Hints:
======
Just two presently:

1) Repeatedly apply these rules:
p+p=p | 2+3=5 2+5=7 2+7=9
p+p=c | 2+7=9 3+5=8 (2+2=4, 3+3=6)
p+c=p | 2+1=3 3+4=7
p+c=c | 2+4=6 2+6=8 3+1=4 3+6=9 5+1=6 5+4=9
c+c=p | 1+4=5 1+6=7 (1+1=2, 4+4=8)
c+c=c | 1+8=9

2) Repeatedly exclude now-impossible numbers from cells

Sorry, but I'm feeling a bit lazy. I created a v1 of the puzzle,
solved it, felt it was a bit easy, removed a bit of the furniture that
I felt was too helpful, and then solved that new version. I don't
want to now have to solve it a third time, noting how I did it.

Let's just say that the interaction between arrows in boxes 5 and 2 is
a good starting point, but box 9's helps out early on too. The p+c=p rule
is particularly useful.


Proof of Uniqueness:
https://sigh.github.io/Interactive-Sudoku-Solver/index.html?q=.%7ER6C1_2_3_5_7%7ER7C2_2_3_5_7%7ER8C3_2_3_5_7%7ER9C4_2_3_5_7%7ER8C5_2_3_5_7%7ER7C6_2_3_5_7%7ER6C7_2_3_5_7%7ER5C8_2_3_5_7%7ER4C9_2_3_5_7%7ER3C8_2_3_5_7%7ER2C7_2_3_5_7%7ER1C6_2_3_5_7%7ER2C5_2_3_5_7%7ER3C4_2_3_5_7%7ER4C3_2_3_5_7%7ER5C2_2_3_5_7%7ER4C4_2_3_5_7%7ER4C6_2_3_5_7%7ER6C6_2_3_5_7%7ER6C4_2_3_5_7.Arrow%7ER4C3%7ER3C4%7ER2C4.Arrow%7ER4C3%7ER3C2%7ER3C1.Arrow%7ER4C3%7ER5C3%7ER6C4.Arrow%7ER8C4%7ER7C5%7ER6C5.Arrow%7ER8C4%7ER9C5%7ER9C6.Arrow%7ER8C4%7ER8C3%7ER9C2.Arrow%7ER3C7%7ER4C6%7ER4C5.Arrow%7ER3C7%7ER2C7%7ER1C8.Arrow%7ER3C7%7ER3C8%7ER4C9.Arrow%7ER6C6%7ER5C7%7ER4C7.Arrow%7ER6C6%7ER7C7%7ER7C8.Arrow%7ER2C5%7ER1C6%7ER1C7.Arrow%7ER7C2%7ER6C1%7ER5C1