[
  {
    "id": "ARR-2026-6F8XRSBM0J9Q2R2B-v1",
    "type": "article",
    "title": "All-Field Morse--Bott Stability at Critical Homogeneous Orbits: Half-Grassmann No-Spinodal Rigidity and Exact Jacobi Metastability",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          15
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-6F8XRSBM0J9Q2R2B",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-6F8XRSBM0J9Q2R2B/versions/v1/",
    "note": "Research preprint; ARR-2026-6F8XRSBM0J9Q2R2B v1. Not peer reviewed by AIRR.",
    "abstract": "Let a compact group act orthogonally on a sphere and let mu be the invariant law of a proper antipodal orbit. We study the exponential orbital potential. At a point of the source orbit, every spherical-harmonic coefficient of the orbit average is a squared norm, giving an exact negative spherical-Laplacian identity at every nonzero field. Provided the source orbit is critical--automatically so when the normal isotropy representation has no fixed vector--irreducibility, or a transitive symmetry of its irreducible normal blocks, upgrades this trace identity to strict Morse--Bott maximality for every field. An explicit torus-orbit counterexample shows why criticality cannot be omitted. Applied to centered projector embeddings of the real, complex, and quaternionic half-Grassmannians, the theorem proves all-field local rigidity of the balanced matrix--Bingham branch and excludes a radial spinodal. In the complex case, exact Jacobi-generator identities yield constrained-Hessian operators for every two-block external spectrum and a sharp weak-field metastability threshold at k=2r/3. A Stein inequality closes every sufficiently high Taylor degree at each fixed multiplicity. The results constrain unresolved intermediate phases but do not claim global spectral optimality, a complete finite-field phase diagram, or an all-distortion rate--distortion function."
  }
]