{"paper":{"title":"Two-Cut Coherence of Quintic Forms: Lifting Separations and Second-Derivative Completeness","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Karthik Sheshadri","submitted_at":"2026-08-06T22:00:44Z","abstract_excerpt":"For a homogeneous polynomial f of degree d, the degree-k restricted strength C_k(f) is the least number of products needed to write f with factor degrees k and d-k. We introduce a two-cut coherence parameter C_{k,l}(f): the least r such that f = sum_{i,j=1}^{r} p_i m_{ij} q_j with deg p_i = k, deg m_{ij} = l-k, and deg q_j = d-l. This requires two degree interfaces to be realized by a single common factorization. We show it equals the minimum common endpoint width of a three-block compressed transfer network, and equivalently the minimum, over all tensor lifts of f through commutative multipli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07611","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/2608.07611/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"}