Kepler-138f?

I couldn't find the PDF for Kepler-138 but the Wikipedians did offer up the vital-statistics: 10.3132068, 13.78110882, 23.0889203 days. And maybe an e at 38. That first one is running faster than 5:4 11 days; it's the local Amalthea, doomed, so let's ignore it. The latter are near-1:2:4. Mass detectable down to 0.187. LET'S DO DIS

Since these are edge-on orbits all over 88.3° I assume we got nothin' between c and d. Let's posit our e at, oh, 85°; a little inclined, as Venus/Earth, just enough we'll likely not see its transit. The equation is, as always, n_c - 3n_d + 2n_e = 0. In degrees/day n_c = 26.122716589941273 and n_d = 15.591894091297114. n_e would be 10.3265 °/d, orbit 34.86 days. Ohhh kay... this looks close to the 38 days what they'd "inferred" of e . . .

We do not, here, own a true resonance; it looks more Uranian than Jovian. It goes similar for the mass-ratios: the planets c and d may (may!) be twice GJ 1002's b and c, but their star is quadruple and, accordingly, everyone is about twice as far. (Probably why nobody's said anything about the resonance.) The tides don't much help constrain evolution, here; c, d, and e should be going out together as b goes in and suffers its own tides.

I do note the eccentricity although Earthlike for c (0.0110) is getting higher for d (0.027, ish). Compare Mars 0.093. Sometimes this implies we're missing a planet on the inside but I'm not seeing K-138 has the space for it. So let's rethink e - let's rethink bigger.

Would this blog be far out of bounds if it proposed a Jovian out there, maybe a Neptunian closer? At double-digit parallax we'll not see it directly. This should however be detectable by the radial method, after a couple of years.