Paper XI: Packets, Arithmetic Realization, and Conditional Comparison

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1 \begingroup\raggedright
2 \section*{Reading this edition}
3 \phantomsection
4 \addcontentsline{toc}{section}{Reading this edition}
5 This monograph presents the finite packet theory and retains the detailed restricted arithmetic constructions. Two separate research companions explain the later progress toward Conjecture 66. They do not replace the monograph's proved statements or turn its conditional comparison into an existence theorem.
6 
7 \subsection*{Five readers with different jobs}
8 \begin{tabular}{@{}>{\raggedright\arraybackslash}p{.28\linewidth}>{\raggedright\arraybackslash}p{.67\linewidth}@{}}\toprule
9 Reader & Route and purpose\\\midrule
10 Core monograph & Finite tame and wild theory, restricted arithmetic constructions, and the exact realization/comparison boundary.\\[7pt]
11 Core visual guide & \href{https://komorebi.invalid/b07/core_visual}{Geometric route through the core paper}. The original arithmetic examples retain their stated scope.\\[7pt]
12 Lean and evidence guide & \href{https://komorebi.invalid/b07/core_lean}{Formal statements, literal excerpts and evidence lineage}. The guide distinguishes the selected source census, compiler replay and arithmetic hypotheses.\\[7pt]
13 Progress paper & \href{https://komorebi.invalid/b07/research_start}{Toward Arithmetic Packet Realization}, 77 pages, v0.4.0. Connected proofs, failed routes, conductor conventions and native-marking conditions.\\[7pt]
14 Research visual atlas & \href{https://komorebi.invalid/b07/atlas_start}{Arithmetic Packet Realization}, 36 pages, v0.5.0. Thirty-two worked plates accompany the progress paper.\\\bottomrule
15 \end{tabular}
16 
17 \subsection*{The endpoint is a quantified construction problem}
18 Conjecture 66 asks for an actual arithmetic witness for each admitted source with its supplied H1--H4 datum. The comparison proposition then uses H5 for that same realized candidate. Historical obligation 66, historical Theorem 16.2, and all-records row 95 refer to this endpoint's lineage. Historical register row 66 is a different statement.
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20 The \href{https://komorebi.invalid/b07/contract}{research contract in Section 1} and \href{https://komorebi.invalid/b07/contract_atlas}{atlas plate V01} make the quantifiers explicit. Supplying finite operators does not construct an arithmetic representation. Likewise, proving a factor identity for a different candidate does not identify the packet's realizer.
21 
22 \subsection*{How to use the links}
23 Keep all five PDFs together with their delivered filenames. The colored reading links resolve to actual pages of the companion files. Section numbers remain the primary mathematical locators. The included JSON concordance records the resolved page destinations for this edition.
24 \clearpage
25 \section*{Current scope and research routes}
26 \phantomsection
27 \addcontentsline{toc}{section}{Current scope and research routes}
28 \begin{tabular}{@{}>{\raggedright\arraybackslash}p{.32\linewidth}>{\raggedright\arraybackslash}p{.63\linewidth}@{}}\toprule
29 Question & Route beyond the core statement\\\midrule
30 Parameter, full character and recovery & \href{https://komorebi.invalid/b07/arithmetic}{Progress Sections 7--10} and \href{https://komorebi.invalid/b07/arithmetic_atlas}{atlas V06--V10}. The full character, central character and noncompact completion remain fixed.\\[8pt]
31 Monomial, Clifford and occurrence routes & \href{https://komorebi.invalid/b07/monomial}{Progress Part II}. The original character route is excluded under its hypotheses. A different corrected character passes a scalar test, but occurrence in the same candidate is still open.\\[8pt]
32 Conductor and capacity & \href{https://komorebi.invalid/b07/conductor}{Progress Sections 22--25} and \href{https://komorebi.invalid/b07/conductor_atlas}{atlas V11--V19}. Swan, ordinary conductor and additive-character epsilon exponent are named separately. Equal numerical invariants need not give equal quotient capacity.\\[8pt]
33 Native markings and allowed repairs & \href{https://komorebi.invalid/b07/markings}{Progress Sections 26--29} and \href{https://komorebi.invalid/b07/markings_atlas}{atlas V20--V29}. A freely transported marking is different from a prescribed native marking. Finite corrections require their stated inputs and permission to change the relevant map.\\[8pt]
34 Remaining arithmetic certificate & \href{https://komorebi.invalid/b07/remaining}{Progress Section 30} and \href{https://komorebi.invalid/b07/remaining_atlas}{atlas V30--V32}. General realization, H5, corrected-character occurrence and the stronger native certificate remain separate tasks.\\\bottomrule
35 \end{tabular}
36 
37 \subsection*{What this revision checks}
38 This revision preserves the paper's structure and detailed construction appendices while correcting several local formulations. The breakwise phase product now uses its actual moving spaces and states the symplectic action explicitly. The twisted-algebra proof uses direct averaging. The type-side pairing fixes its prime-field character, and the tame comparison includes the rank-one conductor and trivial-character Gauss-sum boundaries. Interaction carriers are distinguished from minimal character orbits.
39 
40 Appendix B restores the approximation index \(B^{[j]}\) that was converted into a footnote. The earlier dimension-factor and 44 superscript repairs remain in place. All 15 original construction notes and the exact source diff accompany the release. These source restorations and local mathematical clarifications do not supply a general arithmetic witness.
41 
42 The selected Henniart--Lemaire induction inputs \cite{HenniartLemaire2011} have now been checked against the full official text, including their characteristic, rank and normalization hypotheses. The new source review is bounded to the cited application; it does not establish H5 or corrected-character occurrence.
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44 For the current compiler and axiom results, consult the Lean and evidence guide and the dated verification receipts. Historical evidence retains its original scope. Internal review is not external peer review. The complete Block 2 editable archive remains unrecovered, so its research-reader pages are preserved rather than claimed as a unified source rebuild.
45 
46 \endgroup

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