{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QMDIX43JEKJTF2JOOY2ITXTRAP","short_pith_number":"pith:QMDIX43J","canonical_record":{"source":{"id":"1402.3429","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-14T10:55:34Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4b869e29142248cda3db9b01b13b98ddbe0456d031573acf540ac4269c3af1a3","abstract_canon_sha256":"9d388bc3a4f0429211df3b13e66cfcf5aac47fde449f4c13c28f33b2ec1ed25c"},"schema_version":"1.0"},"canonical_sha256":"83068bf369229332e92e763489de7103c8e76a687ed97fff7f1695ccc0bfbde0","source":{"kind":"arxiv","id":"1402.3429","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3429","created_at":"2026-05-18T02:58:56Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3429v2","created_at":"2026-05-18T02:58:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3429","created_at":"2026-05-18T02:58:56Z"},{"alias_kind":"pith_short_12","alias_value":"QMDIX43JEKJT","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QMDIX43JEKJTF2JO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QMDIX43J","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QMDIX43JEKJTF2JOOY2ITXTRAP","target":"record","payload":{"canonical_record":{"source":{"id":"1402.3429","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-14T10:55:34Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4b869e29142248cda3db9b01b13b98ddbe0456d031573acf540ac4269c3af1a3","abstract_canon_sha256":"9d388bc3a4f0429211df3b13e66cfcf5aac47fde449f4c13c28f33b2ec1ed25c"},"schema_version":"1.0"},"canonical_sha256":"83068bf369229332e92e763489de7103c8e76a687ed97fff7f1695ccc0bfbde0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:56.161378Z","signature_b64":"ZTMr1cCXWiw50rI1bEVeswVnhJYnjE5GHH5MBVsveXVkCuHkq1y4W2m3WW3HAR7M4z/cA/S3rEjGVN28jyXpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83068bf369229332e92e763489de7103c8e76a687ed97fff7f1695ccc0bfbde0","last_reissued_at":"2026-05-18T02:58:56.160779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:56.160779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.3429","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qT8IPp8IMtRTA5xRJoSVr0kW87leWLNstf+i3qQffQViDYiAaq76KPjynSymzkzEYLN/BNEpCmwXvb7SbFZ4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:06:07.075910Z"},"content_sha256":"394fa5d4faf1a169b7c79da49d1b137e3e2db2d6b7be2802b7d4d5ac9aef135f","schema_version":"1.0","event_id":"sha256:394fa5d4faf1a169b7c79da49d1b137e3e2db2d6b7be2802b7d4d5ac9aef135f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QMDIX43JEKJTF2JOOY2ITXTRAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semiclassical hydrodynamics of a quantum Kane model for semiconductors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Giovanni Borgioli, Giovanni Frosali, Luigi Barletti","submitted_at":"2014-02-14T10:55:34Z","abstract_excerpt":"In this paper we derive a semiclassical hydrodynamic system for electron densities and currents in the two energy bands of a semiconductor. We use the semiclassical Wigner equation with a k.p Hamiltonian and a BGK dissipative term to construct the first two moment equations. The closure of the moment system is obtained using the Maximum Entropy Principle, by minimizing a Gibbs free-energy functional under suitable constraints. We prove that the constraint equations can be uniquely solved, i.e. that the local equilibrium state can be parametrized by the density and velocity field. Some BGK-like"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3429","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lzEQjzs9IMmDznB0l83Op7SGONtWPeCHQyyflvhBaPG94IsYW5b2w2efxVMJCU3nBY/LqlpFHZYbL9Gh7u4KBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:06:07.076255Z"},"content_sha256":"a3b5f881006ef72fbaea6ff9242c9fcc9a8b91ebe5a531454c5fee311e79b075","schema_version":"1.0","event_id":"sha256:a3b5f881006ef72fbaea6ff9242c9fcc9a8b91ebe5a531454c5fee311e79b075"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QMDIX43JEKJTF2JOOY2ITXTRAP/bundle.json","state_url":"https://pith.science/pith/QMDIX43JEKJTF2JOOY2ITXTRAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