{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4WWEPGHBAXJ4IUGNMSRX7T3VRX","short_pith_number":"pith:4WWEPGHB","canonical_record":{"source":{"id":"1403.4695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-19T05:28:59Z","cross_cats_sorted":[],"title_canon_sha256":"56214ece29ec4298bf98700f8087539807251b7e7effb03f0f75489a20ccabde","abstract_canon_sha256":"95a43afb071aff5774d82f917e5e12dc7db2f2c2483e74dad544d2b923e7dde6"},"schema_version":"1.0"},"canonical_sha256":"e5ac4798e105d3c450cd64a37fcf758ddd46103eea18881c4531f8ec69a4a7c5","source":{"kind":"arxiv","id":"1403.4695","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4695","created_at":"2026-05-18T01:43:59Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4695v1","created_at":"2026-05-18T01:43:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4695","created_at":"2026-05-18T01:43:59Z"},{"alias_kind":"pith_short_12","alias_value":"4WWEPGHBAXJ4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4WWEPGHBAXJ4IUGN","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4WWEPGHB","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4WWEPGHBAXJ4IUGNMSRX7T3VRX","target":"record","payload":{"canonical_record":{"source":{"id":"1403.4695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-19T05:28:59Z","cross_cats_sorted":[],"title_canon_sha256":"56214ece29ec4298bf98700f8087539807251b7e7effb03f0f75489a20ccabde","abstract_canon_sha256":"95a43afb071aff5774d82f917e5e12dc7db2f2c2483e74dad544d2b923e7dde6"},"schema_version":"1.0"},"canonical_sha256":"e5ac4798e105d3c450cd64a37fcf758ddd46103eea18881c4531f8ec69a4a7c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:59.525641Z","signature_b64":"ijdfTl9/pdry04UrRLzr4GWrRKxSTmVM3s6q093eHOZezlZLR9qoytOef06WSuAh/ojLZ6YM2q1U5ZdhydjMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5ac4798e105d3c450cd64a37fcf758ddd46103eea18881c4531f8ec69a4a7c5","last_reissued_at":"2026-05-18T01:43:59.525032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:59.525032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.4695","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:43:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2LrchQDzWZV5ycTfY53GdoCDqH+i13xzej1xzGy8n7gGqfmWvTapck30XrPcJE6bqNR5qhhpOpx5Ct+LWKZDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:31:52.507971Z"},"content_sha256":"181790ab414c62d4239d1b163bbd9c71ca831d8cf1afb63b42c812f83016cbca","schema_version":"1.0","event_id":"sha256:181790ab414c62d4239d1b163bbd9c71ca831d8cf1afb63b42c812f83016cbca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4WWEPGHBAXJ4IUGNMSRX7T3VRX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thomas-Fermi approximation for coexisting two component Bose-Einstein condensates and nonexistence of vortices for small rotation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amandine Aftalion (LM-Versailles), Benedetta Noris (LM-Versailles), Christos Sourdis","submitted_at":"2014-03-19T05:28:59Z","abstract_excerpt":"We study minimizers of a Gross--Pitaevskii energy describing a two-component Bose-Einstein condensate confined in a radially symmetric harmonic trap and set into rotation. We consider the case of coexistence of the components in the Thomas-Fermi regime, where a small parameter $\\ep$ conveys a singular perturbation. The minimizer of the energy without rotation is determined as the positive solution of a system of coupled PDE's for which we show uniqueness. The limiting problem for $\\ep =0$ has degenerate and irregular behavior at specific radii, where the gradient blows up. By means of a