{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DWIYBBOZY6Q7FPM75VTK7TPIHZ","short_pith_number":"pith:DWIYBBOZ","schema_version":"1.0","canonical_sha256":"1d918085d9c7a1f2bd9fed66afcde83e7b16795c0c3ba6d6552858deeb5049c7","source":{"kind":"arxiv","id":"1903.07306","version":3},"attestation_state":"computed","paper":{"title":"Normalized solutions to the Chern-Simons-Schr\\\"odinger system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tianxiang Gou, Zhitao Zhang","submitted_at":"2019-03-18T08:47:53Z","abstract_excerpt":"In this paper, we study normalized solutions to the Chern-Simons-Schr\\\"odinger system, which is a gauge-covariant nonlinear Sch\\\"oridnger system with a long-range electromagnetic field, arising in nonrelativistic quantum mechanics theory. The solutions correspond to critical points of the underlying energy functional subject to the $L^2$-norm constraint. Our research covers several aspects. Firstly, in the mass subcritical case, we establish the compactness of any minimizing sequence to the associated global minimization problem. As a by-product of the compactness of any minimizing sequence, t"},"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":"1903.07306","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-18T08:47:53Z","cross_cats_sorted":[],"title_canon_sha256":"b85997d0353316053c8d7b6709b95c4bfaf0336a9fd15ba93bec390751e49739","abstract_canon_sha256":"d92437e2fffb0b8c52766100562e2399aaa3bdeb88d43a6db8803dde74ddda28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:00:28.827588Z","signature_b64":"Ou7dvj8p0zBBbIGvawn0j6/EXMXnw8x+NXapx8VL6ijR45tEqsOmxUPaGdksKYz6KK9cm7grKCQ9tmRfFnU/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d918085d9c7a1f2bd9fed66afcde83e7b16795c0c3ba6d6552858deeb5049c7","last_reissued_at":"2026-07-05T02:00:28.827094Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:00:28.827094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normalized solutions to the Chern-Simons-Schr\\\"odinger system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tianxiang Gou, Zhitao Zhang","submitted_at":"2019-03-18T08:47:53Z","abstract_excerpt":"In this paper, we study normalized solutions to the Chern-Simons-Schr\\\"odinger system, which is a gauge-covariant nonlinear Sch\\\"oridnger system with a long-range electromagnetic field, arising in nonrelativistic quantum mechanics theory. The solutions correspond to critical points of the underlying energy functional subject to the $L^2$-norm constraint. Our research covers several aspects. Firstly, in the mass subcritical case, we establish the compactness of any minimizing sequence to the associated global minimization problem. As a by-product of the compactness of any minimizing sequence, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07306","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.07306/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1903.07306","created_at":"2026-07-05T02:00:28.827163+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.07306v3","created_at":"2026-07-05T02:00:28.827163+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07306","created_at":"2026-07-05T02:00:28.827163+00:00"},{"alias_kind":"pith_short_12","alias_value":"DWIYBBOZY6Q7","created_at":"2026-07-05T02:00:28.827163+00:00"},{"alias_kind":"pith_short_16","alias_value":"DWIYBBOZY6Q7FPM7","created_at":"2026-07-05T02:00:28.827163+00:00"},{"alias_kind":"pith_short_8","alias_value":"DWIYBBOZ","created_at":"2026-07-05T02:00:28.827163+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"1907.03433","citing_title":"Normalized ground states for the fractional nonlinear Schr\\\"{o}dinger equations","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DWIYBBOZY6Q7FPM75VTK7TPIHZ","json":"https://pith.science/pith/DWIYBBOZY6Q7FPM75VTK7TPIHZ.json","graph_json":"https://pith.science/api/pith-number/DWIYBBOZY6Q7FPM75VTK7TPIHZ/graph.json","events_json":"https://pith.science/api/pith-number/DWIYBBOZY6Q7FPM75VTK7TPIHZ/events.json","paper":"https://pith.science/paper/DWIYBBOZ"},"agent_actions":{"view_html":"https://pith.science/pith/DWIYBBOZY6Q7FPM75VTK7TPIHZ","download_json":"https://pith.science/pith/DWIYBBOZY6Q7FPM75VTK7TPIHZ.json","view_paper":"https://pith.science/paper/DWIYBBOZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.07306&json=true","fetch_graph":"https://pith.science/api/pith-number/DWIYBBOZY6Q7FPM75VTK7TPIHZ/graph.json","fetch_events":"https://pith.science/api/pith-number/DWIYBBOZY6Q7FPM75VTK7TPIHZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DWIYBBOZY6Q7FPM75VTK7TPIHZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DWIYBBOZY6Q7FPM75VTK7TPIHZ/action/storage_attestation","attest_author":"https://pith.science/pith/DWIYBBOZY6Q7FPM75VTK7TPIHZ/action/author_attestation","sign_citation":"https://pith.science/pith/DWIYBBOZY6Q7FPM75VTK7TPIHZ/action/citation_signature","submit_replication":"https://pith.science/pith/DWIYBBOZY6Q7FPM75VTK7TPIHZ/action/replication_record"}},"created_at":"2026-07-05T02:00:28.827163+00:00","updated_at":"2026-07-05T02:00:28.827163+00:00"}