a8a5e98d7e5fa5b4","target":"record","created_at":"2026-05-18T03:54:16Z","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":"494b5eb40f08d0ff84250509192850fbbbca84d5efd40fc6b3d943631103ba80","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-06-05T09:38:05Z","title_canon_sha256":"7a14a061d94cd9b94ea7c7b7775a5d197afc598697b909d7a3638a7500ed55f0"},"schema_version":"1.0","source":{"id":"1206.0857","kind":"arxiv","version":1}},"canonical_sha256":"1eac8b51f38add3bbecf129aad317f2f315d54ca1ce028b65f1582fd09e4971e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1eac8b51f38add3bbecf129aad317f2f315d54ca1ce028b65f1582fd09e4971e","first_computed_at":"2026-05-18T03:54:16.138020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:16.138020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qXprf+b7AvSr03CgNHXnliSzJbMNHOtWWdHYG96MfZzopuKYxynT+b1mJ/CJb2ykjcg+mbRLmpLxu/R7xCWlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:16.138781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7effa00011320a344e0e577baf8c4a8310288d64cc0dab20a8a5e98d7e5fa5b4","sha256:ee14358f9fca56604217cdacd5d52c79f6636f91a3143eb18e3c361d45a63010"],"state_sha256":"3bbd8ca72da4981cbec8b581b8f3d03ce02dc6701e2302e7aa77e7b2c5f883af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6k57Qiw8TDJ+hah3NfEA+eG5qK4XbFevZr5zlcd0zfZTD/b2eB/GEwT9CqcriA3c5myaHrFOsHWtEGGWTNLKDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:42:51.821421Z","bundle_sha256":"2c15e94e7cdf482ece78eb3f361fbd7bbdf44a5f9b6cc122c2ef55b3398ccb7e"}}