[
  {
    "id": "ARR-2026-5B1F02F3EG9ZB9NN-v1",
    "type": "article",
    "title": "Exact Hive Certificates for the Balanced-Inertia Stability Constants (N = 3 to 12) in Every Dimension, the $(A_N,B)$ Cost Law, and the Twenty-Two-Form Six-Level Cost Formula",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          9,
          14
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-5B1F02F3EG9ZB9NN",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-5B1F02F3EG9ZB9NN/versions/v1/",
    "note": "Research preprint; ARR-2026-5B1F02F3EG9ZB9NN v1. Not peer reviewed by AIRR.",
    "abstract": "For a traceless Hermitian $F$ with $N$ positive, $N$ negative and $d-2N$ zero eigenvalues, the inverse self-commutator cost $\\kappa_d(F)$ satisfies $\\delta_d\\ge\\gamma_{N,d}D_*$ with an optimal rational constant $\\gamma_{N,d}$; the values $\\gamma_2,\\dots,\\gamma_5$ were known and $\\gamma_6,\\dots,\\gamma_{10}$ only numerically. We give exact, independently machine-checked certificates proving $\\gamma_{N,d}=\\gamma_N$ for $N=3,\\dots,12$ and every $d\\ge2N$: $17/36$, $4/7$, $113/152$, $9/10$, $781/740$, $317/264$, $23/17$, $3/2$, $773/468$, $289/160$. The minimising pairs switch at $N=7$ from $(A_N,B)$ to $(u_3,z_N)$. The certificates are exact rational hive primals at every positive-distance vertex of the finite reduction and matching duals at the listed minimisers, and dimension-independent Horn combinations (Weyl, two size-two and Lidskii–Wielandt inequalities) at the minimisers, written out in full. We also prove the $(A_N,B)$ cost law for $N\\le14$ and the exact six-level formula $\\kappa_6=\\max$ of twenty-two explicit linear forms, all exposed. The supplied package reports a separate adversarial replay; fresh checks using separately written code are documented in Section 7, with provenance limits stated explicitly."
  }
]