Gravitational Spin Memory from Scalar-Torsion Coupling: A Derivative Frequency Theory Framework

We demonstrate that gravitational spin memory, conventionally regarded as a signature of massless spin-2 gravitons, can emerge from a purely scalar field theory when the scalar couples to matter through torsion-modified Riemann-Cartan geometry. Derivative Frequency Theory (DFT) posits gravitational phenomena arise from gradients of a massive scalar frequency field \( \omega(x) \) with inverse scale \( \mu^{-1} \sim 17 \) kpc determined from galactic rotation curves. We prove a general theorem: spin memory exists in any theory satisfying (i) asymptotic radiation, (ii) angular momentum sensitivity, (iii) parity-odd transport, and (iv) infrared memory kernel---independent of mediator spin. In DFT, chirality originates not from the scalar field itself but through its coupling to contorsion \( K^\lambda_{\mu\nu} = \xi\epsilon^\lambda{}_{\mu\nu\rho}J^{\rho\sigma}\partial_\sigma\omega \). The theory predicts distinctive Yukawa suppression of memory effects: \( \Delta\tau_{\text{DFT}}/\Delta\tau_{\text{GR}} \sim e^{-\mu D} \), leading to \( \sim \)45\% suppression for galactic LISA sources (\( \mu D \sim 0.6 \)) and complete suppression for extragalactic mergers (\( \mu D \gg 1 \)). We derive consistent predictions across scales: solar system tests satisfied (\( \Delta\gamma \sim 10^{-12} \)), flat rotation curves explained without dark matter, and cosmological perturbations nearly identical to \( \Lambda \)CDM at large scales. Weak equivalence principle violation is \( \mathcal{O}(10^{-47}) \), far below current sensitivity. The framework is falsifiable through three independent tests with clear timelines: galactic rotation curve morphology (JWST/SKA, 2025-2030), LISA memory measurements (2037-2040), and proposed LC oscillator experiments (1-2 years). DFT offers a minimal scalar alternative to GR that is testable, consistent with current data, and potentially transformative if confirmed.