{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TNNKUKWKPDN3JLE5UP4URJF6HY","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":"855d3363350cd3c2d2314ab842eb74db9d9d8a5eda1f38c2ca38416fd472d519","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-05-11T01:25:49Z","title_canon_sha256":"a642f5b6213a5e88317efd964a1e02f198777d920d6e0de69572e00753a8db19"},"schema_version":"1.0","source":{"id":"1505.02465","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02465","created_at":"2026-05-18T01:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02465v2","created_at":"2026-05-18T01:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02465","created_at":"2026-05-18T01:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"TNNKUKWKPDN3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNNKUKWKPDN3JLE5","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNNKUKWK","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:b991a9889dce3110e976f0d097d56e9efac72e2361aaf3d8808f720ade423904","target":"graph","created_at":"2026-05-18T01:28:56Z","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":"The Boltzmann transport equation for phonons is recast directly in terms of the heat-flux by means of iteration followed by truncation at the second order in the spherical harmonic expansion of the distribution function. This procedure displays the heat-flux in an explicitly coordinate-invariant form, and leads to a natural decomposition into two components, namely the solenoidal component in addition to the usual irrotational component. The solenoidal heat-flux is explicitly shown to arise by applying the heat-flux equation to a right-circular cylinder. These findings are important in the con","authors_text":"Ashok T. Ramu, John E. Bowers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-05-11T01:25:49Z","title":"On the solenoidal heat-flux in quasi-ballistic thermal conduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02465","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:c2878b98a770bef8c933785a61fefaae14129ba23fdafe67cfe7ddf3f6a55498","target":"record","created_at":"2026-05-18T01:28:56Z","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":"855d3363350cd3c2d2314ab842eb74db9d9d8a5eda1f38c2ca38416fd472d519","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-05-11T01:25:49Z","title_canon_sha256":"a642f5b6213a5e88317efd964a1e02f198777d920d6e0de69572e00753a8db19"},"schema_version":"1.0","source":{"id":"1505.02465","kind":"arxiv","version":2}},"canonical_sha256":"9b5aaa2aca78dbb4ac9da3f948a4be3e38a48b505fbb2419052b30ff7f34ecde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b5aaa2aca78dbb4ac9da3f948a4be3e38a48b505fbb2419052b30ff7f34ecde","first_computed_at":"2026-05-18T01:28:56.213087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:56.213087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H0Esfg9SMVxbGtfpUwrUeMU6141Px2AFTr90ze6qfcfxo8qISJaE88UaAmjbykcpe05phE5lPvS46AjRcZ+/Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:56.213766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02465","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2878b98a770bef8c933785a61fefaae14129ba23fdafe67cfe7ddf3f6a55498","sha256:b991a9889dce3110e976f0d097d56e9efac72e2361aaf3d8808f720ade423904"],"state_sha256":"f02d0b612b9d42bb3750479eaa170d28cf7a5829af44b42c708aa1a7a375f8ee"}