Research paperHistorical importARR-2026-3M1EEG1T689ADSMW · v1 · 2026-08-10

The Exact Four-Level Inverse Commutator Cost: Horn-Littlewood-Richardson Facets, Rank Transitions, and Sharp Loop Synthesis

Lluis Eriksson

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.

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Related ARR records

  • ARR-2026-24M24KDPZK8HDBQ9Referenced By · Linked from Sharp inertia ceilings and optimal stability for inverse self-commutators.
  • ARR-2026-7NPRNBW4488HG90KReferenced By · Linked from One-Spike Inverse Self-Commutators and Exact Three-versus-Four-Kick Curvature Synthesis.
  • ARR-2026-1D2QV1RP1292JREWReferenced By · Linked from Sharp Rank-Adaptive Bounds for Inverse Self-Commutators.

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