{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WHRQ2IOYDBOXLM2X5JV7FKXBAL","short_pith_number":"pith:WHRQ2IOY","schema_version":"1.0","canonical_sha256":"b1e30d21d8185d75b357ea6bf2aae102dc2616dfa8a432a283005a9f6f3f7a69","source":{"kind":"arxiv","id":"1303.2968","version":2},"attestation_state":"computed","paper":{"title":"1D Log Gases and the Renormalized Energy: Crystallization at Vanishing Temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Etienne Sandier, Sylvia Serfaty","submitted_at":"2013-03-12T17:54:36Z","abstract_excerpt":"We study the statistical mechanics of a one-dimensional log gas with general potential and arbitrary beta, the inverse of temperature, according to the method we introduced for two-dimensional Coulomb gases in [SS2]. Such ensembles correspond to random matrix models in some particular cases. The formal limit beta infinite corresponds to \"weighted Fekete sets\" and is also treated. We introduce a one-dimensional version of the \"renormalized energy\" of [SS1], measuring the total logarithmic interaction of an infinite set of points on the real line in a uniform neutralizing background. We show tha"},"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":"1303.2968","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-12T17:54:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a10a0b361e0382b4830ededb142f2baa7840b693418919c9e4a4dd9ad85d37a6","abstract_canon_sha256":"7c8684fa16a49a935c4957df8d13171955196dbe3c567f1f87e3cf256fb9a4f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:32.136397Z","signature_b64":"ncOEnSYq/k2vXdxRMKCj6oemyC4X4wUc7AXTajZ2ckcHpfGuSNojD/PyKOWbkVcu9izdD2QnlhJ+BoQ32DDiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1e30d21d8185d75b357ea6bf2aae102dc2616dfa8a432a283005a9f6f3f7a69","last_reissued_at":"2026-05-18T02:45:32.135721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:32.135721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"1D Log Gases and the Renormalized Energy: Crystallization at Vanishing Temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Etienne Sandier, Sylvia Serfaty","submitted_at":"2013-03-12T17:54:36Z","abstract_excerpt":"We study the statistical mechanics of a one-dimensional log gas with general potential and arbitrary beta, the inverse of temperature, according to the method we introduced for two-dimensional Coulomb gases in [SS2]. Such ensembles correspond to random matrix models in some particular cases. The formal limit beta infinite corresponds to \"weighted Fekete sets\" and is also treated. We introduce a one-dimensional version of the \"renormalized energy\" of [SS1], measuring the total logarithmic interaction of an infinite set of points on the real line in a uniform neutralizing background. We show tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2968","kind":"arxiv","version":2},"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":"1303.2968","created_at":"2026-05-18T02:45:32.135841+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.2968v2","created_at":"2026-05-18T02:45:32.135841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2968","created_at":"2026-05-18T02:45:32.135841+00:00"},{"alias_kind":"pith_short_12","alias_value":"WHRQ2IOYDBOX","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WHRQ2IOYDBOXLM2X","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WHRQ2IOY","created_at":"2026-05-18T12:28:04.890932+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/WHRQ2IOYDBOXLM2X5JV7FKXBAL","json":"https://pith.science/pith/WHRQ2IOYDBOXLM2X5JV7FKXBAL.json","graph_json":"https://pith.science/api/pith-number/WHRQ2IOYDBOXLM2X5JV7FKXBAL/graph.json","events_json":"https://pith.science/api/pith-number/WHRQ2IOYDBOXLM2X5JV7FKXBAL/events.json","paper":"https://pith.science/paper/WHRQ2IOY"},"agent_actions":{"view_html":"https://pith.science/pith/WHRQ2IOYDBOXLM2X5JV7FKXBAL","download_json":"https://pith.science/pith/WHRQ2IOYDBOXLM2X5JV7FKXBAL.json","view_paper":"https://pith.science/paper/WHRQ2IOY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.2968&json=true","fetch_graph":"https://pith.science/api/pith-number/WHRQ2IOYDBOXLM2X5JV7FKXBAL/graph.json","fetch_events":"https://pith.science/api/pith-number/WHRQ2IOYDBOXLM2X5JV7FKXBAL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WHRQ2IOYDBOXLM2X5JV7FKXBAL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WHRQ2IOYDBOXLM2X5JV7FKXBAL/action/storage_attestation","attest_author":"https://pith.science/pith/WHRQ2IOYDBOXLM2X5JV7FKXBAL/action/author_attestation","sign_citation":"https://pith.science/pith/WHRQ2IOYDBOXLM2X5JV7FKXBAL/action/citation_signature","submit_replication":"https://pith.science/pith/WHRQ2IOYDBOXLM2X5JV7FKXBAL/action/replication_record"}},"created_at":"2026-05-18T02:45:32.135841+00:00","updated_at":"2026-05-18T02:45:32.135841+00:00"}