{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:X3EE26LEIMJFY6JGNT4GT27TRK","short_pith_number":"pith:X3EE26LE","schema_version":"1.0","canonical_sha256":"bec84d796443125c79266cf869ebf38aa8e3a3c4b5188ab48575d4af19712d1a","source":{"kind":"arxiv","id":"math-ph/0401011","version":1},"attestation_state":"computed","paper":{"title":"Applications and generalizations of Fisher-Hartwig asymptotics","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"N.E. Frankel, P.J. Forrester","submitted_at":"2004-01-07T02:21:01Z","abstract_excerpt":"Fisher-Hartwig asymptotics refers to the large $n$ form of a class of Toeplitz determinants with singular generating functions. This class of Toeplitz determinants occurs in the study of the spin-spin correlations for the two-dimensional Ising model, and the ground state density matrix of the impenetrable Bose gas, amongst other problems in mathematical physics. We give a new application of the original Fisher-Hartwig formula to the asymptotic decay of the Ising correlations above $T_c$, while the study of the Bose gas density matrix leads us to generalize the Fisher-Hartwig formula to the asy"},"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":"math-ph/0401011","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-01-07T02:21:01Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"af95fd8bf4593cad4353034477620a268e927e3484312e9b78a2b2b9ef4cb581","abstract_canon_sha256":"ed344a271dce8ff1403ab072b1a65be6aef72ef492f19259ef381f8eff071dfd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:33.594252Z","signature_b64":"OKmsRdG8h+a/qEvsjAjTEQ55ERO/CXzWUh4doLwsVxQDpERquT89EaCF7+QtLSpkiBGxG05jtCD2byc2BDJODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bec84d796443125c79266cf869ebf38aa8e3a3c4b5188ab48575d4af19712d1a","last_reissued_at":"2026-05-18T01:38:33.593678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:33.593678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Applications and generalizations of Fisher-Hartwig asymptotics","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"N.E. Frankel, P.J. Forrester","submitted_at":"2004-01-07T02:21:01Z","abstract_excerpt":"Fisher-Hartwig asymptotics refers to the large $n$ form of a class of Toeplitz determinants with singular generating functions. This class of Toeplitz determinants occurs in the study of the spin-spin correlations for the two-dimensional Ising model, and the ground state density matrix of the impenetrable Bose gas, amongst other problems in mathematical physics. We give a new application of the original Fisher-Hartwig formula to the asymptotic decay of the Ising correlations above $T_c$, while the study of the Bose gas density matrix leads us to generalize the Fisher-Hartwig formula to the asy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0401011","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":"math-ph/0401011","created_at":"2026-05-18T01:38:33.593744+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0401011v1","created_at":"2026-05-18T01:38:33.593744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0401011","created_at":"2026-05-18T01:38:33.593744+00:00"},{"alias_kind":"pith_short_12","alias_value":"X3EE26LEIMJF","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"X3EE26LEIMJFY6JG","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"X3EE26LE","created_at":"2026-05-18T12:25:52.687210+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/X3EE26LEIMJFY6JGNT4GT27TRK","json":"https://pith.science/pith/X3EE26LEIMJFY6JGNT4GT27TRK.json","graph_json":"https://pith.science/api/pith-number/X3EE26LEIMJFY6JGNT4GT27TRK/graph.json","events_json":"https://pith.science/api/pith-number/X3EE26LEIMJFY6JGNT4GT27TRK/events.json","paper":"https://pith.science/paper/X3EE26LE"},"agent_actions":{"view_html":"https://pith.science/pith/X3EE26LEIMJFY6JGNT4GT27TRK","download_json":"https://pith.science/pith/X3EE26LEIMJFY6JGNT4GT27TRK.json","view_paper":"https://pith.science/paper/X3EE26LE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0401011&json=true","fetch_graph":"https://pith.science/api/pith-number/X3EE26LEIMJFY6JGNT4GT27TRK/graph.json","fetch_events":"https://pith.science/api/pith-number/X3EE26LEIMJFY6JGNT4GT27TRK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X3EE26LEIMJFY6JGNT4GT27TRK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X3EE26LEIMJFY6JGNT4GT27TRK/action/storage_attestation","attest_author":"https://pith.science/pith/X3EE26LEIMJFY6JGNT4GT27TRK/action/author_attestation","sign_citation":"https://pith.science/pith/X3EE26LEIMJFY6JGNT4GT27TRK/action/citation_signature","submit_replication":"https://pith.science/pith/X3EE26LEIMJFY6JGNT4GT27TRK/action/replication_record"}},"created_at":"2026-05-18T01:38:33.593744+00:00","updated_at":"2026-05-18T01:38:33.593744+00:00"}