{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YRVNYDLADQCW5AWPZZ4GXVZZAE","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":"15d1f2387e0c4d8503ef1b2bf257f63c9025e1fded4e599f49ebf26b59607b59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-05T23:31:26Z","title_canon_sha256":"890c407052f3e5b0a4888b7fd3afcac853bcd9393939faf904833d971504107a"},"schema_version":"1.0","source":{"id":"2404.04448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.04448","created_at":"2026-07-05T08:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"2404.04448v1","created_at":"2026-07-05T08:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.04448","created_at":"2026-07-05T08:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"YRVNYDLADQCW","created_at":"2026-07-05T08:05:16Z"},{"alias_kind":"pith_short_16","alias_value":"YRVNYDLADQCW5AWP","created_at":"2026-07-05T08:05:16Z"},{"alias_kind":"pith_short_8","alias_value":"YRVNYDLA","created_at":"2026-07-05T08:05:16Z"}],"graph_snapshots":[{"event_id":"sha256:7bbf44721bfefb1b43e9e51a57ea659c20ac555a1d86319ac722022bfe0f878e","target":"graph","created_at":"2026-07-05T08:05:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.04448/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish the existence of a solution to a nonlinear competitive Schr\\\"odinger system whose scalar potential tends to a positive constant at infinity with an appropriate rate. This solution has the property that all components are invariant under the action of a group of linear isometries and each component is obtained from the previous one by composing it with some fixed linear isometry. We call it a pinwheel solution. We describe the asymptotic behavior of the least energy pinwheel solutions when the competing parameter tends to zero and to minus infinity. In the latter case the component","authors_text":"Alberto Salda\\~na, Mayra Soares, M\\'onica Clapp, V\\'ictor A. Vicente-Ben\\'itez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-05T23:31:26Z","title":"Optimal pinwheel partitions and pinwheel solutions to a nonlinear Schr\\\"odinger system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04448","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":"sha256:05034c260469d73169c896c8b65aa37fb7fad5baf4381d9dfcd1f13a90a28947","target":"record","created_at":"2026-07-05T08:05:16Z","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":"15d1f2387e0c4d8503ef1b2bf257f63c9025e1fded4e599f49ebf26b59607b59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-05T23:31:26Z","title_canon_sha256":"890c407052f3e5b0a4888b7fd3afcac853bcd9393939faf904833d971504107a"},"schema_version":"1.0","source":{"id":"2404.04448","kind":"arxiv","version":1}},"canonical_sha256":"c46adc0d601c056e82cfce786bd73901107a6f0b2fd423048e322cd2b9525012","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c46adc0d601c056e82cfce786bd73901107a6f0b2fd423048e322cd2b9525012","first_computed_at":"2026-07-05T08:05:16.854666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:05:16.854666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XLpRgXyiul5/TZIl+ogWEMbJUs0qsFy2Uu+6lecVDjUjr0uafHrZCnr7rGoTeVscYbixpbPh34KpTH/AE3rXBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:05:16.855085Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.04448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05034c260469d73169c896c8b65aa37fb7fad5baf4381d9dfcd1f13a90a28947","sha256:7bbf44721bfefb1b43e9e51a57ea659c20ac555a1d86319ac722022bfe0f878e"],"state_sha256":"646098720e02f97e96703b5531511658d41f7c166fcf5a89be05fe03df45eb86"}