{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QWUCPGAFWGVKVBXDECJND6AYIH","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":"29298f9e77c5ad19feb518d91d1b07293fc2b3a122edc76b212a5fd662650898","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-28T08:35:51Z","title_canon_sha256":"124fda7a2b1f6cf1b45e65a8016f251d5407b6cc5846715b5c7ab0ef915f3c67"},"schema_version":"1.0","source":{"id":"2605.29594","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29594","created_at":"2026-05-29T01:05:49Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29594v1","created_at":"2026-05-29T01:05:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29594","created_at":"2026-05-29T01:05:49Z"},{"alias_kind":"pith_short_12","alias_value":"QWUCPGAFWGVK","created_at":"2026-05-29T01:05:49Z"},{"alias_kind":"pith_short_16","alias_value":"QWUCPGAFWGVKVBXD","created_at":"2026-05-29T01:05:49Z"},{"alias_kind":"pith_short_8","alias_value":"QWUCPGAF","created_at":"2026-05-29T01:05:49Z"}],"graph_snapshots":[{"event_id":"sha256:f0739a69c21f2bea8948e98fe55ba9ed600d82e9190530d3ed5f4a8b291bbab6","target":"graph","created_at":"2026-05-29T01:05:49Z","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/2605.29594/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a determinantal Coulomb gas in the complex plane associated with the external potential $$ Q(z)=\\frac{1}{1-\\tau^2}\\big(|z|^2-\\tau \\text{Re } z^2\\big)-2c\\log|z-a|, $$ where $\\tau\\in[0,1)$, $c\\ge0$, and $a\\ge0$. In the regimes where the associated droplet is simply or doubly connected, we derive the free energy expansion up to and including the constant term, with all coefficients computed explicitly, thereby extending recent results in the isotropic case $\\tau=0$. In particular, we identify the constant term with the Liouville action associated with the droplet. Our result admits a nat","authors_text":"Eui Yoo, Meng Yang, Sung-Soo Byun","cross_cats":["math.CV","math.MP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-28T08:35:51Z","title":"Free energy expansion of determinantal Coulomb gases in the quadratic fields with a point charge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29594","kind":"arxiv","version":1},"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:f2a5aaa89db3628db187969b275e28d0d1483f807234e8dfe71ada8f06a8976f","target":"record","created_at":"2026-05-29T01:05:49Z","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":"29298f9e77c5ad19feb518d91d1b07293fc2b3a122edc76b212a5fd662650898","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-28T08:35:51Z","title_canon_sha256":"124fda7a2b1f6cf1b45e65a8016f251d5407b6cc5846715b5c7ab0ef915f3c67"},"schema_version":"1.0","source":{"id":"2605.29594","kind":"arxiv","version":1}},"canonical_sha256":"85a8279805b1aaaa86e32092d1f81841e5503f65ce35179ec6da1c762f3bacdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85a8279805b1aaaa86e32092d1f81841e5503f65ce35179ec6da1c762f3bacdf","first_computed_at":"2026-05-29T01:05:49.726173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:05:49.726173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k/wB6ciGzjvTD/6bMANhpsgfqrQJYQxIs9zsMXbZfm8LBOCNyV4QVq+Dtgon+VwdyuPuUL+kGkGsWSywmL+IAg==","signature_status":"signed_v1","signed_at":"2026-05-29T01:05:49.727128Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.29594","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2a5aaa89db3628db187969b275e28d0d1483f807234e8dfe71ada8f06a8976f","sha256:f0739a69c21f2bea8948e98fe55ba9ed600d82e9190530d3ed5f4a8b291bbab6"],"state_sha256":"496c665f469c9bb50fef769f022f45986a11eeb0840a76b68012b8a53198651e"}