{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:SD3DFSODBVEDJULNJIJLNLE4IL","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":"944862ba1d55e95ffb9dda2fbbb81bf8b08dd5b0f51fd8acbeae1a124e87d5a6","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-05-29T08:43:43Z","title_canon_sha256":"cfba115d777dde5ab011242e818adac658cd42816a946ee119c0017cae669199"},"schema_version":"1.0","source":{"id":"0905.4806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4806","created_at":"2026-05-18T02:13:30Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4806v1","created_at":"2026-05-18T02:13:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4806","created_at":"2026-05-18T02:13:30Z"},{"alias_kind":"pith_short_12","alias_value":"SD3DFSODBVED","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SD3DFSODBVEDJULN","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SD3DFSOD","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:29f462f7e805089cd7dcf1920e0de8c3f828ed891a37c852e23558b1a423b4f6","target":"graph","created_at":"2026-05-18T02:13:30Z","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 consider the lattice dynamics in the half-space. The initial data are random according to a probability measure which enforces slow spatial variation on the linear scale $\\varepsilon^{-1}$. We establish two time regimes. For times of order $\\varepsilon^{-\\gamma}$, $0<\\gamma<1$, locally the measure converges to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian, in general). For times of order $\\varepsilon^{-1}$, this covariance changes in time and is governed by a semiclassical transport equation.","authors_text":"T.V. Dudnikova","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-05-29T08:43:43Z","title":"Lattice Dynamics in the Half-Space, II. Energy Transport Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4806","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:a871660dd9abafe720e90722209c75b001c20ec0db65e2b8f7ef55f9aaf57a59","target":"record","created_at":"2026-05-18T02:13:30Z","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":"944862ba1d55e95ffb9dda2fbbb81bf8b08dd5b0f51fd8acbeae1a124e87d5a6","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-05-29T08:43:43Z","title_canon_sha256":"cfba115d777dde5ab011242e818adac658cd42816a946ee119c0017cae669199"},"schema_version":"1.0","source":{"id":"0905.4806","kind":"arxiv","version":1}},"canonical_sha256":"90f632c9c30d4834d16d4a12b6ac9c42d4f1c2b893ebe2b68c9c1e0529864097","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90f632c9c30d4834d16d4a12b6ac9c42d4f1c2b893ebe2b68c9c1e0529864097","first_computed_at":"2026-05-18T02:13:30.861428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:30.861428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y4pwMP9OJMT+EyBqBu2HoZZJCkA5pI4b7TBUAe4N/pDIgOkTLBH2VJRqq1P4Fg0oYQvFll4OuAV9i0pstrDOCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:30.862056Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.4806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a871660dd9abafe720e90722209c75b001c20ec0db65e2b8f7ef55f9aaf57a59","sha256:29f462f7e805089cd7dcf1920e0de8c3f828ed891a37c852e23558b1a423b4f6"],"state_sha256":"e740d5ed6102a240405ce9f2fd2ef070aa7a1ea23dee94fcf19cabdca1061352"}