Vacuum Instability And Majorana Spinors of The Black Circle

This paper computes the one-loop effective action and takes the first steps toward the Majorana spinor sector of the Black Circle, using the corrected QNM spectrum from Papers 15–17.

The one-loop imaginary part is revised: Im(W₁₋loop) ≈ 70.848 − 31.009·m²₄ r_s⁻¹, with m²₄ ∈ (0, 0.256) under the cavity bound. The sign is reversed relative to Paper 14's −74.800 r_s⁻¹, which used artifact QNMs. The positive value signals a metastable vacuum consistent with the Black Circle as a condensate rather than a ground state — the first quantum contribution toward testability of the IIB-II norm-gravity conjecture.

The mass slope for the l=0 growing mode is derived analytically via the implicit function theorem: dκ_grow/dm²|_{l=0} = +0.14010, opposite in sign to the l=1 slope −0.2688. The corrected one-loop slope is dσ/dm² = −0.7383 r_s⁻¹.

The quasi-universal growth timescale τ_grow(l=0) ≈ τ_grow(l=1) to 0.33% is explained by a common modulus balance |A_part·2^{iΩ}| ≈ 0.371 r_s⁻¹ independent of l.

The Frobenius–Schur indicator of the spinorial irrep 4_s of GL(2,3) is computed: FS(4_s) = +1, verified with GAP 4.15.1. This establishes that 4_s admits a real structure, charge conjugation C exists with C²=+1, and the Majorana condition ψ=Cψ is representation-theoretically consistent. The remaining obstacle is OS2 (reflection positivity on the compact de Sitter interior, OP 18.7). The four 4_s modes versus three Standard Model generations is declared as OP 18.8, with sterile neutrino as preferred resolution.

Part of the Cayley–Dickson Zero-Divisor Series (Paper 18).