← Radical-FDRS: One-Dimensional Flattening and Elliptic–Chabauty Machinery on the Fixed Slice / R1 · The Cayley transition algebra

Radical-FDRS: One-Dimensional Flattening and Elliptic–Chabauty Machinery on the Fixed Slice R1 · The Cayley transition algebra unsigned in the source

R1: Squareclass Transition Algebra, Rational-Sphere Moves, Cayley Defect Ratios and the Unification with C2

On the rational-edge sphere each face defect is the squareclass of the Cayley ratio ω(x) = (1 − x)/(1 + x) (seed: (25/39)², (17/28)², 233/1913 with 233 = g − c and 1913 = g + c), so a perfect cuboid exists iff the triple-Cayley-root surface has a rational point.

An exact reformulation: 'exists iff' is an exact equivalence and the status line says it is not a proof. R1 unifies C2 of the core into the language of Radical-FDRS; it carries no new existence or nonexistence content.

Connections · Connections

PreviousR0 · Methodology and the first experimental pass · The Radical-FDRS One-Dimensional Flattening Methodology and Its First Experimental Pass: Radical Closure, X-Diagonal Coupling, the Boolean Cube and Squareclass Defect Dynamics

NextR2 · 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

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