{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XWA7NBUPBCA7XXHYCYCJ23KRTI","short_pith_number":"pith:XWA7NBUP","schema_version":"1.0","canonical_sha256":"bd81f6868f0881fbdcf816049d6d519a099626b4c268c7494d3e106710bc8368","source":{"kind":"arxiv","id":"1508.04694","version":2},"attestation_state":"computed","paper":{"title":"Extending the range of validity of Fourier's law into the kinetic transport regime via asymptotic solution of the phonon Boltzmann transport equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","math-ph","math.MP"],"primary_cat":"cond-mat.mes-hall","authors_text":"Jean-Philippe M. P\\'eraud, Nicolas G. Hadjiconstantinou","submitted_at":"2015-08-19T16:30:11Z","abstract_excerpt":"We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of small but finite mean free path from asymptotic solution of the linearized Boltzmann equation in the relaxation time approximation. Our approach uses the ratio of the mean free path to the characteristic system lengthscale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier descrition. We show that, in the bulk, the traditional heat conduction equation using Fourier's law as a constitutive relation is vali"},"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":"1508.04694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-08-19T16:30:11Z","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"title_canon_sha256":"61ae7fb2dcbbecfbefbd5b3fd800cb15f2fa2e440ea3eba03c753aa457d40121","abstract_canon_sha256":"1981bd8f07dce83c5ef2cf247f3d35121667edc4696e2e874b15a1bd6ddde9e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:31.489098Z","signature_b64":"4bmrU1utMLIUfpZ34llqoV9V/2/FRF45X0pfIZX4+N/uCusT0pQeS4NlZ+kwIvcFv7mIF2KduY7AF0D6zU8yAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd81f6868f0881fbdcf816049d6d519a099626b4c268c7494d3e106710bc8368","last_reissued_at":"2026-05-18T01:21:31.488528Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:31.488528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extending the range of validity of Fourier's law into the kinetic transport regime via asymptotic solution of the phonon Boltzmann transport equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","math-ph","math.MP"],"primary_cat":"cond-mat.mes-hall","authors_text":"Jean-Philippe M. P\\'eraud, Nicolas G. Hadjiconstantinou","submitted_at":"2015-08-19T16:30:11Z","abstract_excerpt":"We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of small but finite mean free path from asymptotic solution of the linearized Boltzmann equation in the relaxation time approximation. Our approach uses the ratio of the mean free path to the characteristic system lengthscale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier descrition. We show that, in the bulk, the traditional heat conduction equation using Fourier's law as a constitutive relation is vali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04694","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":"1508.04694","created_at":"2026-05-18T01:21:31.488628+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.04694v2","created_at":"2026-05-18T01:21:31.488628+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04694","created_at":"2026-05-18T01:21:31.488628+00:00"},{"alias_kind":"pith_short_12","alias_value":"XWA7NBUPBCA7","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XWA7NBUPBCA7XXHY","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XWA7NBUP","created_at":"2026-05-18T12:29:50.041715+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/XWA7NBUPBCA7XXHYCYCJ23KRTI","json":"https://pith.science/pith/XWA7NBUPBCA7XXHYCYCJ23KRTI.json","graph_json":"https://pith.science/api/pith-number/XWA7NBUPBCA7XXHYCYCJ23KRTI/graph.json","events_json":"https://pith.science/api/pith-number/XWA7NBUPBCA7XXHYCYCJ23KRTI/events.json","paper":"https://pith.science/paper/XWA7NBUP"},"agent_actions":{"view_html":"https://pith.science/pith/XWA7NBUPBCA7XXHYCYCJ23KRTI","download_json":"https://pith.science/pith/XWA7NBUPBCA7XXHYCYCJ23KRTI.json","view_paper":"https://pith.science/paper/XWA7NBUP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.04694&json=true","fetch_graph":"https://pith.science/api/pith-number/XWA7NBUPBCA7XXHYCYCJ23KRTI/graph.json","fetch_events":"https://pith.science/api/pith-number/XWA7NBUPBCA7XXHYCYCJ23KRTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XWA7NBUPBCA7XXHYCYCJ23KRTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XWA7NBUPBCA7XXHYCYCJ23KRTI/action/storage_attestation","attest_author":"https://pith.science/pith/XWA7NBUPBCA7XXHYCYCJ23KRTI/action/author_attestation","sign_citation":"https://pith.science/pith/XWA7NBUPBCA7XXHYCYCJ23KRTI/action/citation_signature","submit_replication":"https://pith.science/pith/XWA7NBUPBCA7XXHYCYCJ23KRTI/action/replication_record"}},"created_at":"2026-05-18T01:21:31.488628+00:00","updated_at":"2026-05-18T01:21:31.488628+00:00"}