Paper XI: Packets, Arithmetic Realization, and Conditional Comparison

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1 \section*{Two visual routes, one claim map}
2 \phantomsection
3 \addcontentsline{toc}{section}{Two visual routes, one claim map}
4 This is the core visual guide. It explains the mathematical objects and the restricted arithmetic constructions in the monograph. The separate \href{https://komorebi.invalid/b07/visual_atlas}{36-page research atlas} explains the subsequent comparison tests, failed routes and remaining certificate. The two guides are complementary, not competing versions of the same document.
5 
6 \begin{tabular}{@{}>{\raggedright\arraybackslash}p{.28\linewidth}>{\raggedright\arraybackslash}p{.67\linewidth}@{}}\toprule
7 Start with the question & Continue to the linked reader\\\midrule
8 What is being realized? & \href{https://komorebi.invalid/b07/visual_contract}{Monograph realization contract} and \href{https://komorebi.invalid/b07/visual_v01}{research plate V01}. Finite comparison and arithmetic existence are different assertions.\\[9pt]
9 How does recovery preserve the candidate? & \href{https://komorebi.invalid/b07/visual_recovery}{Monograph restricted constructions} and \href{https://komorebi.invalid/b07/visual_v10}{research plate V10}. A changed assembly carrier does not mean a changed inducing representation.\\[9pt]
10 Why do numerical tests not settle attachment? & \href{https://komorebi.invalid/b07/visual_conductors}{Progress Sections 22--25} and \href{https://komorebi.invalid/b07/visual_v15}{research plates V11--V19}. The full and skipped rank-eight profiles have capacities six and four despite the same three numerical invariants.\\[9pt]
11 What does a dyadic marking retain? & \href{https://komorebi.invalid/b07/visual_marks}{Progress Sections 26--29} and \href{https://komorebi.invalid/b07/visual_v20}{research plates V20--V29}. Squares, section products, native choices and phase data must not be collapsed into one commutator form.\\[9pt]
12 What is formally checked? & \href{https://komorebi.invalid/b07/visual_lean_input}{Lean guide: the existence input} and \href{https://komorebi.invalid/b07/visual_lean_signature}{the conditional signature}. A supplied field in a structure is not constructed by typesetting its declaration.\\\bottomrule
13 \end{tabular}
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15 Keep the five reader PDFs together. These links use the actual companion pages, while the original lessons keep their source-note and section anchors. No diagram in either guide certifies arithmetic inputs that its source argument leaves open.
16 \clearpage
17 \section*{Reading corrections without changing the contract}
18 \phantomsection
19 \addcontentsline{toc}{section}{Reading corrections without changing the contract}
20 \textbf{One candidate throughout.} A source-defined induction candidate and a directly constructed type candidate are not identified merely by notation. Occurrence, full-character normalization and the noncompact extension must concern the same representation. The \href{https://komorebi.invalid/b07/visual_occurrence}{Part II occurrence analysis} retains the excluded original route and the corrected route's remaining obligation.
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22 \textbf{A transported mark is not a prescribed native mark.} The positive scalar-pushout attachment carries the supplied finite marking through a center-fixing homomorphism. It does not identify that output with an independently fixed host subgroup. Conversely, the stronger native problem must not be inserted as a new premise into the different transported-marking result.
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24 \textbf{The equal-capacity example is conditional.} At rank eight the full profile has exactly six quotient dimensions. The finite Arf test applies when the actual native refinement is independently prescribed. The abstract six-dimensional forms in the research atlas are examples, not a computation of that candidate's native square bits.
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26 \textbf{A successful finite repair has inputs.} The transvection starts with an allowed symplectic map and an isotropic discrepancy vector. The odd-action correction starts with genuine supplied finite actions. Neither constructs the arithmetic normalizer or chooses every honest phase. See \href{https://komorebi.invalid/b07/visual_repairs}{plates V25--V29}.
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28 \subsection*{Evidence and publication status}
29 This revision rebuilds the core guide from its editable source and preserves its Python-generated vector figures. The historical matrix calculations and ordinary construction arguments keep their dates and scopes. The Lean and evidence guide records the separate current compiler replay; the PDF build itself does not certify arithmetic constructors.
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31 The versioned ledger distinguishes publication and formal verification from the open arithmetic endpoints. The selected Henniart--Lemaire source interface has now been checked against the full official text, including its normalization conventions. The complete Block 2 editable archive remains unavailable. Its research-reader pages are preserved. No external peer review is claimed.
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33 For the final same-candidate comparison, read \href{https://komorebi.invalid/b07/visual_comparison}{the monograph comparison proposition} alongside \href{https://komorebi.invalid/b07/visual_v32}{research plate V32}. The conjecture itself does not assert the independent H5 step.

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