Hyperdimensional computing (HDC), also referred to as vector symbolic architectures (VSA), represents information with high-dimensional vectors and a compact algebra of primitives. This paper establishes an explicitly unitary embedding from discrete bipolar HDC/VSA vectors to coherent broadband waveforms and develops a common wave-domain realization of the core HDC/VSA primitives within that embedding. Under the resulting RFC/UWE stack, bundling becomes linear superposition, permutation becomes coherent phase evolution, binding is reproduced by nonlinear spectral mixing together with an engineered aliasing step that restores circular-convolution structure, and similarity is recovered as a calibrated differential-power readout. Full-wave FDTD studies validate the physically nontrivial parts of this program, including array-level readout in a mutually coupled setting and the binding pipeline under realistic propagation. In a documented $N=1000$ mutually coupled-array calibration, the predicted interaction effect appears with the expected sign pattern and order of magnitude, yielding a coupled Correlation Contrast Ratio of approximately $8.7 \times 10^{-5}$. The result is a wave-geometric duality for HDC/VSA: existing symbolic operations admit a physically grounded waveform realization, while coherence, isolation, and readout sensitivity remain the central engineering constraints for future hardware.

翻译：超维计算（HDC），也称为向量符号架构（VSA），采用高维向量及紧凑的原初代数表示信息。本文建立了从离散双极性HDC/VSA向量到相干宽带波形的显式酉嵌入，并在此嵌入中实现了核心HDC/VSA原初算子的通用波域实现。在由此产生的RFC/UWE堆栈中，捆绑操作退化为线性叠加，置换操作体现为相干相位演化，绑定操作通过非线性频谱混合与重构循环卷积结构的工程化混叠步骤实现，相似度则通过校准差分功率读出机制恢复。全波FDTD仿真验证了该方案中物理非平凡部分的有效性，包括互耦环境下的阵列级读出机制及实际传播条件下的绑定管线。在记录的$N=1000$互耦阵列校准实验中，预测的相互作用效应呈现预期符号模式与量级，产生约$8.7 \times 10^{-5}$的耦合相关对比度。由此建立的HDC/VSA波-几何对偶性表明：现有符号操作具有物理可实现的波形基础，而相干性、隔离性与读出灵敏度仍是未来硬件实现的核心工程约束。