{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5KALOAE6DUYIJD46MBXD5M3WM7","short_pith_number":"pith:5KALOAE6","schema_version":"1.0","canonical_sha256":"ea80b7009e1d30848f9e606e3eb37667fe841b2d9d173f5f03f810fa5495f287","source":{"kind":"arxiv","id":"1707.07495","version":2},"attestation_state":"computed","paper":{"title":"Ground States of Two-Component Attractive Bose-Einstein Condensates I: Existence and Uniqueness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Shuai Li, Xiaoyu Zeng, Yujin Guo","submitted_at":"2017-07-24T11:39:53Z","abstract_excerpt":"We study ground states of two-component Bose-Einstein condensates (BEC) with trapping potentials in $R^2$, where the intraspecies interaction $(-a_1,-a_2)$ and the interspecies interaction $-\\beta$ are both attractive, $i.e,$ $a_1$, $a_2$ and $\\beta $ are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated $L^2$-critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as $\\beta \\nearrow \\beta ^*=a^*+\\sqrt{(a^*-a_1"},"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":"1707.07495","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-24T11:39:53Z","cross_cats_sorted":[],"title_canon_sha256":"5d73e4a385593ddd7bff680242bcf29b0515074e0a2165c5d494214ff0d70acc","abstract_canon_sha256":"2b20b156a30f3edb5decaf36a78bb7c017af7e039c0429101c21e65815b6a153"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:40.930546Z","signature_b64":"8VYfMCnn9kE92EXDqmG4G7yv8wPCo2GuPpavy3/fcx/P3nErUtkvmG3xhmJ7K1k+PY2U1iMsWmaGbi1rbOWUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea80b7009e1d30848f9e606e3eb37667fe841b2d9d173f5f03f810fa5495f287","last_reissued_at":"2026-05-17T23:48:40.929999Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:40.929999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground States of Two-Component Attractive Bose-Einstein Condensates I: Existence and Uniqueness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Shuai Li, Xiaoyu Zeng, Yujin Guo","submitted_at":"2017-07-24T11:39:53Z","abstract_excerpt":"We study ground states of two-component Bose-Einstein condensates (BEC) with trapping potentials in $R^2$, where the intraspecies interaction $(-a_1,-a_2)$ and the interspecies interaction $-\\beta$ are both attractive, $i.e,$ $a_1$, $a_2$ and $\\beta $ are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated $L^2$-critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as $\\beta \\nearrow \\beta ^*=a^*+\\sqrt{(a^*-a_1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07495","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":"1707.07495","created_at":"2026-05-17T23:48:40.930077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07495v2","created_at":"2026-05-17T23:48:40.930077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07495","created_at":"2026-05-17T23:48:40.930077+00:00"},{"alias_kind":"pith_short_12","alias_value":"5KALOAE6DUYI","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5KALOAE6DUYIJD46","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5KALOAE6","created_at":"2026-05-18T12:31:00.734936+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/5KALOAE6DUYIJD46MBXD5M3WM7","json":"https://pith.science/pith/5KALOAE6DUYIJD46MBXD5M3WM7.json","graph_json":"https://pith.science/api/pith-number/5KALOAE6DUYIJD46MBXD5M3WM7/graph.json","events_json":"https://pith.science/api/pith-number/5KALOAE6DUYIJD46MBXD5M3WM7/events.json","paper":"https://pith.science/paper/5KALOAE6"},"agent_actions":{"view_html":"https://pith.science/pith/5KALOAE6DUYIJD46MBXD5M3WM7","download_json":"https://pith.science/pith/5KALOAE6DUYIJD46MBXD5M3WM7.json","view_paper":"https://pith.science/paper/5KALOAE6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07495&json=true","fetch_graph":"https://pith.science/api/pith-number/5KALOAE6DUYIJD46MBXD5M3WM7/graph.json","fetch_events":"https://pith.science/api/pith-number/5KALOAE6DUYIJD46MBXD5M3WM7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5KALOAE6DUYIJD46MBXD5M3WM7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5KALOAE6DUYIJD46MBXD5M3WM7/action/storage_attestation","attest_author":"https://pith.science/pith/5KALOAE6DUYIJD46MBXD5M3WM7/action/author_attestation","sign_citation":"https://pith.science/pith/5KALOAE6DUYIJD46MBXD5M3WM7/action/citation_signature","submit_replication":"https://pith.science/pith/5KALOAE6DUYIJD46MBXD5M3WM7/action/replication_record"}},"created_at":"2026-05-17T23:48:40.930077+00:00","updated_at":"2026-05-17T23:48:40.930077+00:00"}