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R10 · 2-adic local openness (a negative result)
Radical-FDRS: One-Dimensional Flattening and Elliptic–Chabauty Machinery on the Fixed Slice
R10 · 2-adic local openness (a negative result)
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R10: 2-Adic Local Openness, Sharp Boundary Neighborhoods and the Failure of Pure Formal-Group Isolation
A negative strategy result: both gates are nonzero squares at the four boundary points, so local solutions have open 2-adic neighbourhoods (v₂(m) ≥ 7, v₂(m ∓ 1) ≥ 8) and purely local squarehood can never isolate the boundary.
The paper says outright that it 'does not produce the hoped-for local nonexistence theorem'.
This page is worth reading on its own: it says exactly why purely local arguments cannot suffice, which is why R11–R23 turn to global Mordell–Weil and quadratic-Chabauty tools.
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