{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ID52JULKHE6D6IN3R3I2GA5OKI","short_pith_number":"pith:ID52JULK","schema_version":"1.0","canonical_sha256":"40fba4d16a393c3f21bb8ed1a303ae521f6b59a71b5e200f88640c7e60b469bd","source":{"kind":"arxiv","id":"1412.3386","version":2},"attestation_state":"computed","paper":{"title":"On the Accuracy of the Non-Classical Transport Equation in 1-D Random Periodic Media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nucl-th"],"primary_cat":"cond-mat.dis-nn","authors_text":"Kai Krycki, Richard Vasques","submitted_at":"2014-12-09T20:39:12Z","abstract_excerpt":"We present a first numerical investigation of the accuracy of the recently proposed {\\em non-classical transport equation}. This equation contains an extra independent variable (the path-length $s$), and models particle transport taking place in random media in which a particle's distance-to-collision is {\\em not} exponentially distributed. To solve the non-classical equation, one needs to know the $s$-dependent ensemble-averaged total cross section $\\Sigma_t(s)$, or its corresponding path-length distribution function $p(s)$. We consider a 1-D spatially periodic system consisting of alternatin"},"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":"1412.3386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2014-12-09T20:39:12Z","cross_cats_sorted":["math-ph","math.MP","nucl-th"],"title_canon_sha256":"6a673781f166bf32fad1bcf87a88d40ce6cf725e5acb8664e20c306234dbb9fc","abstract_canon_sha256":"fa8ba8d9d730610d13a6c4db68601a8e4e72d8a6579607446278cd5014c925f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:33.326958Z","signature_b64":"PR5orUUII5wA20lFUE9XFvnCkKXlqfIE0NpuwD4Z21rudyMQ8Vhzr/nWh5jvKcrqZZijnUQHhddhluoXhQVNAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40fba4d16a393c3f21bb8ed1a303ae521f6b59a71b5e200f88640c7e60b469bd","last_reissued_at":"2026-05-17T23:57:33.326355Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:33.326355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Accuracy of the Non-Classical Transport Equation in 1-D Random Periodic Media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nucl-th"],"primary_cat":"cond-mat.dis-nn","authors_text":"Kai Krycki, Richard Vasques","submitted_at":"2014-12-09T20:39:12Z","abstract_excerpt":"We present a first numerical investigation of the accuracy of the recently proposed {\\em non-classical transport equation}. This equation contains an extra independent variable (the path-length $s$), and models particle transport taking place in random media in which a particle's distance-to-collision is {\\em not} exponentially distributed. To solve the non-classical equation, one needs to know the $s$-dependent ensemble-averaged total cross section $\\Sigma_t(s)$, or its corresponding path-length distribution function $p(s)$. We consider a 1-D spatially periodic system consisting of alternatin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3386","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":"1412.3386","created_at":"2026-05-17T23:57:33.326458+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.3386v2","created_at":"2026-05-17T23:57:33.326458+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3386","created_at":"2026-05-17T23:57:33.326458+00:00"},{"alias_kind":"pith_short_12","alias_value":"ID52JULKHE6D","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"ID52JULKHE6D6IN3","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"ID52JULK","created_at":"2026-05-18T12:28:33.132498+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/ID52JULKHE6D6IN3R3I2GA5OKI","json":"https://pith.science/pith/ID52JULKHE6D6IN3R3I2GA5OKI.json","graph_json":"https://pith.science/api/pith-number/ID52JULKHE6D6IN3R3I2GA5OKI/graph.json","events_json":"https://pith.science/api/pith-number/ID52JULKHE6D6IN3R3I2GA5OKI/events.json","paper":"https://pith.science/paper/ID52JULK"},"agent_actions":{"view_html":"https://pith.science/pith/ID52JULKHE6D6IN3R3I2GA5OKI","download_json":"https://pith.science/pith/ID52JULKHE6D6IN3R3I2GA5OKI.json","view_paper":"https://pith.science/paper/ID52JULK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.3386&json=true","fetch_graph":"https://pith.science/api/pith-number/ID52JULKHE6D6IN3R3I2GA5OKI/graph.json","fetch_events":"https://pith.science/api/pith-number/ID52JULKHE6D6IN3R3I2GA5OKI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ID52JULKHE6D6IN3R3I2GA5OKI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ID52JULKHE6D6IN3R3I2GA5OKI/action/storage_attestation","attest_author":"https://pith.science/pith/ID52JULKHE6D6IN3R3I2GA5OKI/action/author_attestation","sign_citation":"https://pith.science/pith/ID52JULKHE6D6IN3R3I2GA5OKI/action/citation_signature","submit_replication":"https://pith.science/pith/ID52JULKHE6D6IN3R3I2GA5OKI/action/replication_record"}},"created_at":"2026-05-17T23:57:33.326458+00:00","updated_at":"2026-05-17T23:57:33.326458+00:00"}