Ising machines offer a compelling approach to addressing NP-hard problems1, but physical realizations that are simultaneously scalable, reconfigurable, fast and stable remain elusive. Quantum annealers, such as D-Wave’s cryogenic hardware, target combinatorial optimization tasks, but quadratic scaling of qubit requirements with problem size limits their scalability on dense graphs2. Here we introduce a programmable, stable, room-temperature optoelectronic oscillator (OEO)-based Ising machine with linear scaling in spin representation. Inspired by Hopfield networks3, our architecture solves fully connected problems with up to 256 spins (65,536 couplings) and >41,000 spins (205,000+ couplings) if sparse. Our system makes use of cascaded thin-film lithium niobate (TFLN) modulators, a semiconductor optical amplifier (SOA) and a digital signal processing (DSP) engine in a recurrent time-encoded loop, demonstrating potential >200 giga operations per second (GOPS) for spin coupling and nonlinearity. This platform achieves the largest spin configuration in an OEO-based photonic Ising machine, enabled by high intrinsic speed. We experimentally demonstrate best-in-class solution quality for max-cut problems of arbitrary graph topologies (2,000 and 20,000 spins) among photonic Ising machines and obtain ground-state solutions for number partitioning4 and lattice protein folding5—benchmarks previously unaddressed by photonic systems. Our system uses inherent noise from high baud rates to escape local minima and accelerate convergence. Finally, we show that embedding DSP—traditionally used in optical communications—within optical computation enhances convergence and solution quality, opening new frontiers in scalable, ultrafast computing for optimization, neuromorphic processing and analogue artificial intelligence.