https://neckpinch.com/authors/james-j-munden/New arXiv papers by James J. Munden, from Neckpinch Tue, 10 Nov 2026 08:52:45 GMT https://neckpinch.com/papers/2611.12828/arxiv:2611.12828Mon, 09 Nov 2026 00:00:00 GMTJames J. Munden — By the Skew-Torsion Holonomy Theorem of Olmos and Reggiani (2012), the 15-sphere S¹⁵ admits no non-trivial naturally reductive metric under any transitive Lie group, precluding geodesic integration via canonical Ambrose-Singer connections. Simultaneously, Nikonorov (2013) established that every Spin(9)-invariant metric on S¹⁵ is a geodesic orbit (GO) space. We integrate the geodesic flow on this non-naturally reductive GO manifold via the Lie Subalgebra Closure Principle: whenever the slice generators of a multi-axial reductive decomposition close into a finite-rank reductive Lie subalgebra, the geodesic vector equations decouple into an algebraic eigenvalue problem. Using the 16-dimensional spin representation and Vol'per's decomposition spin(9) = spin(7) ⊕ p₁ ⊕ p₂, we prove that the slice generators X₁ ∈ p₂ and Y₁ ∈ p₁ close into u(2) ≅ su(2) ⊕ u(1) ⊂ so(16). The generator M = αX₁ + βY₁ has the four-mode spectrum Ω∈ \ |R ± 3α|, |R ± α| \ (R = √(α² + β²)), yielding a closed-form 4-projector decomposition and Euler-Cartan factorization for exp(αX₁ + βY₁). Under the normalized Ricci flow, we prove that the Bourguignon-Karcher squashed Einstein metric at t = 3/11 (λ= 64) is an unstable repeller separating sub-Riemannian fiber collapse from the round sphere basin. Finally, on the deformed Cayley plane OP² = F₄/Spin(9), we prove universal CROSS never-Einstein rigidity, establish the 15-dimensional three-stratum Whitney stratification of the cut locus Cut(q₀) at non-polar basepoints q₀, and prove Blaschke and Besse rigidity for all λ> 0.Ricci flowEinstein metricsHomogeneous spacesStability & uniquenessEigenvalues & spectrum https://neckpinch.com/papers/2611.12821/arxiv:2611.12821Mon, 09 Nov 2026 00:00:00 GMTJames J. Munden — We study the one-parameter family of Riemannian metrics g_λ induced by the Hamiltonian cotangent deformation H_λ= H₀ + fracλ2\|J\|² on simply connected space forms of constant curvature κ∈ \1, 0, −1\, where J is the momentum map of the isotropy action fixing a base point. The master reciprocal identity 1/f_λ² = 1/s_κ² + λ governing the warping function controls the geometry of the family and implies that radial geodesic acceleration is independent of λ. From this mechanism we derive three classes of results: (1) Curvature and rigidity: closed-form sectional curvatures, the sharp positivity trichotomy, pointwise and global Brendle-Schoen 1/4-pinching windows on Sⁿ⁺¹, never-Einstein rigidity for λ≠ 0, and the realization of Hamilton's steady cigar soliton on (ℍ², g₁) as the unique gradient Ricci soliton in the family. (2) Dynamics and stability: iso-kinematic decoupling into unperturbed radial motion and uniform precession Ω= λL, closed-form Clairaut integration, the transcendental inward conjugate point law with Euclidean inversion r₀ R^* = 1/λ, and stratified A₃ cusp caustics. (3) Integrability and spectral theory: maximal superintegrable rational pericenter invariants on ℝⁿ⁺¹, transverse Killing rigidity on curved space forms, Fuchsian Heun spectral reduction with modulus τ= 1 + λ/κ, and essential spectrum gap collapse to [0, ∞) on ℍⁿ⁺¹. Extensions to anisotropic sphere families and intrinsic deformations of compact rank-one symmetric spaces (ℂPⁿ, ℍPⁿ, OP²) are also established.Ricci solitonsAncient solutionsCurvature pinchingSphere theoremsStability & uniquenessEigenvalues & spectrum