{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LPHMRFAVYPZG2YNRUP5CEQJVSW","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":"54d38cce58f5b4f7fe562b50f5e77dffc1ba4d5d5cb9b3cb79f193ad9c8631c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-07T13:38:18Z","title_canon_sha256":"6b0d1b71f450cdb798adb8e9aef9da7e3d38d9066c6a5dacccbaeea737e28dba"},"schema_version":"1.0","source":{"id":"1506.02262","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02262","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02262v1","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02262","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"pith_short_12","alias_value":"LPHMRFAVYPZG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LPHMRFAVYPZG2YNR","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LPHMRFAV","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:010b2b7f78552f869a8c7324c26ab0dc9277621db9e7ec6f249ecb1c4f57a6c8","target":"graph","created_at":"2026-05-18T01:01:29Z","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 consider the system of coupled elliptic equations \\[ \\begin{cases} -\\Delta u - \\lambda_1 u = \\mu_1 u^3+ \\beta u v^2 \\\\ -\\Delta v- \\lambda_2 v = \\mu_2 v^3 +\\beta u^2 v \\end{cases} \\text{in $\\mathbb{R}^3$}, \\] and study the existence of positive solutions satisfying the additional condition \\[ \\int_{\\mathbb{R}^3} u^2 = a_1^2 \\quad \\text{and} \\quad \\int_{\\mathbb{R}^3} v^2 = a_2^2. \\] Assuming that $a_1,a_2,\\mu_1,\\mu_2$ are positive fixed quantities, we prove existence results for different ranges of the coupling parameter $\\beta>0$. The extension to systems with an arbitrary number of componen","authors_text":"Louis Jeanjean, Nicola Soave, Thomas Bartsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-07T13:38:18Z","title":"Normalized solutions for a system of coupled cubic Schr\\\"odinger equations on $\\mathbb{R}^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02262","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:f6f5e3749f82812407622fda60ec8aa3830f95ea113b612db1eab33105672a02","target":"record","created_at":"2026-05-18T01:01:29Z","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":"54d38cce58f5b4f7fe562b50f5e77dffc1ba4d5d5cb9b3cb79f193ad9c8631c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-07T13:38:18Z","title_canon_sha256":"6b0d1b71f450cdb798adb8e9aef9da7e3d38d9066c6a5dacccbaeea737e28dba"},"schema_version":"1.0","source":{"id":"1506.02262","kind":"arxiv","version":1}},"canonical_sha256":"5bcec89415c3f26d61b1a3fa22413595b7a6134339bae4ab8a95366185663c88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bcec89415c3f26d61b1a3fa22413595b7a6134339bae4ab8a95366185663c88","first_computed_at":"2026-05-18T01:01:29.237700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:29.237700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/uuOKD+R/Aew9if6bZi5I9xng3YupHUX9XqnzYr4fiYiNprCtP1EiRGSsXAMB0R9pejk3Lb9PrNUeI7TRRrvDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:29.238129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02262","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6f5e3749f82812407622fda60ec8aa3830f95ea113b612db1eab33105672a02","sha256:010b2b7f78552f869a8c7324c26ab0dc9277621db9e7ec6f249ecb1c4f57a6c8"],"state_sha256":"b03983ca3e33390023fb485ce493ed24693d856f02d863c56a656fae9b52f181"}