pertur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4695","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:43:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5bOq5GINrjMyxrs9m2uBSzKHnyEJuHDJCKSYDceG3wViICTmwTaOuz5l86OKAb3hbszgtyiPf4uZpmssTJ7VAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:31:52.508332Z"},"content_sha256":"b7cf86b984c9d4cc82ff5584f920446a1f2b5139dd479c8576a1b3da1ec5c3c4","schema_version":"1.0","event_id":"sha256:b7cf86b984c9d4cc82ff5584f920446a1f2b5139dd479c8576a1b3da1ec5c3c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WWEPGHBAXJ4IUGNMSRX7T3VRX/bundle.json","state_url":"https://pith.science/pith/4WWEPGHBAXJ4IUGNMSRX7T3VRX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WWEPGHBAXJ4IUGNMSRX7T3VRX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T14:31:52Z","links":{"resolver":"https://pith.science/pith/4WWEPGHBAXJ4IUGNMSRX7T3VRX","bundle":"https://pith.science/pith/4WWEPGHBAXJ4IUGNMSRX7T3VRX/bundle.json","state":"https://pith.science/pith/4WWEPGHBAXJ4IUGNMSRX7T3VRX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WWEPGHBAXJ4IUGNMSRX7T3VRX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4WWEPGHBAXJ4IUGNMSRX7T3VRX","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":"95a43afb071aff5774d82f917e5e12dc7db2f2c2483e74dad544d2b923e7dde6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-19T05:28:59Z","title_canon_sha256":"56214ece29ec4298bf98700f8087539807251b7e7effb03f0f75489a20ccabde"},"schema_version":"1.0","source":{"id":"1403.4695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4695","created_at":"2026-05-18T01:43:59Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4695v1","created_at":"2026-05-18T01:43:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4695","created_at":"2026-05-18T01:43:59Z"},{"alias_kind":"pith_short_12","alias_value":"4WWEPGHBAXJ4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4WWEPGHBAXJ4IUGN","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4WWEPGHB","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:b7cf86b984c9d4cc82ff5584f920446a1f2b5139dd479c8576a1b3da1ec5c3c4","target":"graph","created_at":"2026-05-18T01:43:59Z","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":"We study minimizers of a Gross--Pitaevskii energy describing a two-component Bose-Einstein condensate confined in a radially symmetric harmonic trap and set into rotation. We consider the case of coexistence of the components in the Thomas-Fermi regime, where a small parameter $\\ep$ conveys a singular perturbation. The minimizer of the energy without rotation is determined as the positive solution of a system of coupled PDE's for which we show uniqueness. The limiting problem for $\\ep =0$ has degenerate and irregular behavior at specific radii, where the gradient blows up. By means of a pertur","authors_text":"Amandine Aftalion (LM-Versailles), Benedetta Noris (LM-Versailles), Christos Sourdis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-19T05:28:59Z","title":"Thomas-Fermi approximation for coexisting two component Bose-Einstein condensates and nonexistence of vortices for small rotation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4695","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":"sha256:181790ab414c62d4239d1b163bbd9c71ca831d8cf1afb63b42c812f83016cbca","target":"record","created_at":"2026-05-18T01:43:59Z","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":"95a43afb071aff5774d82f917e5e12dc7db2f2c2483e74dad544d2b923e7dde6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-19T05:28:59Z","title_canon_sha256":"56214ece29ec4298bf98700f8087539807251b7e7effb03f0f75489a20ccabde"},"schema_version":"1.0","source":{"id":"1403.4695","kind":"arxiv","version":1}},"canonical_sha256":"e5ac4798e105d3c450cd64a37fcf758ddd46103eea18881c4531f8ec69a4a7c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5ac4798e105d3c450cd64a37fcf758ddd46103eea18881c4531f8ec69a4a7c5","first_computed_at":"2026-05-18T01:43:59.525032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:59.525032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ijdfTl9/pdry04UrRLzr4GWrRKxSTmVM3s6q093eHOZezlZLR9qoytOef06WSuAh/ojLZ6YM2q1U5ZdhydjMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:59.525641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:181790ab414c62d4239d1b163bbd9c71ca831d8cf1afb63b42c812f83016cbca","sha256:b7cf86b984c9d4cc82ff5584f920446a1f2b5139dd479c8576a1b3da1ec5c3c4"],"state_sha256":"b04f4cbc7458395bbbe0c999117cef03a98ffb76c5911ba38aa75d53d1acf22f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JME7h5hE26ix2Gb/buxtXzjRMlIfONVaCxt2y9HVFf32tdkffhW2OueM9RH46tLo8rOxNopKIvnlkPBoFdujBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:31:52.510298Z","bundle_sha256":"cee676e8f9bdcda62253e27269dcf3828c77d4af7cf09794c0a04e905ca73bd3"}}