{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:SYKWEI4YKIPRMFXEUUR3JY4LCH","short_pith_number":"pith:SYKWEI4Y","schema_version":"1.0","canonical_sha256":"9615622398521f1616e4a523b4e38b11cb940c027d0b190d410614a328f7369d","source":{"kind":"arxiv","id":"math-ph/0301042","version":2},"attestation_state":"computed","paper":{"title":"Random matrix averages and the impenetrable Bose gas in Dirichlet and Neumann boundary conditions","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"N. E. Frankel, P. J. Forrester, T. M. Garoni","submitted_at":"2003-01-31T02:31:00Z","abstract_excerpt":"The density matrix for the impenetrable Bose gas in Dirichlet and Neumann boundary conditions can be written in terms of $<\\prod_{l=1}^n| \\cos\\phi_1-\\cos\\theta_l|\n  |\\cos\\phi_2-\\cos\\theta_l|>$, where the average is with respect to the eigenvalue probability density function for random unitary matrices from the classical groups $Sp(n)$ and $O^+(2n)$ respectively. In the large $n$ limit log-gas considerations imply that the average factorizes into the product of averages of the form $<\\prod_{l=1}^n|\\cos\\phi-\\cos\\theta_l>$. By changing variables this average in turn is a special case of the funct"},"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/0301042","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2003-01-31T02:31:00Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"7a85fbd7bee890e668d0fdacf52136afe16406ce13ed4b00760faf9fcad28a60","abstract_canon_sha256":"693d3c1bfc4eefacde3f9c6b850bbf9e34a9809b5c13aff77c0361eb35ed9ec7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:33.934564Z","signature_b64":"5EnxAw+BP7AwrrtTdU72U5mgMCzcYObeT/By7b8YTS2wSIfLEzCNzj58/BYG7FxJcLqMlw1kvegL+VkjA2G0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9615622398521f1616e4a523b4e38b11cb940c027d0b190d410614a328f7369d","last_reissued_at":"2026-05-18T01:38:33.934094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:33.934094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random matrix averages and the impenetrable Bose gas in Dirichlet and Neumann boundary conditions","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"N. E. Frankel, P. J. Forrester, T. M. Garoni","submitted_at":"2003-01-31T02:31:00Z","abstract_excerpt":"The density matrix for the impenetrable Bose gas in Dirichlet and Neumann boundary conditions can be written in terms of $<\\prod_{l=1}^n| \\cos\\phi_1-\\cos\\theta_l|\n  |\\cos\\phi_2-\\cos\\theta_l|>$, where the average is with respect to the eigenvalue probability density function for random unitary matrices from the classical groups $Sp(n)$ and $O^+(2n)$ respectively. In the large $n$ limit log-gas considerations imply that the average factorizes into the product of averages of the form $<\\prod_{l=1}^n|\\cos\\phi-\\cos\\theta_l>$. By changing variables this average in turn is a special case of the funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0301042","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":"math-ph/0301042","created_at":"2026-05-18T01:38:33.934161+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0301042v2","created_at":"2026-05-18T01:38:33.934161+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0301042","created_at":"2026-05-18T01:38:33.934161+00:00"},{"alias_kind":"pith_short_12","alias_value":"SYKWEI4YKIPR","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"SYKWEI4YKIPRMFXE","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"SYKWEI4Y","created_at":"2026-05-18T12:25:52.051335+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/SYKWEI4YKIPRMFXEUUR3JY4LCH","json":"https://pith.science/pith/SYKWEI4YKIPRMFXEUUR3JY4LCH.json","graph_json":"https://pith.science/api/pith-number/SYKWEI4YKIPRMFXEUUR3JY4LCH/graph.json","events_json":"https://pith.science/api/pith-number/SYKWEI4YKIPRMFXEUUR3JY4LCH/events.json","paper":"https://pith.science/paper/SYKWEI4Y"},"agent_actions":{"view_html":"https://pith.science/pith/SYKWEI4YKIPRMFXEUUR3JY4LCH","download_json":"https://pith.science/pith/SYKWEI4YKIPRMFXEUUR3JY4LCH.json","view_paper":"https://pith.science/paper/SYKWEI4Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0301042&json=true","fetch_graph":"https://pith.science/api/pith-number/SYKWEI4YKIPRMFXEUUR3JY4LCH/graph.json","fetch_events":"https://pith.science/api/pith-number/SYKWEI4YKIPRMFXEUUR3JY4LCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SYKWEI4YKIPRMFXEUUR3JY4LCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SYKWEI4YKIPRMFXEUUR3JY4LCH/action/storage_attestation","attest_author":"https://pith.science/pith/SYKWEI4YKIPRMFXEUUR3JY4LCH/action/author_attestation","sign_citation":"https://pith.science/pith/SYKWEI4YKIPRMFXEUUR3JY4LCH/action/citation_signature","submit_replication":"https://pith.science/pith/SYKWEI4YKIPRMFXEUUR3JY4LCH/action/replication_record"}},"created_at":"2026-05-18T01:38:33.934161+00:00","updated_at":"2026-05-18T01:38:33.934161+00:00"}