Posted by: @lendor-77

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The question I am asking comes one step earlier: before the final model was fixed, how many alternative constructions could the author have tried?

If, for example, the ephemeris contained 12 bodies or points in a fixed order, and the author preserved that order while simply deciding where to stop, he would have had 12 possible global constructions available:

1 column,
2 columns,
3 columns,
…
up to all 12 columns.

And having made this “choice,” every member of the column enters as fixed, thus immediately negating whatever freedom you imagined this initial “choice,” one which actually precedes the point at which the analysis of ultimate freedoms begins, to have bought you.

You may choose a column because it gets you a ‘5’ in the third row, which is what you want. But then, with this you have to take, say, a ‘4’ in row one (whether you want it or not, no freedom to choose otherwise). You then choose a column that gives you the ‘4’ in row one, which is what you want here, but with this you have to take a ‘7’ in row three (whether you want it or not, no freedom to choose otherwise). And on it goes, the same at every step. Put all of these operations together, and the most you can achieve is to get one row only to what you want, and even this depends on whether the columns actually afford the values required to complete your single row. As your method requires a particular result from every row, it is hopelessly lost.

I am afraid I cannot continue with this. As a problem in analysis, subject to precise analytical methods that have been detailed and applied already, it simply does not merit, nor warrant, the excessive level of repeated re-presentation that it has already suffered.

Posted by: @shaqmeister

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You then choose a column that gives you the ‘4’ [a ‘6’] in row one, …