Quantum and Circuits

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1 \hypertarget{q:source-lineage}{%
2 \section*{Source lineage}\label{q:source-lineage}}
3 
4 The four primary literature entries are provided in the accompanying
5 reference fragment. Ramanujan's work supplies the arithmetic lineage.
6 Vaidyanathan's papers establish the signal-processing setting of
7 Ramanujan spaces and filter banks. The internal Komorebi lineage is
8 \emph{Stratified Universality for Resolved Representations}, v1.16.0,
9 Proposition 21.11, printed page 189, with Boundary 21.12 on the
10 distinction between character orders and coefficient-residue lanes.
11 
12 The local authoritative source set for the finite example consists of
13 \texttt{Worked\_Example.md}, the original reproducibility verifier, the
14 earlier four-module checked source and proof-boundary document, and the
15 later five-module checked source with its verification records. Their
16 exact filenames, source hashes, and evidence classification are listed
17 in the release provenance and the Lean guide. The traditional paper
18 supplies self-contained mathematical proofs, while those companion
19 records make the implementation and formal scope inspectable.
20 
21 % Primary-source attribution checked 2026-10-07 UTC.
22 % Journal Parts I and II: metadata authenticated; no uninspected equation numbers.
23 
24 

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