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Search the paper sections, open their original context and follow the checks they actually cite. The knowledge atlas explains the result; this library locates its source.

Numeric twin

det16 mirror gap theorem en

The companion probe is [formula in source] It uses the exact four-mode determinant projectors and open-chain hopping machinery of the frozen v1002 route. All [formula in source] checks pass. The direct comparison is: [formula in source] Every entry lies above [formula in source] with [formula in source] for the two-cluster endpoint pair and [formula in source] for the three–four cluster chains. Except at the smallest

Opening source excerpt. Formulas and the full argument remain in the original document.

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documents/articles--2026-08-30--det16_mirror_gap_theorem_en/sections/003-subsection-the-norm-count.tex · lines 65 to 131

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What this source index covers

The public registry includes 116 document views, 6,693 section records and 985 physical LaTeX sources. Active publication documents, research material and archives retain their recorded roles. This is source navigation, not a new semantic review or proof run.