{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GI47R63TOCZI4253UEF5FOUDWL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"df8a22bb3d926a3ab60038d33ccd556eee03d22b58305ba0e387adca6ad6a4e9","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2010-04-14T21:37:45Z","title_canon_sha256":"d1b41c8505a89f636fa1a2cc250dfb4a5f536a955f82b8f957d53580e8dc8c48"},"schema_version":"1.0","source":{"id":"1004.2513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2513","created_at":"2026-05-18T02:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2513v1","created_at":"2026-05-18T02:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2513","created_at":"2026-05-18T02:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"GI47R63TOCZI","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GI47R63TOCZI4253","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GI47R63T","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:1fdf3b74c0a05a8c8df1114dfcdf802bc447af49c28bc74c56f1c5ae86ceebb3","target":"graph","created_at":"2026-05-18T02:08:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In one of the very few exact quantum mechanical calculations of fugacity coefficients, Dodd and Gibbs (\\textit{J. Math.Phys}.,\\textbf{15}, 41 (1974)) obtained $b_{2}$ and $b_{3}$ for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For $b_{2}$, we have shown (\\textit{Mol. Phys}.,\\textbf{103}, 1301 (2005)) that Dodd and Gibbs' result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in 1 dimension. Now, we develop an exact expression for $b_","authors_text":"A. Amaya-Tapia, M. Lassaut, S. Y. Larsen","cross_cats":["cond-mat.quant-gas","cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2010-04-14T21:37:45Z","title":"Third Bose Fugacity Coefficient in One Dimension, as a Function of Asymptotic Quantities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2513","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c552af7e0dfa624152d04ec9be699c82508e29365e2cd5519dbac8e929901486","target":"record","created_at":"2026-05-18T02:08:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"df8a22bb3d926a3ab60038d33ccd556eee03d22b58305ba0e387adca6ad6a4e9","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2010-04-14T21:37:45Z","title_canon_sha256":"d1b41c8505a89f636fa1a2cc250dfb4a5f536a955f82b8f957d53580e8dc8c48"},"schema_version":"1.0","source":{"id":"1004.2513","kind":"arxiv","version":1}},"canonical_sha256":"3239f8fb7370b28e6bbba10bd2ba83b2cade792ff280e047dd878aaf612f24d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3239f8fb7370b28e6bbba10bd2ba83b2cade792ff280e047dd878aaf612f24d6","first_computed_at":"2026-05-18T02:08:05.442873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:05.442873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KBh5dpkqu3ULAZQ5yCMISDVXVT72czcu9uxAiI/txvCTMNFeHBaxHdt1DPSr4xflKyhnvrFascmJxgZ+7F/2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:05.443428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.2513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c552af7e0dfa624152d04ec9be699c82508e29365e2cd5519dbac8e929901486","sha256:1fdf3b74c0a05a8c8df1114dfcdf802bc447af49c28bc74c56f1c5ae86ceebb3"],"state_sha256":"7d901bb4b07082b86877a96508540d4e2bd42d0d0a686f7aab0e3a52f83df8cd"}