[
  {
    "id": "ARR-2026-3M1EEG1T689ADSMW-v1",
    "type": "article",
    "title": "The Exact Four-Level Inverse Commutator Cost: Horn-Littlewood-Richardson Facets, Rank Transitions, and Sharp Loop Synthesis",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          10
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-3M1EEG1T689ADSMW",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-3M1EEG1T689ADSMW/versions/v1/",
    "note": "Archived manuscript; ARR-2026-3M1EEG1T689ADSMW v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "For a prescribed traceless Hermitian four-level target F, we determine exactly the least product of Hilbert-Schmidt norms of Hermitian A,B satisfying -i[A,B]=F. With ordered eigenvalues lambda_1 >= ... >= lambda_4, the answer is the maximum of four explicit linear spectral forms. The lower bounds are Horn-Littlewood-Richardson certificates and four closed constructions attain them. On every nonzero spectral stratum, the least optimal rank is exactly max(n_+(F),n_-(F)), closing all chamber walls and degenerations. We also prove a finite-dimensional Horn linear-program reduction, the sharp tax 1 <= kappa_4/(||F||_1/2) <= 2 with complete equality cases, and the exact balanced three-kick action S_2^2=12 sqrt(3) kappa_4. Exact symbolic and deterministic LP certificates accompany the manuscript."
  }
]