{"paper":{"title":"Tree suspensions and transfer functions for single degree Tur\\'an spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Haotian Yang, Hong Liu, Jiangdong Ai, Laihao Ding","submitted_at":"2026-07-07T17:26:18Z","abstract_excerpt":"For integers $1\\le \\ell<k$, let $\\Pi^k_\\ell$ denote the single-forbidden $\\ell$-degree Tur\\'an spectrum of $k$-uniform hypergraphs. We introduce transfer functions for this spectrum: explicit functions $f$ such that, for every $F$, there is another single $k$-graph $F^*$ with $\\pi_\\ell(F^*)=f(\\pi_\\ell(F))$. This gives a mechanism for producing new single-forbidden densities while retaining full control of the resulting value.\n  Our transfer functions are realized by a new family of suspension-type operations, called tree suspensions. From these operations we obtain three explicit maps: one act"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06518","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/2607.06518/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"}