{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5AKBBD2G7XSLUSCTIEJGCXAIFN","short_pith_number":"pith:5AKBBD2G","schema_version":"1.0","canonical_sha256":"e814108f46fde4ba48534112615c082b44215d4d995ba4b562c01a15f9f18042","source":{"kind":"arxiv","id":"1409.5484","version":1},"attestation_state":"computed","paper":{"title":"Ground-state Bethe root densities and quantum phase transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Ian Marquette, Jon Links","submitted_at":"2014-09-18T22:49:10Z","abstract_excerpt":"Exactly solvable models provide a unique method, via qualitative changes in the distribution of the ground-state roots of the Bethe Ansatz equations, to identify quantum phase transitions. Here we expand on this approach, in a quantitative manner, for two models of Bose--Einstein condensates. The first model deals with the interconversion of bosonic atoms and molecules. The second is the two-site Bose--Hubbard model, widely used to describe tunneling phenomena in Bose--Einstein condensates. For these systems we calculate the ground-state root density. This facilitates the determination of anal"},"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":"1409.5484","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-09-18T22:49:10Z","cross_cats_sorted":["cond-mat.quant-gas","math-ph","math.MP"],"title_canon_sha256":"496377a46bed5d225e241d03dd0a44dfcb47f2530019f4aa5bbdd807c93e8381","abstract_canon_sha256":"02a27f559ef21b219aa13ec5282d4cce02c1682afcc9101dab85456b5785de28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:01.221181Z","signature_b64":"pWCKmRwIodGeLkrL4SbvE2lwJUzIyZBnv63XO+tiCY6FgwS3X8MtQsxNZq3AyxT2Pj8quBNkCV7v50uAMal5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e814108f46fde4ba48534112615c082b44215d4d995ba4b562c01a15f9f18042","last_reissued_at":"2026-05-18T01:42:01.220745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:01.220745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground-state Bethe root densities and quantum phase transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Ian Marquette, Jon Links","submitted_at":"2014-09-18T22:49:10Z","abstract_excerpt":"Exactly solvable models provide a unique method, via qualitative changes in the distribution of the ground-state roots of the Bethe Ansatz equations, to identify quantum phase transitions. Here we expand on this approach, in a quantitative manner, for two models of Bose--Einstein condensates. The first model deals with the interconversion of bosonic atoms and molecules. The second is the two-site Bose--Hubbard model, widely used to describe tunneling phenomena in Bose--Einstein condensates. For these systems we calculate the ground-state root density. This facilitates the determination of anal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5484","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":"1409.5484","created_at":"2026-05-18T01:42:01.220803+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.5484v1","created_at":"2026-05-18T01:42:01.220803+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5484","created_at":"2026-05-18T01:42:01.220803+00:00"},{"alias_kind":"pith_short_12","alias_value":"5AKBBD2G7XSL","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5AKBBD2G7XSLUSCT","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5AKBBD2G","created_at":"2026-05-18T12:28:14.216126+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/5AKBBD2G7XSLUSCTIEJGCXAIFN","json":"https://pith.science/pith/5AKBBD2G7XSLUSCTIEJGCXAIFN.json","graph_json":"https://pith.science/api/pith-number/5AKBBD2G7XSLUSCTIEJGCXAIFN/graph.json","events_json":"https://pith.science/api/pith-number/5AKBBD2G7XSLUSCTIEJGCXAIFN/events.json","paper":"https://pith.science/paper/5AKBBD2G"},"agent_actions":{"view_html":"https://pith.science/pith/5AKBBD2G7XSLUSCTIEJGCXAIFN","download_json":"https://pith.science/pith/5AKBBD2G7XSLUSCTIEJGCXAIFN.json","view_paper":"https://pith.science/paper/5AKBBD2G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.5484&json=true","fetch_graph":"https://pith.science/api/pith-number/5AKBBD2G7XSLUSCTIEJGCXAIFN/graph.json","fetch_events":"https://pith.science/api/pith-number/5AKBBD2G7XSLUSCTIEJGCXAIFN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5AKBBD2G7XSLUSCTIEJGCXAIFN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5AKBBD2G7XSLUSCTIEJGCXAIFN/action/storage_attestation","attest_author":"https://pith.science/pith/5AKBBD2G7XSLUSCTIEJGCXAIFN/action/author_attestation","sign_citation":"https://pith.science/pith/5AKBBD2G7XSLUSCTIEJGCXAIFN/action/citation_signature","submit_replication":"https://pith.science/pith/5AKBBD2G7XSLUSCTIEJGCXAIFN/action/replication_record"}},"created_at":"2026-05-18T01:42:01.220803+00:00","updated_at":"2026-05-18T01:42:01.220803+00:00"}