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 ω(x) with inverse scale μ−1 ∼ 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 Kμλν = ξελμνρJρσ∂σω. The theory predicts distinctive Yukawa suppression of memory effects: ∆τDFT/∆τGR ∼ e−μD, leading to ∼45% suppression for galactic LISA sources (μD ∼ 0.6) and com- plete suppression for extragalactic mergers (μD ≫ 1). We derive consistent predictions across scales: solar system tests satisfied (∆γ ∼ 10−12), flat rotation curves explained without dark matter, and cosmological perturbations nearly identical to ΛCDM at large scales. Weak equivalence principle violation is 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 mea- surements (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.