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Summary paper examines arithmetic-closure judgement in a quantized real domain, indicating new insights.
This standalone summary paper presents the cumulative arithmetic-closure judgement developed across GRSC Papers16-62. It follows the progression from finite reading units and ledgered operations through projection certificates, obstruction ledgers, finite closure networks, presentation packages, Seal(M,G), and StableFiniteHigherInterface(H). The paper concludes that the background presupposition of real-number completeness cannot serve as a background presupposition in the arithmetic universe, and introduces the quantized real domain at the endpoint of the judgement chain. The archive contains synchronized Markdown, TeX, and PDF editions together with a file manifest and the documentation license.
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Wangyue (2026) studied this question.
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