{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HIPIWRGIQGAZT47GUVESXCMIJR","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":"1261ba2f422e9471457fe5a8637a75913c678e5aef24bc7a5b988cecd49909a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-10T13:36:30Z","title_canon_sha256":"a3a9733c4842eb8d2394d33fbc99d10db7df5a18179331aacaae7b34bae0e604"},"schema_version":"1.0","source":{"id":"1810.04524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04524","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04524v1","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04524","created_at":"2026-05-18T00:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"HIPIWRGIQGAZ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HIPIWRGIQGAZT47G","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HIPIWRGI","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:17e8cdaa038fd57ab8ef93524d5403344148bad94a806f8a8d66e0bf82a51db3","target":"graph","created_at":"2026-05-18T00:03:39Z","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 prove, using variational methods, the existence in dimension two of positive vector ground states solutions for the Bose-Einstein type systems \\begin{equation} \\begin{cases} -\\Delta u+\\lambda_1u=\\mu_1u(e^{u^2}-1)+\\beta v\\left(e^{uv}-1\\right) \\text{ in } \\Omega, &\\\\ -\\Delta v+\\lambda_2v=\\mu_2v(e^{v^2}-1)+\\beta u\\left(e^{uv}-1\\right)\\text{ in } \\Omega, &\\\\ u,v\\in H^1_0(\\Omega) \\end{cases} \\end{equation} where $\\Omega$ is a bounded smooth domain, $\\lambda_1,\\lambda_2>-\\Lambda_1$ (the first eigenvalue of $(-\\Delta,H^1_0(\\Omega))$, $\\mu_1,\\mu_2>0$ and $\\beta$ is either positive (small or large) ","authors_text":"Daniele Cassani, Hugo Tavares, Jianjun Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-10T13:36:30Z","title":"Bose fluids and positive solutions to weakly coupled systems with critical growth in dimension two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04524","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:e4bd4d55f01537c6009f51ff9c5e86b9209a7288aa31b999a039035effcedba6","target":"record","created_at":"2026-05-18T00:03:39Z","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":"1261ba2f422e9471457fe5a8637a75913c678e5aef24bc7a5b988cecd49909a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-10T13:36:30Z","title_canon_sha256":"a3a9733c4842eb8d2394d33fbc99d10db7df5a18179331aacaae7b34bae0e604"},"schema_version":"1.0","source":{"id":"1810.04524","kind":"arxiv","version":1}},"canonical_sha256":"3a1e8b44c8818199f3e6a5492b89884c46f3cd21fb4d3d51db360344f7b090e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a1e8b44c8818199f3e6a5492b89884c46f3cd21fb4d3d51db360344f7b090e5","first_computed_at":"2026-05-18T00:03:39.863391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:39.863391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tBofonmxdXmNptNi/P5yRvWubIvG1lIb4iZ0Sd3jRIMPlHGxNOgIXNEVlxKrJExbaqJTegL4ZVaBCOkomuoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:39.863901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4bd4d55f01537c6009f51ff9c5e86b9209a7288aa31b999a039035effcedba6","sha256:17e8cdaa038fd57ab8ef93524d5403344148bad94a806f8a8d66e0bf82a51db3"],"state_sha256":"99b7cf5276b0fce3d9d4d6ca051c549673bcb3b0e4004c7b4cb0c1d751e9e807"}