{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ID52JULKHE6D6IN3R3I2GA5OKI","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":"fa8ba8d9d730610d13a6c4db68601a8e4e72d8a6579607446278cd5014c925f6","cross_cats_sorted":["math-ph","math.MP","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2014-12-09T20:39:12Z","title_canon_sha256":"6a673781f166bf32fad1bcf87a88d40ce6cf725e5acb8664e20c306234dbb9fc"},"schema_version":"1.0","source":{"id":"1412.3386","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3386","created_at":"2026-05-17T23:57:33Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3386v2","created_at":"2026-05-17T23:57:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3386","created_at":"2026-05-17T23:57:33Z"},{"alias_kind":"pith_short_12","alias_value":"ID52JULKHE6D","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ID52JULKHE6D6IN3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ID52JULK","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:476396429b300508a7769c9d141e524ccdb6de434bb2a299008f8c1f3655b8a7","target":"graph","created_at":"2026-05-17T23:57:33Z","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":"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","authors_text":"Kai Krycki, Richard Vasques","cross_cats":["math-ph","math.MP","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2014-12-09T20:39:12Z","title":"On the Accuracy of the Non-Classical Transport Equation in 1-D Random Periodic Media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3386","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":"sha256:3063404318cbddc53353acb1ff43f37f7a8e139ec53ef74c7278d53e29497bbd","target":"record","created_at":"2026-05-17T23:57:33Z","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":"fa8ba8d9d730610d13a6c4db68601a8e4e72d8a6579607446278cd5014c925f6","cross_cats_sorted":["math-ph","math.MP","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2014-12-09T20:39:12Z","title_canon_sha256":"6a673781f166bf32fad1bcf87a88d40ce6cf725e5acb8664e20c306234dbb9fc"},"schema_version":"1.0","source":{"id":"1412.3386","kind":"arxiv","version":2}},"canonical_sha256":"40fba4d16a393c3f21bb8ed1a303ae521f6b59a71b5e200f88640c7e60b469bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40fba4d16a393c3f21bb8ed1a303ae521f6b59a71b5e200f88640c7e60b469bd","first_computed_at":"2026-05-17T23:57:33.326355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:33.326355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PR5orUUII5wA20lFUE9XFvnCkKXlqfIE0NpuwD4Z21rudyMQ8Vhzr/nWh5jvKcrqZZijnUQHhddhluoXhQVNAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:33.326958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3386","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3063404318cbddc53353acb1ff43f37f7a8e139ec53ef74c7278d53e29497bbd","sha256:476396429b300508a7769c9d141e524ccdb6de434bb2a299008f8c1f3655b8a7"],"state_sha256":"d570884e2210cfde20adcb47864f6e00665d6eccebca7522a8ec2495d679d961"}