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1 \subsection*{Primary context}
2 \begin{enumerate}[label={[C\arabic*]},leftmargin=2.5em]
3 % Five verified primary entries. All exact propositions are proved in the manuscript.
4 \item NIST Digital Library of Mathematical Functions,
5 \href{https://dlmf.nist.gov/16.2}{\S16.2} and
6 \href{https://dlmf.nist.gov/18.5}{\S18.5}.
7 Generalized hypergeometric series and Chebyshev conventions.
8 Relevant definitions and convergence hypotheses inspected.
9 
10 \item G. Teschl,
11 \emph{Jacobi Operators and Completely Integrable Nonlinear Lattices},
12 Mathematical Surveys and Monographs 72, American Mathematical Society, 2000.
13 \href{https://www.mat.univie.ac.at/~gerald/ftp/book-jac/jacop.pdf}{Author's online edition},
14 \S\S1.1 and 2.1.
15 Jacobi continued-fraction and Weyl-function context.
16 The sign of a Weyl function changes when $(J-z)^{-1}$ is replaced by $(z-J)^{-1}$.
17 
18 \item S. V. Kozyrev,
19 ``Wavelet theory as $p$-adic spectral analysis,''
20 \emph{Izvestiya: Mathematics} 66(2), 367--376 (2002).
21 \href{https://doi.org/10.1070/IM2002v066n02ABEH000381}{doi:10.1070/IM2002v066n02ABEH000381}.
22 Published English Theorems 2 and 7 inspected.
23 The $\mathbb Q_p$ Vladimirov setting supplies wavelet context;
24 the present $\mathbb Z_p$ level-diagonal construction is proved separately.
25 
26 \item D. Aharonov, A. Ambainis, J. Kempe and U. Vazirani,
27 ``Quantum Walks on Graphs,''
28 \emph{Proceedings of STOC 2001}, 50--59.
29 \href{https://doi.org/10.1145/380752.380758}{doi:10.1145/380752.380758}.
30 \href{https://arxiv.org/abs/quant-ph/0012090v2}{arXiv:quant-ph/0012090v2},
31 25 May 2002, \S3.1 inspected.
32 Standard coined-walk context; the product-graph arc construction and its continuity identities are proved here.
33 
34 \item P. P. Vaidyanathan,
35 ``Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial,''
36 \emph{Proceedings of the IEEE} 78(1), 56--93 (1990).
37 \href{https://doi.org/10.1109/5.52200}{doi:10.1109/5.52200}.
38 \href{https://authors.library.caltech.edu/records/x720m-mr760}{Caltech author-repository record}.
39 Metadata and abstract inspected; full PDF retrieval failed.
40 Polyphase history and terminology only.
41 \end{enumerate}
42 
43 \subsection*{Scope of the literature check}
44 The hypergeometric bottom parameters used here are positive, so the nonpositive-integer exclusions in \S16.2 do not arise. The Chebyshev formulas use the standard first- and second-kind definitions. These scalar conventions do not supply an unbounded-operator domain.
45 
46 The cited Teschl, Kozyrev, and Aharonov--Ambainis--Kempe--Vazirani passages are used only for the contextual comparisons stated above. Their settings differ from the finite tree, compact adic hierarchy, and irregular arc graph of this volume. The comparison is limited to the explicit uses recorded for each reference. The Vaidyanathan PDF could not be retrieved; its metadata and author abstract establish only the stated historical context. All exact model propositions in this volume carry internal derivations. No exhaustive novelty search or literature-priority claim is made.

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