Radical-FDRS: One-Dimensional Flattening and Elliptic–Chabauty Machinery on the Fixed Slice
R22 and R23 · the end of the series and a corrigendum
unsigned in the source
The Certified Height Audit and First Quadratic-Chabauty Root Filtering, and the QC Pole-Cancellation Corrigendum, the True Mock Branch and a Cross-Prime Mordell–Weil Height Barrier
R22: shows R19's heights survive the minimal-model audit and starts quadratic-Chabauty root filtering in the prototype disk (series 20u + 8u² + 22u³ mod 121, boundary target ω* = 9757), reporting a second 'mock' branch u = 3 (mod 11) — a series and branch that R23 supersedes. R23: corrects R22's omitted pole-cancellation term (series 43u + 19u² + 22u³ mod 121; branches u = 0 and u_mock = 42170 mod 11^5) and, with 11-primary Mordell–Weil data at six primes plus r = ±1 mod 256, builds 33,600 CRT lattices (modulus N = 1029304283393515824664282755428096) implying H(r) ≥ 76,108,490,872,046 for any rational point on that branch — explicitly 'not yet a fixed-slice nonexistence theorem'.
The end of the series: a corrected quadratic-Chabauty lift and a global congruence-height lower bound; it is not a nonexistence theorem.
Do not read R22 without the correction of R23: 'first genuine QC root filtering', 'certified' and 'the fixed-slice theorem is now genuinely within a small number of p-adic lifting steps' are overstated, and its central series and the u = 3 branch were wrong. The headline of R23, 'a boundary point against one mock branch', omits the other 1440 p-adic candidates (720 other targets × 2 roots) that §12 of R23 itself counts; 'certified' and 'height barrier' need careful reading. The finite-prime, lattice and Hensel arithmetic was fully reproduced in the pre-publication read-through; the quadratic-Chabauty series itself was not independently verified.