Full-Flag Spectral Locking and Polarized Neutrino Signatures from a Sterile-Portal Dark Sector

We develop a sterile-portal dark-sector extension of a three-flavor full-flag construction in which the residual selector phase is fixed by the Frobenius matching relation $$\cos(3\phi_\star) = \frac{1}{3}.$$ A Dirac dark multiplet and a vectorlike sterile-neutrino mediator multiplet are assigned affine mass operators of the common form $$M_X = A_X I + B_X H(\phi_\star), \qquad M_N = A_N I + B_N H(\phi_\star).$$ As a result, the dark, sterile, and light-neutrino sectors share a common selector eigenframe. The signed affine spectra of the dark and sterile triplets obey the same normalized cubic one-third invariant, together with a parameter-free triplet-spacing relation on common-sign branches. A separated sterile mediator decouples the coupling controlling dark-matter annihilation from active-sterile neutrino mixing. In a representative benchmark with $$m_X = 500 \text{ GeV}, \qquad m_N = 250 \text{ GeV}, \qquad m_S = 1 \text{ TeV},$$ the exact tree-level $X\bar{X} \to N\bar{N}$ matrix element, inserted into the relativistic thermal average and a constant-$g_\star$ Boltzmann treatment, gives a symmetric Dirac relic abundance $$\Omega_X h^2 \simeq 0.12$$ for a perturbative portal coupling $\lambda_D \simeq 1.26$. The late-time cascade $$X\bar{X} \to N\bar{N}, \qquad N \to Z\nu, \ h\nu, \ W\ell,$$ produces a correlated neutrino signature. The $Z\nu$ and $h\nu$ channels possess normalization-independent kinematic endpoints that reconstruct $m_X$ and $m_N$. Because the sterile mediator is produced longitudinally polarized in the chiral scalar portal, the primary neutrino spectra are linearly tilted rather than flat box spectra. Their slopes are fixed by the masses reconstructed from the endpoints and therefore introduce no additional continuous shape parameter in the minimal branch. In the aligned sterile extension, the same Full-Flag selector fixes the production flavor and hence the decohered Galactic flavor vector. The primary $Z\nu$ and $h\nu$ components consequently share one selector-determined flavor composition. Semi-analytic charged-lepton secondary calculations further show that the high-energy tail retains substantial sensitivity to the same flavor structure. The resulting phenomenology is therefore not a rate-only dark-matter signal but an overconstrained set of mutually related observables: $$\text{spectral support} \longrightarrow \text{mass reconstruction} \longrightarrow \text{polarization slopes} \longrightarrow \text{flavor composition} \longrightarrow \text{triplet spectral consistency}.$$ We formulate a detector-facing, normalization-profiled search strategy based on reconstructed energy, Galactic-Centre direction, and event topology. A full public-Monte-Carlo shower simulation and collaboration-specific IceCube/KM3NeT sensitivity analysis are deliberately left outside the scope of the present theory/phenomenology study and constitute natural follow-up work. This paper is a dark-sector sequel to: B. Lee, Full-Flag Cohomology and Frobenius Quiver Rigidity: Deriving $\cos 3\phi = 1/3$ in a Four-Dimensional Effective Completion, Zenodo, Version v2.0 (2026), DOI: 10.5281/zenodo.23138053.