Tripartite Palindromic Partition of Integer (HP 50g) Challenge

[Gerald H]

Today, the 26th day of the competition, we have two complete solutions, from peruna & 2old2randr.

peruna's solution is theoretically easily understandable, as are the programmes, a paradigm of economy & carefully optimised for UserRPL.
However, for large numbers an inordinately large time is required.

2old2randr's solution is a baroque masterpiece, fully based on the proof, a document requiring commitment to get to the end, producing programmes opulently large & full of bi-, tri- & quadrifurcations (& some larger ones), the development of which was kindly displayed in this thread, allowing members to assist & critique.
Larger numbers are dealt with in respectably short times.

Which should win a prize?

No time limit was set for the competition, so perhaps other members will contribute more solutions, accordingly competition stays open for another week.

Indeed, 3298 has hinted that he will produce a solution - another approach to the problem would be interesting.