{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VRRFEGYNSZD5QESIQSMPKIR5TL","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":"dd5cb7c4a97e01bd412115e61b0c45517b93f798284e5328fbaf260d404316f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-29T08:30:48Z","title_canon_sha256":"e090dc5b89809088e709c73f0679e240516ff446536a8d94c6f0fe781994b401"},"schema_version":"1.0","source":{"id":"1901.10164","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10164","created_at":"2026-05-17T23:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10164v2","created_at":"2026-05-17T23:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10164","created_at":"2026-05-17T23:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"VRRFEGYNSZD5","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VRRFEGYNSZD5QESI","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VRRFEGYN","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:a9f0c33d8563d7d80f68a31300968ec4d56240d9bb2529e88e7353a578d4d2c9","target":"graph","created_at":"2026-05-17T23:44:29Z","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":"This article addresses the homogenization of linear Boltzmann equation when the optical parameters are highly heterogeneous in the energy variable. We employ the method of two-scale convergence to arrive at the homogenization result. In doing so, we show the induction of a memory effect in the homogenization limit. We also provide some numerical experiments to illustrate our results. In the Appendix, we treat a related case of the harmonic oscillator.","authors_text":"Francesco Salvarani, Harsha Hutridurga, Olga Mula","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-29T08:30:48Z","title":"Homogenization in the energy variable for a neutron transport model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10164","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":"sha256:798b86b6edfba66d90b255eaaedbe2841236340bc3dfc264261273a9f632ba42","target":"record","created_at":"2026-05-17T23:44:29Z","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":"dd5cb7c4a97e01bd412115e61b0c45517b93f798284e5328fbaf260d404316f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-29T08:30:48Z","title_canon_sha256":"e090dc5b89809088e709c73f0679e240516ff446536a8d94c6f0fe781994b401"},"schema_version":"1.0","source":{"id":"1901.10164","kind":"arxiv","version":2}},"canonical_sha256":"ac62521b0d9647d812488498f5223d9ac7958b1afb3211b85e39e18094f497fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac62521b0d9647d812488498f5223d9ac7958b1afb3211b85e39e18094f497fc","first_computed_at":"2026-05-17T23:44:29.476004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:29.476004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p/73wuP1OCNajBPJaT/tF/4eJrFa+f1x5mq2i6bps4H7iPMglNgBGVaUuy5UkCRMcZ6KnW2dDZaEJa7N6Ot6BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:29.476637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.10164","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:798b86b6edfba66d90b255eaaedbe2841236340bc3dfc264261273a9f632ba42","sha256:a9f0c33d8563d7d80f68a31300968ec4d56240d9bb2529e88e7353a578d4d2c9"],"state_sha256":"05809a022c570950aa6f24de67707bb57d083869ec0b7fab27701f2b46c7e18d"}