Candidate collapse-noise correlators from Generalized Trace Dynamics: a Hubble-scale spectral line under structural assumptions

Abstract

We present a conditional construction of candidate CSL-type collapse-noise correlators inspired by Generalized Trace Dynamics (GTD). The construction is not a parameter-free derivation from the minimal GTD Grassmann algebra. It rests on a chain of explicit structural postulates, listed in Section 1; within that auxiliary structure the spectral form and amplitude follow by computation rather than by phenomenological fitting. The resulting narrow-band spectrum at the Hubble scale lies outside the bands of current CSL bounds, so the framework is not in tension with existing high-frequency data. We compute the two-point function of a candidate collapse-noise operator associated with the GTD aikyon decomposition $q_i = q_B + a_0\beta_i q_F$. In the minimal Grassmann algebra, $q_F$ appears only multiplied by Grassmann generators $\beta_i$, the reduction of $\mathrm{Tr}(q_F^\dagger\Gamma^\mu q_F)$ to ghost-mode operators is obstructed by the nilpotent $\delta\beta = \beta_2 - \beta_1$, and the pure-fermion coefficient $\beta_1\beta_2$ has no ordinary sign, modulus, or inverse. We therefore introduce an auxiliary canonical fermionic Fock-space sector for $q_F$, equivalently replacing the nilpotent pure-fermion coefficient by an ordinary effective scalar body parameter. This replacement is an independent structural postulate, not a consequence of the original minimal action. Under this auxiliary postulate, together with a scalar bilinear $J = \mathrm{Tr}(q_F^\dagger q_F)$ as bath operator, positive-norm canonical quantization, and an effective sign choice $\sigma = \pm1$ for the scalarized pure-fermion sector, elementary Wick contraction gives a Wightman line at $|\omega| = 2\omega_0$ with amplitude $A_J = (\hbar/2m_R\omega_0 L_{\mathrm{aik}}^2)^2\cdot N\cdot D$. The cosmological identification $\omega_0 \sim H_0$ places the line at twice the Hubble scale. [truncated]