{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:KPT6JMJSSQC6EGK7ET3FDK2OF5","short_pith_number":"pith:KPT6JMJS","schema_version":"1.0","canonical_sha256":"53e7e4b1329405e2195f24f651ab4e2f59bea4a0489fa0db7fdac8b1f1d24bdf","source":{"kind":"arxiv","id":"1312.6828","version":3},"attestation_state":"computed","paper":{"title":"Scaling of R\\'enyi entanglement entropies of the free Fermi-gas ground state: a rigorous proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander V. Sobolev, Hajo Leschke, Wolfgang Spitzer","submitted_at":"2013-12-24T14:36:42Z","abstract_excerpt":"In a remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Dimitri Gioev and Israel Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bi-partite von-Neumann entanglement entropy of non-interacting fermions in multi-dimensional Euclidean space at zero temperature. Based on recent progress by one of us (A.V.S.) in semi-classical functional calculus for pseudo-differential operators with discontinuous symbols, we provide here a complete proof of that formula and of its generalization to R\\'enyi entropies of all orders $\\alpha>0$. The special case $\\alpha=1/"},"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":"1312.6828","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-24T14:36:42Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"title_canon_sha256":"db971ee7b6122911f34bc456a18513c0ede83f4a4672e50fd73981c103f2b5fb","abstract_canon_sha256":"09717f850f8ecd98113ee107efa4ace0a54a743fe2b5b1f1098011340f4dc711"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:56.358464Z","signature_b64":"je/i/sKMAqRcPE17cgQa/VWh8Ko5waZ6RHz0u46jUIYdYQHYHqP7N5Le7hdbeTtdzSe6xkg+sXSwnFJE4EBRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53e7e4b1329405e2195f24f651ab4e2f59bea4a0489fa0db7fdac8b1f1d24bdf","last_reissued_at":"2026-05-18T02:25:56.358053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:56.358053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaling of R\\'enyi entanglement entropies of the free Fermi-gas ground state: a rigorous proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander V. Sobolev, Hajo Leschke, Wolfgang Spitzer","submitted_at":"2013-12-24T14:36:42Z","abstract_excerpt":"In a remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Dimitri Gioev and Israel Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bi-partite von-Neumann entanglement entropy of non-interacting fermions in multi-dimensional Euclidean space at zero temperature. Based on recent progress by one of us (A.V.S.) in semi-classical functional calculus for pseudo-differential operators with discontinuous symbols, we provide here a complete proof of that formula and of its generalization to R\\'enyi entropies of all orders $\\alpha>0$. The special case $\\alpha=1/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6828","kind":"arxiv","version":3},"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":"1312.6828","created_at":"2026-05-18T02:25:56.358119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.6828v3","created_at":"2026-05-18T02:25:56.358119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6828","created_at":"2026-05-18T02:25:56.358119+00:00"},{"alias_kind":"pith_short_12","alias_value":"KPT6JMJSSQC6","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"KPT6JMJSSQC6EGK7","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"KPT6JMJS","created_at":"2026-05-18T12:27:51.066281+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/KPT6JMJSSQC6EGK7ET3FDK2OF5","json":"https://pith.science/pith/KPT6JMJSSQC6EGK7ET3FDK2OF5.json","graph_json":"https://pith.science/api/pith-number/KPT6JMJSSQC6EGK7ET3FDK2OF5/graph.json","events_json":"https://pith.science/api/pith-number/KPT6JMJSSQC6EGK7ET3FDK2OF5/events.json","paper":"https://pith.science/paper/KPT6JMJS"},"agent_actions":{"view_html":"https://pith.science/pith/KPT6JMJSSQC6EGK7ET3FDK2OF5","download_json":"https://pith.science/pith/KPT6JMJSSQC6EGK7ET3FDK2OF5.json","view_paper":"https://pith.science/paper/KPT6JMJS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.6828&json=true","fetch_graph":"https://pith.science/api/pith-number/KPT6JMJSSQC6EGK7ET3FDK2OF5/graph.json","fetch_events":"https://pith.science/api/pith-number/KPT6JMJSSQC6EGK7ET3FDK2OF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KPT6JMJSSQC6EGK7ET3FDK2OF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KPT6JMJSSQC6EGK7ET3FDK2OF5/action/storage_attestation","attest_author":"https://pith.science/pith/KPT6JMJSSQC6EGK7ET3FDK2OF5/action/author_attestation","sign_citation":"https://pith.science/pith/KPT6JMJSSQC6EGK7ET3FDK2OF5/action/citation_signature","submit_replication":"https://pith.science/pith/KPT6JMJSSQC6EGK7ET3FDK2OF5/action/replication_record"}},"created_at":"2026-05-18T02:25:56.358119+00:00","updated_at":"2026-05-18T02:25:56.358119+00:00"}