*(background color: truly is the nightmare before xmas around here lately. seems as if santa died this year.)* when in doubt, write some code. this idea occurred to me and is similar to `hybrid3`

experiment from 12/2018. the idea there is to just run the hybrid optimizer to find large ‘cm’ max glide index trajectories for fixed bit widths. here that is changed to ‘cg’ glide length. what will be the pattern of results? this generates 500 trajectories after 10K optimization iterations and then sorts results from longest to shortest by ‘cg’ and looks at the initial bit patterns. some of the hypothesis is confirmed. it turns out they are all utilizing a 1-lsb triangle to generate very long glides; this explains the lsbs. the msbs are harder to characterize. this grid plots the inverse of the bits and the msbs line up on the right in the same ‘cg’ order, longest to shortest bottom to top.

but generally this all fits into a brand new hypothesis. the idea is that generally the longest glides by bit width utilize the 1-lsb run structure. this would seem to explain a lot of other experiments that optimized but did not look further at the bit structure. the similar `hybrid3`

experiment did find/ notice the 1-runs but didnt notice at the time the probable lsb link. there was a series of experiments to find longest glides or trajectories limiting by 1-run lengths. my suspicion now is that for those longest trajectories found, the 1-runs tend to be in the lsb. it would have been simple to check at the time, but didnt. recall this experiment is showing that starting from random seeds, optimization of the longest glides all converge to this 1-lsb bit structure. therefore it seems likely (all) other optimization schemes (eg bitwise etc) would tend to follow the same pattern.

this is a very simple idea building on lots of prior analysis/ features but hasnt been surfaced from this angle until now. it also reminds me of the `construct49`

experiment from 9/2019. the basic idea there was that, iterating, the way 1-runs eventually intersect with the lsb seem to have the key effect on glide lengths.

some days it seems like a proof is still far off or unreachable, and other days it seems like just a slight twist or change of focus could bring out the path to solution. when simple unifying ideas are found that were previously missed, as here, its a cause for optimism.

💡 building on this, general proof idea: the longest glides have long lsb 1-runs, up to a point. all shorter glides have shorter or missing lsb 1-runs. this points to some kind of induction on the lsb 1-run length. this rough idea has come up previously. from prior observations there are instances of adjacent lsb 1-runs in trajectories, but maybe they are limited in size somehow? thinking it over, have not yet studied yet the *scaled* lsb 1-run… ❓