05/11/17 tough puzzle from sudoku.com.au

A complete proof

1) First eliminations : [a5=8%cell, i5=7%cell, i3=9%col, i1=4%col, i8=6%col, g3=6%col, g2=5%col, h3=7%cell, g5=1%col, c8=1%col, h4=2%block, h6=5%col, a6=6%cell, a4=5%cell, e4=6%col, d7=6%col, b1=6%col, b3=2%block, e2=9%row, e9=4%col, h7=4%col, h9=9%col, h8=8%col, e8=2%cell, e6=8%col, i6=3%cell, i4=8%cell, e1=1%col, h2=1%col, h1=3%col, c1=5%cell, d3=5%col] lead to 51 filled cells.

2) Look at only possibles a7=3,a7=2 in their cell. Whether a7=2 (in which case g7=3%cell) or a7=3, in both cases, we have no more {c7=3, f7=3}. Now easy fillings up to 53 filled cells. (If needed, c2=3%col, a2=7%cell)

3) Look at only possibles d2=4,b2=4 in their row. Whether b2=4 (in which case c5=4%col) or d2=4, in both cases, we have no more {d5=4}.
Now easy fillings up to 81 filled cells. (If needed, d5=2%cell, f1=2%col, f6=7%col, d6=1%cell, b4=1%col, b6=9%cell, c5=4%cell, f5=9%cell, c3=8%cell, c7=9%cell, f3=4%cell, f4=3%cell, f8=5%cell, b8=7%cell, b9=8%cell, f9=1%cell, d9=3%cell, a9=2%cell, g9=7%cell, g8=3%cell, g7=2%cell, f7=8%cell, b7=5%cell, a7=3%cell, d4=4%cell, d2=8%cell, b2=4%cell, d1=7%col)

Short hints for a proof

4-FC needed here:

1) easy to 51 filled.
2) looking at 23 in a7g7, eliminate some, then easy to 53 filled.
3) looking at 4 in R2, eliminate d5=4. Then easy to unique solution.

Forbidding-chain-like proof

4-FC needed here :

around 51 filled : (a7=3)==(a7=2)--(g7=2)==(g7=3) forbids {c7=3, f7=3}
around 53 filled : (d2=4)==(b2=4)--(c3=4)==(c5=4) forbids {d5=4}

Equivalence with 2005/09/30

Now applying the same "dictionary" (renaming numbers, replacing cells) to proof of 05/09/30 you will mechanically get a proof of today's. E.g. first filled cell in 05/09/30 was e7=9%cell; in today's it becomes a5=8%cell. Try it ! Or see the method explained step by step on 10/08 example.
In case that you be lazy enough not to find it by yourself, see hints for today's proof (automatically derived from 05/09/30's proof).