{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JBLPSYOOCLWRJGPY2W5PZTGRS5","short_pith_number":"pith:JBLPSYOO","schema_version":"1.0","canonical_sha256":"4856f961ce12ed1499f8d5bafcccd1975daa993853306818644e92e35326009e","source":{"kind":"arxiv","id":"1802.10374","version":1},"attestation_state":"computed","paper":{"title":"Extreme statistics and index distribution in the classical $1d$ Coulomb gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Abhishek Dhar, Anupam Kundu, Gregory Schehr, Sanjib Sabhapandit, Satya N. Majumdar","submitted_at":"2018-02-28T11:50:46Z","abstract_excerpt":"We consider a one-dimensional gas of $N$ charged particles confined by an external harmonic potential and interacting via the one-dimensional Coulomb potential. For this system we show that in equilibrium the charges settle, on an average, uniformly and symmetrically on a finite region centred around the origin. We study the statistics of the position of the rightmost particle $x_{\\max}$ and show that the limiting distribution describing its typical fluctuations is different from the Tracy-Widom distribution found in the one-dimensional log-gas. We also compute the large deviation functions wh"},"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":"1802.10374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-02-28T11:50:46Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"18fcbc95bbd1c0fe29f9ac8af2e8cf1d7800ed635dc6c7b72a31afe9d088baa8","abstract_canon_sha256":"538363a89e19e69b18e10c8ee1605644574c7fbf293013560b075398a166e459"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:12.779927Z","signature_b64":"n3Wr/Y/7dx7NJ4Efn8Wd012q3gopXKP9uGI/TY/zutMwrpk8P7dm6ntQtJ5riYVSCsG38B3emJeIxHMoGdSgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4856f961ce12ed1499f8d5bafcccd1975daa993853306818644e92e35326009e","last_reissued_at":"2026-05-18T00:02:12.779217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:12.779217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extreme statistics and index distribution in the classical $1d$ Coulomb gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Abhishek Dhar, Anupam Kundu, Gregory Schehr, Sanjib Sabhapandit, Satya N. Majumdar","submitted_at":"2018-02-28T11:50:46Z","abstract_excerpt":"We consider a one-dimensional gas of $N$ charged particles confined by an external harmonic potential and interacting via the one-dimensional Coulomb potential. For this system we show that in equilibrium the charges settle, on an average, uniformly and symmetrically on a finite region centred around the origin. We study the statistics of the position of the rightmost particle $x_{\\max}$ and show that the limiting distribution describing its typical fluctuations is different from the Tracy-Widom distribution found in the one-dimensional log-gas. We also compute the large deviation functions wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10374","kind":"arxiv","version":1},"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":"1802.10374","created_at":"2026-05-18T00:02:12.779337+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.10374v1","created_at":"2026-05-18T00:02:12.779337+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10374","created_at":"2026-05-18T00:02:12.779337+00:00"},{"alias_kind":"pith_short_12","alias_value":"JBLPSYOOCLWR","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JBLPSYOOCLWRJGPY","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JBLPSYOO","created_at":"2026-05-18T12:32:31.084164+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/JBLPSYOOCLWRJGPY2W5PZTGRS5","json":"https://pith.science/pith/JBLPSYOOCLWRJGPY2W5PZTGRS5.json","graph_json":"https://pith.science/api/pith-number/JBLPSYOOCLWRJGPY2W5PZTGRS5/graph.json","events_json":"https://pith.science/api/pith-number/JBLPSYOOCLWRJGPY2W5PZTGRS5/events.json","paper":"https://pith.science/paper/JBLPSYOO"},"agent_actions":{"view_html":"https://pith.science/pith/JBLPSYOOCLWRJGPY2W5PZTGRS5","download_json":"https://pith.science/pith/JBLPSYOOCLWRJGPY2W5PZTGRS5.json","view_paper":"https://pith.science/paper/JBLPSYOO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.10374&json=true","fetch_graph":"https://pith.science/api/pith-number/JBLPSYOOCLWRJGPY2W5PZTGRS5/graph.json","fetch_events":"https://pith.science/api/pith-number/JBLPSYOOCLWRJGPY2W5PZTGRS5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JBLPSYOOCLWRJGPY2W5PZTGRS5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JBLPSYOOCLWRJGPY2W5PZTGRS5/action/storage_attestation","attest_author":"https://pith.science/pith/JBLPSYOOCLWRJGPY2W5PZTGRS5/action/author_attestation","sign_citation":"https://pith.science/pith/JBLPSYOOCLWRJGPY2W5PZTGRS5/action/citation_signature","submit_replication":"https://pith.science/pith/JBLPSYOOCLWRJGPY2W5PZTGRS5/action/replication_record"}},"created_at":"2026-05-18T00:02:12.779337+00:00","updated_at":"2026-05-18T00:02:12.779337+00:00"}