The higher they climb

Step back a moment to single symmetric returns: like, oh, 1-0-1-6 for Mars or 2-0-1-6 for Venus. I am looking here at high h. I am beating my head against the Earth-Mars cycler, 3-9-1-7.

This means the array of "s_j", as the Society Of Russell And Ocampo puts it, should itself be a single-member society. h_j = {9}. Fracking f_j = {6}. Am I missing anything here? No flippin' returns. Just six flies by Earth over three synodic periods.

That h means, half-years "allotted" to the returns.

As long as h doesn't barf up five or six returns, as long as it stays under 8, I'm good. Then 3-9-1-7 says { 72 45 45 45 45 72 }. 4-9-1-12, 4-9-1-14, 4-11-1-10, 4-13-1-6 are similar. Then there's 4-9-2-8: {83 45 45 45 45 83 24}. Their Table 4 consistently brackets six f_j's for that first symmetric-return.

I do not know how this is even possible. This cycler should have six angles, yes. Those angles should all be identical. Nu?

(Apart from that, I see that 4-8-1-8 broke Newton; but, Russell and Ocampo didn't use that cycler themselves, so whatevs.) UPDATE 3/25: nah, I had failed to cast an int into a double where f_j was odd. I have solutions now for all of it.

I see it again 5-9-2-8, 5-9-3-6, 5-10-3-7. 6-8-3-11. So: the problems kick in h ≥ 9 and, as the synods get higher, the walls close in on us.

It's not about my maths nor even their maths - those work great. It's about the iterations. Somehow in the Russell / Ocampo universe, {6} is {1,4,1}.

It may all be moot for me anyway.