Machine Societies

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1 \clearpage
2 \section{Final edition and verification scope}\label{app:release-review}
3 \noindent\textbf{Final monograph edition, 15 October 2026.} This edition preserves the 62 theorem and proposition statements and their prose proofs from text edition 1.0.0. It adds the linked index, completes the presentation review, and records a targeted mathematical self-review with a fresh run of the finite reference programs.
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5 \subsection*{Mathematical review}
6 The review covers Propositions~\ref{prop:deterrence-tv}, \ref{prop:enforcement-garbling}, and~\ref{prop:joint-robust}, Theorems~\ref{thm:joint-enforcement} and~\ref{thm:robust-staffing}, all four theorem and proposition results in Section~\ref{sec:joint-synthesis}, and all six in Section~\ref{sec:accountability}. It checks the shared-monitor quantifier, finite-horizon and indefinite safety, certified service, exact abstraction, strategic inspection, privacy, appeal capacity, authorized endings, and guarded handover.
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8 No failed implication was identified in those 15 results under their written hypotheses. Their mathematical statements and proof bodies required no change. The other 47 retained theorem and proposition proofs were not newly audited in this targeted pass. The detailed claim cards, dependencies, boundary cases, and source comparisons accompany the source package.
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10 \subsection*{Exact finite checks}
11 The delivered rerun passed 75 groups containing 922,032 assertions using integers and exact rational arithmetic. The checks include separate finite-policy searches, rational optimization comparisons, matching and direct-assignment comparisons, and deliberate invalid-certificate controls. Each group states its actual input range. The quotient checks cover two specified refinement families, not every possible concrete refinement.
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13 The examples also keep their contracts distinct. The joint audit-and-service example needs five execution units. The accountability example needs eight, including the final record and revocation. Its five primitive transitions count separately from those eight execution units. Passing these bounded checks supports the reference constructions. It does not replace the general proofs.
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15 \subsection*{Release boundary}
16 The finalized package contains the reading PDF, editable sources, local fonts and figure assets, exact reference programs, reproducible checks, and the review records. The original source release remains available as provenance. The theorem index and contents use the page numbers of this reading edition.
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18 This is a theoretical monograph with a recorded project self-review. It makes no claim of independent peer review or proof-assistant verification. Physical implementation, authority, trusted evidence, observation laws, and environmental coverage remain explicit assumptions of the models. The research questions in Section~\ref{sec:problems} remain open.

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