{"paper":{"title":"The framework to unify all complexity dichotomy theorems for Boolean tensor networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Mingji Xia","submitted_at":"2026-03-10T09:31:41Z","abstract_excerpt":"Fixing an arbitrary set $\\mathcal{F}$ of complex-valued functions over Boolean variables yields a counting problem $\\#\\mathcal{F}$. Taking only functions from $\\mathcal{F}$ to form a tensor network as the problem's input, the counting problem $\\#\\mathcal{F}$ asks for the value of the tensor network. These dichotomy or quasi-dichotomy theorems form a partial order according to the inclusion relations of the problem subclasses they characterize. As the number of known dichotomy theorems increases, the number of maximal elements in this partially ordered set first grows, and then shrinks when a n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.09417","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/2603.09417/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"}