The idea of local mending is introduced in this work: https://arxiv.org/abs/2102.08703
The {1,3,4}-orientation problem is defined in this work: https://arxiv.org/abs/1702.05456
This program is a simple computational proof that shows that {1,3,4}-orientations are locally mendable. More precisely, given any partial solution, one can "patch" any hole by orienting edges within the subgraph induced by a 3 × 3 square.
To try it out, simply run:
./mending-134-orientations.py
The program will simply check each possible scenario: after deleting the edges within a 3 × 3 square, what are the possible indegrees of the 8 boundary nodes; there are 1296 cases to check. The program will find a feasible orientation for each case, and it will also print out a solution for each case.
The file mending-134-orientations.txt shows what the output will look like.