A Core-Agnostic Validation Framework for Structural Similarity Metrics in One-Dimensional Signals

This repository presents a methodological framework for the external validation of structural similarity metrics applied to one-dimensional signals. Structural similarity scores are widely used in chemometrics, spectroscopy, and signal analysis, yet their interpretation is often ambiguous: high or low values may arise from trivial statistical properties rather than genuine structural organization. The material provided here addresses this issue by introducing a core-agnostic validation framework based on null models and scale-resolved statistical diagnostics. The framework treats any similarity metric as a black box producing a scalar output. Statistical credibility is assessed externally by comparing observed similarity scores against distributions obtained under controlled signal randomizations, including phase randomization, iterative amplitude-adjusted Fourier transform (IAAFT) surrogates, and block-shuffle perturbations. A scale-dependent diagnostic z(B)z(B)z(B) is used to localize structural effects across organizational scales. Importantly, validation does not require access to the internal implementation of the similarity metric. As an illustrative case study, the framework is applied to SISSI (Spectral Integrity and Structural Similarity Index), a structural similarity measure for one-dimensional signals. SISSI is used here solely as an example to demonstrate the behavior of the validation protocol; the core implementation of the metric is not distributed. The emphasis of this repository is on methodology and falsifiability, not on benchmarking or performance claims. The materials include: a complete methodological specification of the validation framework, formal definitions and statistical safeguards, an algorithmic summary of the validation procedure, illustrative examples on chemical spectra and industrial vibration signals, a clear separation between computation, validation, and interpretation. This work is intended for researchers and practitioners who use similarity metrics and require robust, reproducible criteria to assess whether observed similarities reflect meaningful structure or are explainable by null hypotheses. The framework is applicable to both open and proprietary similarity measures and supports independent verification without disclosure of internal algorithms.