Tripartite Palindromic Partition of Integer (HP 50g) Challenge

[3298]

Unfortunately, that version of the paper looks identical to version 1 on arXiv (minus an index and clickable links), so the release history seems to be the other way around. Version 1 avoids that particular problem by having an additional case to handle it (apparently there was a flawed attempt to improve it by eliminating unnecessary cases for version 2), but there are a couple other changes, from inconsequential things like some different phrasing across the first three pages and a bunch of spelling corrections throughout the paper, to algorithm-changing things like an adjustment to the limit between types A6 and B2, or making an argument that case II.2.ii.b is unnecessary (thus simplifying the conditions for II.2.ii.a), or splitting up II.2.ii.c because another argument wasn't valid for 7-digit numbers of types A5 and A6 (which incidentally are treated as if they were a digit shorter, making them fall into the small-numbers range we seem to be having trouble with - and now I'm curious whether I should apply the small-number prohibition on Algorithm V to them or not, because the large-number section doesn't mention that).
There's also the elimination of cases IV.2.ii.c (leading to IV.2.ii.d getting renamed and condition-simplified) and IV.3.ii (that leaves IV.3.i as all that's left of IV.3), the addition of IV.4.iii with two subcases .a and .b (and two unnamed sub-subcases each), the elimination of IV.5.iii.e, and a redo of IV.5.v.b and IV.5.v.c.
Algorithm V was rephrased to account for the fact that decrementing both middle digits by 1 can lead to the other one becoming 0, re-triggering the condition for Algorithm V. (It should have been also adjusted to account for the newly emerged difference between the type A5/B1 and A6/B2 cutoffs, but that's a minor oversight.)
In 4-digit numbers, cases iii.a with \(\delta_3 \neq 1\) and iii.b were redone. In 5-digit numbers, cases vii, viii, and viii (yes, version 1 has two named viii here...) were replaced by a single case called vii. 6-digit numbers with \(\delta_5 \neq 1\) get their case iii replaced by a paragraph arguing that this case isn't actually possible, and the following cases iv and v consequently get their names decremented to iii and iv.
6-digit numbers with \(\delta_5=1\) see a change in the justification for case ii (and some missing definitions for \(z_1\), \(c_1\), \(z_2\), and \(c_2\), though similar problems with subsequent cases remain - you can easily fill in those gaps at least). Version 2 also adds case iii.d and corrects the mistake that there were again two identically named cases - the second iii and following iv obviously get renamed to iv and v. The (former) second iii gets split up into sub-cases .a and .b (the old content is found in .a, whereas .b is all-new). All sub-cases of old iv.c (new name: v.c) received a correction in their final digit. There are also fresh sub-cases v.d and v.e, which seem to be written by another author given the very different style (which I find much harder to comprehend) - the new iv.b belongs into that group too.

I hope I caught all the actually important changes here... there was much alt-tabbing back and forth to visually identify changed areas, but I can't guarantee that I did catch all of them.