QMDIX43JEKJTF2JOOY2ITXTRAP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T13:06:07Z","links":{"resolver":"https://pith.science/pith/QMDIX43JEKJTF2JOOY2ITXTRAP","bundle":"https://pith.science/pith/QMDIX43JEKJTF2JOOY2ITXTRAP/bundle.json","state":"https://pith.science/pith/QMDIX43JEKJTF2JOOY2ITXTRAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QMDIX43JEKJTF2JOOY2ITXTRAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QMDIX43JEKJTF2JOOY2ITXTRAP","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":"9d388bc3a4f0429211df3b13e66cfcf5aac47fde449f4c13c28f33b2ec1ed25c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-14T10:55:34Z","title_canon_sha256":"4b869e29142248cda3db9b01b13b98ddbe0456d031573acf540ac4269c3af1a3"},"schema_version":"1.0","source":{"id":"1402.3429","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3429","created_at":"2026-05-18T02:58:56Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3429v2","created_at":"2026-05-18T02:58:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3429","created_at":"2026-05-18T02:58:56Z"},{"alias_kind":"pith_short_12","alias_value":"QMDIX43JEKJT","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QMDIX43JEKJTF2JO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QMDIX43J","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:a3b5f881006ef72fbaea6ff9242c9fcc9a8b91ebe5a531454c5fee311e79b075","target":"graph","created_at":"2026-05-18T02:58:56Z","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":"In this paper we derive a semiclassical hydrodynamic system for electron densities and currents in the two energy bands of a semiconductor. We use the semiclassical Wigner equation with a k.p Hamiltonian and a BGK dissipative term to construct the first two moment equations. The closure of the moment system is obtained using the Maximum Entropy Principle, by minimizing a Gibbs free-energy functional under suitable constraints. We prove that the constraint equations can be uniquely solved, i.e. that the local equilibrium state can be parametrized by the density and velocity field. Some BGK-like","authors_text":"Giovanni Borgioli, Giovanni Frosali, Luigi Barletti","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-14T10:55:34Z","title":"Semiclassical hydrodynamics of a quantum Kane model for semiconductors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3429","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":"sha256:394fa5d4faf1a169b7c79da49d1b137e3e2db2d6b7be2802b7d4d5ac9aef135f","target":"record","created_at":"2026-05-18T02:58:56Z","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":"9d388bc3a4f0429211df3b13e66cfcf5aac47fde449f4c13c28f33b2ec1ed25c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-14T10:55:34Z","title_canon_sha256":"4b869e29142248cda3db9b01b13b98ddbe0456d031573acf540ac4269c3af1a3"},"schema_version":"1.0","source":{"id":"1402.3429","kind":"arxiv","version":2}},"canonical_sha256":"83068bf369229332e92e763489de7103c8e76a687ed97fff7f1695ccc0bfbde0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83068bf369229332e92e763489de7103c8e76a687ed97fff7f1695ccc0bfbde0","first_computed_at":"2026-05-18T02:58:56.160779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:56.160779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZTMr1cCXWiw50rI1bEVeswVnhJYnjE5GHH5MBVsveXVkCuHkq1y4W2m3WW3HAR7M4z/cA/S3rEjGVN28jyXpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:56.161378Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3429","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:394fa5d4faf1a169b7c79da49d1b137e3e2db2d6b7be2802b7d4d5ac9aef135f","sha256:a3b5f881006ef72fbaea6ff9242c9fcc9a8b91ebe5a531454c5fee311e79b075"],"state_sha256":"7a8ba386547507b7e407547efc1f5ac1bee8a8ff41bccb33e27849828f4cdfa1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/Q1sXMI9QGHygL/r7dqVUA4E57DPu1ruV0EhX7ISEKo813GRshCwms7C2C3WFF6I0WBG+J7+tlyyG5yncA5Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:06:07.078251Z","bundle_sha256":"4a8388e2f9522e80a2b7330db833e2d7135bb408cfa6652a4b0a58fb9989432c"}}