← The Perfect Cuboid · PROGRAM-PERFECT-CUBOID · RADICAL-FDRS

Radical-FDRS: One-Dimensional Flattening and Elliptic–Chabauty Machinery on the Fixed Slice

Radical-FDRS · 2026-10-03 to 10-06 · 25 files (R0, the R0 first experimental pass, R1–R23)

Radical-FDRS (radicals — Boolean cube — squareclass defect dynamics) writes the perfect cuboid as a 'one-dimensional flattening' problem: the six squareclasses κ_i must all equal 1, and the seed (448, 495, 840; 1073) is the single-defect state K = (1, 1, 1, 233·1913, 1, 1). R1–R4 rewrite it exactly as the Twin-Psi square system and its fixed fibres (generically genus-5 curves; the historical slices n = 7/32 and n = 11/45 are two charts of the seed); R5–R8 find a three-family elliptic decomposition, a gate-swap involution and a genus-2 quotient, and bring n = 7/32 to a double square-value problem on a shared E₀′; R9–R16 do the first real computations (Mordell–Weil sieves at finite primes, the negative result on 2-adic local openness, Sylow-2 refinement and the gate swap, a canonical cover and dual sieves — nothing eliminated at two new primes); R17–R23 build the specification and a custom backend for 11-adic quadratic Chabauty (a local normal form, formal logarithms, Mazur–Tate heights, coupled local images that shrink the target set to 721 classes, root filtering and one correction), and stop at 'H(r) ≥ 76,108,490,872,046 for any rational point on that mock branch', explicitly 'not a nonexistence theorem'.

Honest status: the status line of every one of the 25 files says it is not a proof of perfect-cuboid existence or nonexistence (R17 adds that the final Coleman / p-adic-height zero computation is not executed in the present runtime). The whole line treats a single fixed fibre n = 7/32 (and its twin slice 11/45): even if this one slice were excluded completely, n can still vary and the perfect cuboid problem would not be settled. The rank-1 inputs (E_f, E₀, E₋) are 'historical rank theorems' inherited from the G-line of the core and are not derived here. The conjectures R-A…R-D are not theorems; 'certified' means the output of the authors' own exact-integer code.

Four corrigenda (marked on the pages): R3 → R4 (a wrong genus statement); R9 → R11 (an omitted prime p = 4,195,001); R19 → R20 ('global minimal model' is wrong at 2; 'crosses the height barrier' is premature); R22 → R23 ('first genuine QC root filtering' is overstated, the central series and the u = 3 branch were wrong, and the headline of R23 itself omits the 1440 other p-adic candidates counted in its §12). Please read along this chain and not the corrected papers alone.

What the pre-publication read-through reproduced: the scan and compatibility table of R0 pass 1; the table and sieve of R9; the eight classes of R11 and that p = 4,195,001 was the only omitted prime; that p = 6,291,881 is the only prime in [4.2×10⁶, 8.26×10⁶] with projected order ≥ 2^19 (R12); the mod-17 certificate of R14; the counts and orders of R15; the non-isogeny of R16; the counts of R17 (#H(F₁₁) = 20); U₀, U₋, both coefficient series and the elimination relation of R18; the discriminant valuations and Kodaira types of R20; the 721 classes, nine Iwasawa logarithms, the list and the checksum of R21; the finite-prime / lattice / Hensel arithmetic of R23. Not independently verified: the quadratic-Chabauty series of R22 and R23 themselves, and the Mazur–Tate sigma constants and heights of R19. This checks arithmetic inside exact computations and is not an independent referee.

Authorship and provenance: none of the 25 files carries an author or AI-role line (headers carry only Series / Branch / Phase / Date / Status), and this site does not guess. Dates 2026-10-03 to 10-06; the one-day differences between header dates and file times for R12 and R21 are just a midnight rollover. The task brief said 26 files; the folder actually holds 25 (the R0 methodology, R0 pass 1, R1–R23). Size: 591,654 bytes, about 47,000 English words and 5,700 display equations, all in English; the pages render in the browser on load and are heavy. Reading path: R0 → R2 → R3/R4 → R5–R7 → R8 → R9 → R10 (a negative result) → R11/R12 → R13–R16 → R17–R19 → R20/R21 → R22/R23. For the background on the perfect cuboid see the case overview.