← Radical-FDRS: One-Dimensional Flattening and Elliptic–Chabauty Machinery on the Fixed Slice / R3 and R4 · a corrigendum

Radical-FDRS: One-Dimensional Flattening and Elliptic–Chabauty Machinery on the Fixed Slice R3 and R4 · a corrigendum unsigned in the source

The Reciprocal Splitting State and the Square-Lift Quotient Surface, and Its Correction: Conic Base Fibers, Elliptic Square-Lift Gates and the Five-Elliptic Decomposition of the Fixed Fiber

R3: face closure iff the reciprocal quadratic xT² − 2gT + x splits iff the Cayley ratio is a square, giving a symmetric square-lift surface Φ(R) + Φ(S) + Φ(T) = 2 whose all-square rational point is a perfect cuboid (and a claim that fixed-coordinate fibres have genus 1, which R4 corrects). R4: the fixed-coordinate fibre is a genus-0 conic, the genus ladder is 0 → 1 → 3 → 5, and the generic genus-5 fibre decomposes as Jac(C_n) ~ E1 × E2 × Q0 × Q+ × Q− (five elliptic factors), without yet identifying them with the historical curves.

Both are exact structural analyses whose status lines say they are not proofs; R4 is the corrigendum round for R3. R3 contains one exact-sounding but wrong genus statement (fixed-coordinate fibres have genus 1) that R4 corrects: read R3 only together with R4. The discriminant, resultant and quartic-invariant formulas of R4 were re-verified symbolically in the pre-publication read-through.

Connections · Connections

PreviousR2 · Twin-Psi and genus 5 · R2: The Twin-Psi Square System, the Fixed-Fiber Genus-5 Reconstruction and the Unification of the 7/32 and 11/45 Slices

NextR5–R7 · the three-family decomposition and the genus-2 quotient · The Generic Three-Family Elliptic Decomposition, the Möbius Gate-Swap Automorphism and the Hyperelliptic E_0 Bridge

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