The Solar System as an Instance of the Developmental Operator

This paper applies the Developmental Geometry (DG) framework to Sol's orbital register and tests its predictions against ephemeris-grade measurements. The framework's commitment to integer shell-index assignments nM = 3 and nJ = 11 for Mercury and Jupiter — structural, not fitted — predicts the dimensionless ratio aJ/aM = (11/3) ² = 121/9 = 13. 4444 with no free parameters. Sol delivers aJ/aM = 13. 4406, agreeing with the framework's parameter-free prediction to 0. 028%. The gauge-independent ratio relation is the strongest empirical claim in the paper; equivalent gauge presentations under the geometric-mean joint gauge u_⊙ = 0. 043005 AU (integer n with symmetric ±0. 014% residuals) and the displaced gauge u_⊙' = 0. 042995 AU (with identical fractional shift f = +0. 000572 at zero residual) are presented as downstream displays of the same gauge-independent fact. Derivations supported: Cascade depth CS = 2^ (-N) from master-operator collapse sequence at the host register, with N the host's internal stellar zone count (Sol: N = 2, CS_⊙ = 0. 249964 vs. ideal CS₂ = 0. 250000). Confirmed at four host systems spanning two zone counts: TRAPPIST-1 (N=1), Sol, 55 Cnc, and HD 10180 (N=2). The high-leverage N ≥ 3 test remains open. Earth–spiral coupling vw (rE) = ω·rE ≈ 429 km/s from the balance-axis condition combined with Parker geometry, sitting within the observed slow-stream distribution at 1 AU. Cascade structure 7, 5, 3, 1 at the radial register from the same 2 + 2 → 2 bifurcation primitive operating at the operator register. Empirically supported: Sol's shell-ruler fit at sub-3% for 7 of 9 bodies, with structurally-meaningful residuals at Venus and Earth (the latter reading State A's pristine r₅^ (A) = 1. 075 AU vs. current 1. 000 AU). Yamazaki–Oda (2002, Science) 100 kyr periodicity in paleomagnetic intensity: framework provides a candidate wind-coupling mechanism alongside existing alternatives (sediment lock-in, climate-core coupling). ALMA-resolved disk features clustering at framework shell positions across multiple systems with system-specific gauges. Discipline: derived predictions are distinguished from empirically supported claims throughout. The paper registers open work explicitly (Venus residual structural reading; N ≥ 3 test; higher-order cascade-depth offset). The framework is developed in detail in the DG corpus on Zenodo: Shape of Two (10. 5281/zenodo. 19458184), Arc III (10. 5281/zenodo. 19598450 / 19598623), Arc 4 (10. 5281/zenodo. 19673796), Arc 5 (10. 5281/zenodo. 19685725), Arc 6 (10. 5281/zenodo. 19899286), Arc 7 (10. 5281/zenodo. 19923776), Arc 8 (10. 5281/zenodo. 20030252), Shell Capacity (10. 5281/zenodo. 19580262), Paper E (10. 5281/zenodo. 19210681), Paper 2 (10. 5281/zenodo. 18974548), Book of Timing and Tiles (10. 5281/zenodo. 19412491).