{"paper":{"title":"A calibration in $\\mathbf R^{16}$ and Federer's product question","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Roger Z\\\"ust","submitted_at":"2025-03-16T08:08:59Z","abstract_excerpt":"Building upon the construction of a Cayley calibration adapted to a complex structure, we introduce a calibration $\\Phi$ in $\\bigwedge^8 \\mathbf R^{16}$ with $|\\Phi^2| = 294$. This enables us to show that the product of two orthogonally supported calibrations is not necessarily a calibration, thereby providing a negative answer to a question posed by Federer. Dadok and Harvey developed a general method for constructing calibrations as outer products of two unit spinors in the Clifford algebra. We show that $\\Phi$ arises from the product of two spinors with norm $1$ and $\\sqrt{2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.12402","kind":"arxiv","version":1},"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/2503.12402/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"}