{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EJK3SFPWF7G22MADEALTBBAI6O","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":"9f8ff846ff273a6bf495ec5d13955e37e4a2bb01aad37c0917a362afcdab3792","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2014-04-08T09:34:13Z","title_canon_sha256":"8645db936fc246e1a1f367a8a08c1418a7f2bbbdb385643b3bf0ede0ac1eee14"},"schema_version":"1.0","source":{"id":"1404.2055","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2055","created_at":"2026-05-18T00:47:16Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2055v3","created_at":"2026-05-18T00:47:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2055","created_at":"2026-05-18T00:47:16Z"},{"alias_kind":"pith_short_12","alias_value":"EJK3SFPWF7G2","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EJK3SFPWF7G22MAD","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EJK3SFPW","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:54b97e6ffc3185eac323d432bd919ed0523106857ab44a5436c44e2e2801d878","target":"graph","created_at":"2026-05-18T00:47:16Z","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":"Using Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models, we have investigated the properties of electron gas inside two-dimensional (2D) Wigner-Seitz (WS) cells in presence of a strong orthogonal quantizing magnetic field. The electron-electron Coulomb exchange interaction in quasi-2D case is obtained. The exact form of exchange term in 2D is derived making the width of the system tending to zero. Further, using the exchange term, the Thomas-Fermi-Dirac equation in 2D is established. It has been observed that only the ionized WS cell can have finite radius in the Thomas-Fermi model, even i","authors_text":"Sanchari De, Somenath Chakrabarty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2014-04-08T09:34:13Z","title":"The Thomas-Fermi and the Thomas-Fermi-Dirac Models in Two-Dimension- the Effect of Strong Quantizing Magnetic Field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2055","kind":"arxiv","version":3},"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":"sha256:0dd70daa0a2d3facf60dd36d235a707d38d004370e5fa765de14b0a5aabbb76e","target":"record","created_at":"2026-05-18T00:47:16Z","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":"9f8ff846ff273a6bf495ec5d13955e37e4a2bb01aad37c0917a362afcdab3792","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2014-04-08T09:34:13Z","title_canon_sha256":"8645db936fc246e1a1f367a8a08c1418a7f2bbbdb385643b3bf0ede0ac1eee14"},"schema_version":"1.0","source":{"id":"1404.2055","kind":"arxiv","version":3}},"canonical_sha256":"2255b915f62fcdad30032017308408f3b825f414ae79c0ffce5652f0d1e1154a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2255b915f62fcdad30032017308408f3b825f414ae79c0ffce5652f0d1e1154a","first_computed_at":"2026-05-18T00:47:16.037470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:16.037470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8OA8o/w2nWJ22zgxW3Bf3/FmJq49O1gWCe090wDTndLXRgDxYUxsHGTR2JFhX78bt+Jw+xgzasyjOW3CAyA6CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:16.038302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2055","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dd70daa0a2d3facf60dd36d235a707d38d004370e5fa765de14b0a5aabbb76e","sha256:54b97e6ffc3185eac323d432bd919ed0523106857ab44a5436c44e2e2801d878"],"state_sha256":"edf440b829148d095ddb00d77ea05e792ede493a1fbc43197a9d6d2b8ea90f81"}