Cross-Scale Statistical Tests of Orbital Period-Ratio Structure: Narrow-Band Excess, Satellite-System Lattice Specificity, and Host Independence

Abstract: Kepler multi-planet systems exhibit resonance excess in adjacent period ratios (Lissauer et al. 2011; Fabrycky et al. 2014) and peas-in-a-pod log-uniform architectures (Weiss et al. 2018). We analyze orbital period-ratio structure at two scales with a unified methodology. Results: (1) the narrow band [1.35, 2.0] fraction is 37.2%, 2.18x the prior 17.1% (binomial p=3e-42), dominated by non-resonant continuous density (valley 1.10x), with no independent resonance peak; (2) satellite systems (316 pairs) hit 10 low-order lattice points 59 times vs 40 expected from a random-grid-set control (1.48x, p=0.011); the Galilean 1:2:4 Laplace chain has offsets <1%; (3) resonance rate is uncorrelated with host age (496 systems, r=+0.001, p=0.99) — flat in the mature regime (0.3-18 Gyr), complementary to the early decline of Dai et al. 2024; (4) independent of [Fe/H] (240 systems, p>0.35); (5) strictly matching pairs show net positive offset +15 pp (bootstrap p=0.001, low-order dominated), consistent with tidal parking at the upper edge of resonances; (6) the narrow band is a packing projection within the Hill-stability framework (after controlling for Delta, P ratio vs mass r=+0.785, p<0.001); the r<1.2 interval contains only 0.5%; (7) the random-grid-set control reveals the apparent all-pairs lattice excess to be a peas-in-a-pod log-uniform projection (p=0.66), establishing the protocol. All numbers are verified by reproduction scripts.