{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:W6HMR2S2YMWDNB7EUDRJZHCNVV","short_pith_number":"pith:W6HMR2S2","schema_version":"1.0","canonical_sha256":"b78ec8ea5ac32c3687e4a0e29c9c4dad77b142afb2940d022744c960b434c23c","source":{"kind":"arxiv","id":"1903.08783","version":1},"attestation_state":"computed","paper":{"title":"A Reciprocal Formulation of Nonexponential Radiative Transfer. 3: Binary Mixtures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Eugene d'Eon","submitted_at":"2019-03-21T00:22:49Z","abstract_excerpt":"We derive the form of reciprocal generalized radiative transfer (RGRT) that includes the Levermore-Pomraning attenuation law for paths leaving a deterministic origin. The resulting model describes linear transport within multi-dimensional stochastic binary mixtures with Markovian mixing statistics and nonstochastic albedo and phase function. The derivation includes a new attenuation law and related free-path distribution between collisions, which was previously estimated using a Monte Carlo approach. We also show that previous stationary descriptions of binary mixtures with binomial mixing sta"},"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":"1903.08783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-03-21T00:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"ab31f9cf9545e51f395fc48fea4c9f7833031e02a006ddbc163b85ec7406e3fc","abstract_canon_sha256":"909b522462f4ea9f2f52226ee1450486ffd1aec022706662ba80b3c8f9dcbf5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:43.942282Z","signature_b64":"zDqLGfAqsN9mqpnK0bAjb/JSz1z+WpRHNZi616r2B6SDPilPoIDrox/j1s4+MDslItPsVi1nQDo3AxcB8XbaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b78ec8ea5ac32c3687e4a0e29c9c4dad77b142afb2940d022744c960b434c23c","last_reissued_at":"2026-05-17T23:50:43.941738Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:43.941738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Reciprocal Formulation of Nonexponential Radiative Transfer. 3: Binary Mixtures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Eugene d'Eon","submitted_at":"2019-03-21T00:22:49Z","abstract_excerpt":"We derive the form of reciprocal generalized radiative transfer (RGRT) that includes the Levermore-Pomraning attenuation law for paths leaving a deterministic origin. The resulting model describes linear transport within multi-dimensional stochastic binary mixtures with Markovian mixing statistics and nonstochastic albedo and phase function. The derivation includes a new attenuation law and related free-path distribution between collisions, which was previously estimated using a Monte Carlo approach. We also show that previous stationary descriptions of binary mixtures with binomial mixing sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08783","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1903.08783","created_at":"2026-05-17T23:50:43.941821+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.08783v1","created_at":"2026-05-17T23:50:43.941821+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08783","created_at":"2026-05-17T23:50:43.941821+00:00"},{"alias_kind":"pith_short_12","alias_value":"W6HMR2S2YMWD","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"W6HMR2S2YMWDNB7E","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"W6HMR2S2","created_at":"2026-05-18T12:33:30.264802+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/W6HMR2S2YMWDNB7EUDRJZHCNVV","json":"https://pith.science/pith/W6HMR2S2YMWDNB7EUDRJZHCNVV.json","graph_json":"https://pith.science/api/pith-number/W6HMR2S2YMWDNB7EUDRJZHCNVV/graph.json","events_json":"https://pith.science/api/pith-number/W6HMR2S2YMWDNB7EUDRJZHCNVV/events.json","paper":"https://pith.science/paper/W6HMR2S2"},"agent_actions":{"view_html":"https://pith.science/pith/W6HMR2S2YMWDNB7EUDRJZHCNVV","download_json":"https://pith.science/pith/W6HMR2S2YMWDNB7EUDRJZHCNVV.json","view_paper":"https://pith.science/paper/W6HMR2S2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.08783&json=true","fetch_graph":"https://pith.science/api/pith-number/W6HMR2S2YMWDNB7EUDRJZHCNVV/graph.json","fetch_events":"https://pith.science/api/pith-number/W6HMR2S2YMWDNB7EUDRJZHCNVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W6HMR2S2YMWDNB7EUDRJZHCNVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W6HMR2S2YMWDNB7EUDRJZHCNVV/action/storage_attestation","attest_author":"https://pith.science/pith/W6HMR2S2YMWDNB7EUDRJZHCNVV/action/author_attestation","sign_citation":"https://pith.science/pith/W6HMR2S2YMWDNB7EUDRJZHCNVV/action/citation_signature","submit_replication":"https://pith.science/pith/W6HMR2S2YMWDNB7EUDRJZHCNVV/action/replication_record"}},"created_at":"2026-05-17T23:50:43.941821+00:00","updated_at":"2026-05-17T23:50:43.941821+00:00"}