{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Q3OKYLKZS42XDBK2OK77JNWQPG","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":"fc2b6adf4e090c902ed4de38708fc42575587b9b00a6fa0db72c25dc123292c6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-01T16:58:57Z","title_canon_sha256":"6a2da3c39c25901896b075fda48eade5b1249fd1e8df771a22d0cb1a022a5e89"},"schema_version":"1.0","source":{"id":"1907.00923","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00923","created_at":"2026-07-05T02:32:12Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00923v4","created_at":"2026-07-05T02:32:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00923","created_at":"2026-07-05T02:32:12Z"},{"alias_kind":"pith_short_12","alias_value":"Q3OKYLKZS42X","created_at":"2026-07-05T02:32:12Z"},{"alias_kind":"pith_short_16","alias_value":"Q3OKYLKZS42XDBK2","created_at":"2026-07-05T02:32:12Z"},{"alias_kind":"pith_short_8","alias_value":"Q3OKYLKZ","created_at":"2026-07-05T02:32:12Z"}],"graph_snapshots":[{"event_id":"sha256:350207251d3d6ed9f8d5707a66ffe522237da4b4538e076161795c04e8a1e0a6","target":"graph","created_at":"2026-07-05T02:32:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1907.00923/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We examine a Coulomb gas consisting of $n$ identical repelling point charges at an arbitrary inverse temperature $\\beta$, subjected to a suitable external field. We prove that the gas is effectively localized to a small neighbourhood of the \"droplet\" -- the support of the equilibrium measure determined by the external field. More precisely, we prove that the distance between the droplet and the vacuum is with very high probability at most proportional to $$\\sqrt{\\dfrac {\\log n}{\\beta n}}.$$ This order of magnitude is known to be \"tight\" when $\\beta=1$ and the external field is radially symmetr","authors_text":"Yacin Ameur","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-01T16:58:57Z","title":"A localization theorem for the planar Coulomb gas in an external field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00923","kind":"arxiv","version":4},"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:be5f140a6f11b7ce940a50491d4baf0977ddafe336ca94b81929fb3b98ab7a42","target":"record","created_at":"2026-07-05T02:32:12Z","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":"fc2b6adf4e090c902ed4de38708fc42575587b9b00a6fa0db72c25dc123292c6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-01T16:58:57Z","title_canon_sha256":"6a2da3c39c25901896b075fda48eade5b1249fd1e8df771a22d0cb1a022a5e89"},"schema_version":"1.0","source":{"id":"1907.00923","kind":"arxiv","version":4}},"canonical_sha256":"86dcac2d59973571855a72bff4b6d079a2db3a601f124f894c93afd2c8a37f4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86dcac2d59973571855a72bff4b6d079a2db3a601f124f894c93afd2c8a37f4d","first_computed_at":"2026-07-05T02:32:12.261648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:32:12.261648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SvzQ8G0onNPzKiBQ8FNgT+yadbfyM5wpTJn1L4xV866PYEEveojrnO56H2knkt9RCFthNu1U6rhB4Vto3B91AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:32:12.262197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.00923","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be5f140a6f11b7ce940a50491d4baf0977ddafe336ca94b81929fb3b98ab7a42","sha256:350207251d3d6ed9f8d5707a66ffe522237da4b4538e076161795c04e8a1e0a6"],"state_sha256":"a331ea247c2292076fd7dc2576940fb1559b3902596f2f43c20feaf9fa0acb23"}