This proof has been kindly supplied courtesy of Bruno Greco. For more sudoku proofs check out Bruno's Sudoku Proofs.

We expose proof of uniqueness using abbreviated notation suggested by Andrei Zelevinsky

The notation used is as follows:

Cells: a1, a2, ..., i9 (as in chess).

Rows: R1, R2, ..., R9 (bottom to top).

Columns: Ca, Cb, ..., Ci (left to right).

Blocks: Bb2, Bb5, ..., Bh8 (labeled by central cells).

Moves followed by simple comments:

e4=7; (empty comment meaning that the only possibility for e4 is 7).

e4=7 %R; (e4 is the only possibility for 7 in its row R4).

e4=7 %C; (e4 is the only possibility for 7 in its column Ce).

e4=7 %B; (e4 is the only possibility for 7 in its block Be5).

Following simple eliminations.

a3=8%row, b5=8%box, c3=1%row, a2=6%box, c9=6%box, a9=9%box, h3=6%box, i6=6%box, b2=4%row, e2=7%row, f1=9%box, d1=4%box, h8=7%row, e7=2%cell, d7=6%cell, f5=6%box, g5=1%row, i1=1%box, g1=8%box, h1=2%box, d5=2%row, f3=2%box, d3=3%box, e3=5%box, c5=7%row, b1=7%box, c1=3%box, a1=5%box, h5=9%row, c8=4%cell, a6=4%row, f7=4%cell give:

Let us add remaining possibilities in some cells, to find the next steps:

Looking at cells i2 and i7, we see that they must contain 3 and 9, no matter the order. So i8≠3%col. It follows b8=3%row and b7=5%cell;. We're now at (adding again significant remaining possibilities in some cells):

Here, What if e6=1? then a8=1%r, b9=1%c : too much 1's in Bb8. Hence e6=9%.
Please note this is a perfect example of pentagonal configuration
From here, simple eliminations lead to unique solution.
(Details if needed : c4=9%box, d4=5%row, e4=8%box, d9=8%box, i8=8%box, f9=7%box, d6=7%box, g4=7%box, e8=1%box, b9=1%box, b7=5%box, c6=5%box, b8=3%box, a8=2%box, b6=2%box, i4=2%box, h4=4%box, i9=4%box, g6=3%box, i7=3%box, g7=9%box, i2=9%box, f4=3%box, h2=3%box, g2=5%box, h9=5%box, g9=2%box, f6=1%box, a4=1%box).

Remark 1 : I wonder if this puzzle and the 09/18 one are not exactly the same structure (compare the proof of both)... The grid creating program may be lacking imagination...

Remark 2 : We have here a very pure example of pentagonal configuration