This work extends the derivative‑order ladder program by developing a canonical anchored realization and gauge moduli framework. It introduces differential and packet projectors which organize derivative‑order spectra into canonical shells and packets, and provides exact deflation procedures that recover shells from coarser packets. The paper proves that finite windows of derivative ratios determine the underlying source up to a scalar factor, enabling exact finite‑window recovery. It constructs gauge moduli that decouple amplitude and phase information, showing that canonical packet projectors and gauge moduli fully determine the solution. The results highlight the existence of finite‑window source recovery laws and unify the analysis of derivative‑order ladders through anchored realizations.
Mohammad Abu-Ghuwaleh (Tue,) studied this question.