The Unified Hybrid Format (UHF): A Phase-Coherent Representation Bridging Continuum and Quantization

We introduce the Unified Hybrid Format (UHF) — a novel data representation framework that integrates spectral continuity, quantized phase reconstruction, and local coherence into a single adaptive format. Unlike traditional codecs (e.g., JPEG, MP3) or learned embeddings (e.g., CLIP, Word2Vec), UHF dynamically shifts between smooth and discrete modes of representation based on the internal phase structure of the signal. UHF is defined by a triadic model: Rcont: a continuum projection via low-frequency spectral filtering, Rdisc: a reconstruction from quantized phase with original magnitudes, κ(x): a coherence map expressing the local structural order of phase. The hybrid form is computed by κ\kappaκ-weighted blending of these projections, producing a format that responds not to external instructions but to the morphology of the input itself. We present the mathematical foundation of UHF, reference implementations in 1D and 2D (signals and images), and quantitative comparisons to conventional formats. We also demonstrate potential applications in phase-aware compression, structure-preserving visualization, generative art, and as an interface to coherence-based AI models. UHF provides not just compression — it provides a form-sensitive, reactive substrate for multimodal computation. This work establishes the core architecture for coherence-centric data processing and invites further development of UHF as a general-purpose carrier of structure across domains.