{"paper":{"title":"Polynomial Almost-Complex Curves in $\\hat{\\mathbb{S}}^{2,4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Parker Evans","submitted_at":"2022-08-30T17:20:30Z","abstract_excerpt":"For solutions to the $\\mathfrak{g}_2$ affine Toda field equations in $\\mathbb{C}$ with respect to \\emph{polynomial} holomorphic sextic differential $q$, we study the associated almost-complex curves $\\nu_q: \\mathbb{C} \\rightarrow \\hat{\\mathbb{S}}^{2,4}$. The asymptotic boundary $\\Delta := \\partial_{\\infty}(\\nu_q)$ of $\\nu_q$ is found to be a polygon in $\\mathsf{Ein}^{2,3}$ with $\\mathsf{deg} q + 6$ vertices. The polygon $\\Delta$ satisfies an \\emph{annihilator property}, which is related to a $\\mathsf{G}_2'$-invariant discrete metric $d_3: \\mathsf{Ein}^{2,3} \\times \\mathsf{Ein}^{2,3} \\rightarro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14409","kind":"arxiv","version":2},"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/2208.14409/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"}