{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SR7Y7CYC6HPUP5UKLYMTAJSSTM","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":"528270097ddbc630d342bdb143c75c3826560a0088a552118c2fe8a374a6ce0f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2010-04-29T12:11:00Z","title_canon_sha256":"50a35c5195ce4e5dded41d875770e9b22776947265c96f0b14692d7ea352c0d4"},"schema_version":"1.0","source":{"id":"1004.5260","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5260","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5260v2","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5260","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"pith_short_12","alias_value":"SR7Y7CYC6HPU","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SR7Y7CYC6HPUP5UK","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SR7Y7CYC","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:169c2f484af3fbf80163a6d686642bd28158d9a24b18721044810a1dbc69cc2b","target":"graph","created_at":"2026-05-18T02:24:15Z","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":"Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states show some pattern if the Fourier transform is partially negative. The latter confirms the co","authors_text":"Andras Suto","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2010-04-29T12:11:00Z","title":"Ground state at high density"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5260","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":"sha256:200088dd1607d6d294aacaaf6d83cc950f4ad804944b36f66cb7d77d0df9bb74","target":"record","created_at":"2026-05-18T02:24:15Z","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":"528270097ddbc630d342bdb143c75c3826560a0088a552118c2fe8a374a6ce0f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2010-04-29T12:11:00Z","title_canon_sha256":"50a35c5195ce4e5dded41d875770e9b22776947265c96f0b14692d7ea352c0d4"},"schema_version":"1.0","source":{"id":"1004.5260","kind":"arxiv","version":2}},"canonical_sha256":"947f8f8b02f1df47f68a5e193026529b2f739a3ca665b3f384e7e306dabdb4f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"947f8f8b02f1df47f68a5e193026529b2f739a3ca665b3f384e7e306dabdb4f6","first_computed_at":"2026-05-18T02:24:15.086615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:15.086615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HlQgfnBOJ5cjZg5vWoQpw5TBB1t7x5+wjrYcJ7d2wx+YbqrtH4ntn3Mx8BKEc7nf8jfJSGLNBtpUsxFvWD8JCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:15.087306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5260","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:200088dd1607d6d294aacaaf6d83cc950f4ad804944b36f66cb7d77d0df9bb74","sha256:169c2f484af3fbf80163a6d686642bd28158d9a24b18721044810a1dbc69cc2b"],"state_sha256":"6187461e0ff29bf5844942c8052687715815fc9e3bbc81f544089d660e363821"}