{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OO4PW2GXW6IKT46JGFTM6EPM5F","short_pith_number":"pith:OO4PW2GX","schema_version":"1.0","canonical_sha256":"73b8fb68d7b790a9f3c93166cf11ece97469f511528a3f6437a74a645037f88b","source":{"kind":"arxiv","id":"1404.1315","version":2},"attestation_state":"computed","paper":{"title":"Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Sylvain Prolhac","submitted_at":"2014-04-04T17:10:56Z","abstract_excerpt":"We consider the spectrum of the totally asymmetric simple exclusion process on a periodic lattice of $L$ sites. The first eigenstates have an eigenvalue with real part scaling as $L^{-3/2}$ for large $L$ with finite density of particles. Bethe ansatz shows that these eigenstates are characterized by four finite sets of positive half-integers, or equivalently by two integer partitions. Each corresponding eigenvalue is found to be equal to the value at its saddle point of a function indexed by the four sets. Our derivation of the large $L$ asymptotics relies on a version of the Euler-Maclaurin f"},"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":"1404.1315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-04-04T17:10:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f6fd31a5bc1bf86f1b82e41d1409a187bdb4e5dffd2531765520ded67370b3a5","abstract_canon_sha256":"523519e529bad79ed8b48608eb6babbfcc2d96e10e207599cf87c681c973e31b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:53.970198Z","signature_b64":"LWYAtjiNfnhsJjBN7FhzRPx2VJSnPP092yC/JUHY6u3Qj5HuMp4kFf1rshAdvNm6qqCeaaFIjl6AHsno1/BrAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73b8fb68d7b790a9f3c93166cf11ece97469f511528a3f6437a74a645037f88b","last_reissued_at":"2026-05-18T02:43:53.969771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:53.969771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Sylvain Prolhac","submitted_at":"2014-04-04T17:10:56Z","abstract_excerpt":"We consider the spectrum of the totally asymmetric simple exclusion process on a periodic lattice of $L$ sites. The first eigenstates have an eigenvalue with real part scaling as $L^{-3/2}$ for large $L$ with finite density of particles. Bethe ansatz shows that these eigenstates are characterized by four finite sets of positive half-integers, or equivalently by two integer partitions. Each corresponding eigenvalue is found to be equal to the value at its saddle point of a function indexed by the four sets. Our derivation of the large $L$ asymptotics relies on a version of the Euler-Maclaurin f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1315","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":"1404.1315","created_at":"2026-05-18T02:43:53.969839+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.1315v2","created_at":"2026-05-18T02:43:53.969839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1315","created_at":"2026-05-18T02:43:53.969839+00:00"},{"alias_kind":"pith_short_12","alias_value":"OO4PW2GXW6IK","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OO4PW2GXW6IKT46J","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OO4PW2GX","created_at":"2026-05-18T12:28:41.024544+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/OO4PW2GXW6IKT46JGFTM6EPM5F","json":"https://pith.science/pith/OO4PW2GXW6IKT46JGFTM6EPM5F.json","graph_json":"https://pith.science/api/pith-number/OO4PW2GXW6IKT46JGFTM6EPM5F/graph.json","events_json":"https://pith.science/api/pith-number/OO4PW2GXW6IKT46JGFTM6EPM5F/events.json","paper":"https://pith.science/paper/OO4PW2GX"},"agent_actions":{"view_html":"https://pith.science/pith/OO4PW2GXW6IKT46JGFTM6EPM5F","download_json":"https://pith.science/pith/OO4PW2GXW6IKT46JGFTM6EPM5F.json","view_paper":"https://pith.science/paper/OO4PW2GX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.1315&json=true","fetch_graph":"https://pith.science/api/pith-number/OO4PW2GXW6IKT46JGFTM6EPM5F/graph.json","fetch_events":"https://pith.science/api/pith-number/OO4PW2GXW6IKT46JGFTM6EPM5F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OO4PW2GXW6IKT46JGFTM6EPM5F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OO4PW2GXW6IKT46JGFTM6EPM5F/action/storage_attestation","attest_author":"https://pith.science/pith/OO4PW2GXW6IKT46JGFTM6EPM5F/action/author_attestation","sign_citation":"https://pith.science/pith/OO4PW2GXW6IKT46JGFTM6EPM5F/action/citation_signature","submit_replication":"https://pith.science/pith/OO4PW2GXW6IKT46JGFTM6EPM5F/action/replication_record"}},"created_at":"2026-05-18T02:43:53.969839+00:00","updated_at":"2026-05-18T02:43:53.969839+00:00"}