← Radical-FDRS: One-Dimensional Flattening and Elliptic–Chabauty Machinery on the Fixed Slice / R17–R19 · the quadratic-Chabauty specification and a custom backend

Radical-FDRS: One-Dimensional Flattening and Elliptic–Chabauty Machinery on the Fixed Slice R17–R19 · the quadratic-Chabauty specification and a custom backend unsigned in the source

The Quadratic-Chabauty Local Normal Form at p = 11, 11-Saturation with Custom Formal Elliptic Logarithms, and Mazur–Tate 11-Adic Heights with Calibration of the Bielliptic Quadratic-Chabauty Function

R17: a specification round that diagonalises the differentials, finds p = 11 good ordinary, reduces the global problem to four of twenty residue disks (one symmetry orbit around (1, 961408)), and states that the final Coleman / p-adic-height zero computation is not executed in that runtime. R18: a custom 11-adic backend that proves Q and P_− are 11-saturated, computes the formal elliptic logarithms (U_0, U_−) and an explicit analytic relation ν_− = Φ_11(ν_0 − 1) of 11^5 precision between the two Mordell–Weil coefficients. R19: reconstructs the Mazur–Tate 11-adic sigma functions to obtain the global heights h_11(Q) = 58966 and h_11(P_−) = 3035 (mod 11^5) and the calibration constants α_1, α_2 of the explicit bielliptic quadratic-Chabauty function.

A specification and a custom backend: R17 'presents no invented p-adic height constants'; §39 of R18 says what is not computed; the final quadratic-Chabauty height computation is not executed. R19 calls Y² = X³ − 2MX² + L²X a 'global minimal model' (wrong at 2, corrected in R20) and 'crosses the global-height barrier' is premature; its constants are provisional until R22. The pre-publication read-through independently reproduced U_0, U_−, both coefficient series and the elimination relation of R18; the sigma constants and heights of R19 were not re-derived.

Connections · Connections

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