Mathematical statements, published methods and exploratory observations have different evidential status. These summaries retain that distinction and point to their sources.
Published mathematical result
For generalized Walsh systems Ψₐ with integer a ≥ 2, the 2013 paper studies uniform greedy convergence after changing a function on a set of small measure. The correction assumption is essential to the statement’s scope; this is not a claim for every unchanged function.
On the uniform convergence of the greedy algorithm in a generalized Walsh systemPublished mathematical result
The 2014 joint paper with Jürgen Müller establishes maximal families of limit functions for Walsh–Fourier series of W-continuous functions on small subsets of [0,1]. Both the W-continuity setting and the restriction to small sets belong to the result.
Universality properties of Walsh–Fourier seriesPublished method & experiments
WHSDA-AI associates selected Walsh coefficients with documented feature-group comparisons and versioned explanation cards. The contribution is representation and governance within a supervised pipeline; an unselected orthogonal transform cannot improve Euclidean rankings.
WHSDA-AI: Interpretable Walsh-Hadamard Spectral Deviation Analysis for Structured Artificial Intelligence Applications in Banking SectorKnown estimates · manuscript under revision
For N = 2ᵐ, dyadic I with |I| ≥ 2 and normalized Haar vector hᵢ, define Cᵢ(x) = 2|⟨x,hᵢ⟩|/√|I|. Then |Cᵢ(x)−Cᵢ(y)| ≤ 2‖x−y‖₂/√|I|. Regularized coefficient-group energies have bounded-set Lipschitz estimates for ε > 0. These elementary component estimates do not prove global stability of the standardized HWSF-43 map or shift invariance.
Stable Dyadic Spectral Fingerprints Based on Haar–Walsh Transforms for Discrete Signal and Data AnalysisExploratory software evidence
The six-record MIT-BIH pilot and paired offline XQRS follow-up show that classification from reference-derived RR does not transfer automatically to detected RR. Scores are conditional on matched detections; missed events remain separate. The records were inspected during development. This motivates a detector-aware benchmark, rather than a clinical-effectiveness claim.
Inside SPECTRA EdgeMed