Overview
========
- 5s, and [46]s, or, better, [DF]s
- Kropke probe
- Start filling the GWs
- Connect letters to numbers
- Speedrun

5s and [DF]s
------------
There's clearly more info in the corners than in row 5, whjich is the only thing that can distinguish N from 10-N, so solve primarily using A-I rather than numbers. If doing that, you can colour, but it's purely cosmetic.
Immediately, the fou 5s can only go in the middle of the horseshoes.
4s and 6s are also restricted, and can't both of the endpoints of the GW. WLOG make r2c2 'D'.
Next to the F and D corner markings you must have A and I along the GW, so corner-mark them too.
Colour the GWs if desired.

Kropke probe
------------
The white kropke between the black one changes parity, so must contain a 3, connecting to a [234]
However, r5c8 can't be a 4 as it's in line with a [DF] pair.
Likewise, r5c7 can't be a 4 as it would connect +3x6X4.
=> row 5 looks like [57]+46]x[23]+[23]x[146]X[469]
=> r6c9 is a 5
=> r[46]c9 is a [46] pair as it must contain a D

Start Filling the GWs
---------------------
Box 9's F is in r7c7, next to an A
Box 8's D is in row 7, as it can't be on row 9, which is a [5F] pair and something that can't be n an X with an F.
=> box 7's D is in r9c3, next to an I
The [BC] pair in box 9 can only sandwich H or I, but I's gone in the row, so r9c9 is H
=> box 3 cans an [HI] pair in column 8, and r2c9 is G, sandwiched by an [AB] pair
=> r8c9 is C and r9c8 is B
=> on teh GW r9c7 is I amd r9c7 is G
Technically, we know r[456]c7 are [BHI], but that could be [289] or [821] - either way, r5c7 is 2
=> Row 5 becomes 5+4x2+3x6X4
=> column 1's 5 is in r4c1 and its D (so 4 or 6) can't be in row 5, so is in r6c1
=> r9c4 is the 5 and r9c5 is the F, pushing row 1's 5 into r1c6
=> row 9 is left with an [AC] pair in r1c[16]
=> r8c6 on the X is [GI]
In box 1, because r1c2 is sandwiched next to a G, it can't be C and we know the A is in row 2, so is the B
=> r1c9 is A and r3c9 is B
=> row 1's F is foreced into r1c4

The X in box 2 is now uniquely specified. It's [BHI] over [ACDG], and the only pair summing to 10 is I/A.
The B in column 1 must be in r7c1
The [GHI] triplet in column 1 makes r3c1 the F, next to an A, resolving the C and G in box 1
=> r9c1 is C, r8c1 is H, r7c2 is G, and r7c3 is A
=> r5c1 is I
=> r9c6 is A connecting to the I on r8c6

Connect letters to numbers
--------------------------
The 4 in row 6 is in box 4 and can only be the D in r6c1 (it can't be an F on the X, as the D would also be on the X)
=> D is 4, A is 1, I is 9, etc.
At this point, I turned the 5 digits into letters, rather than turning all the letters into digits, as going numeric can be done as a final sweep before completion.

Speedrun
--------
r5c3 is now G, r6c3 is B connecting to the H on r6c2, which lets you complete box 4
Column 7's [HI] in box 6 can now be resolved with the I in r6c7 and H in r4c7
=> box 5's I is in r4c4 and its A is in r6c4, resolving the [AG] in box 6
=> The [CF] in row 6 is resolved, as is the H
In box 2, r2c4 is B and r2c6 is H
Likewise, r1c5 is D, resolving the [CD] in box 3, placing the I in r3c8 along the GW, and the H in r1c8
In box 8, r8c4 is G, making r8c5 the G, and r7c[456] is D-H-C, etc, etc, you're home and dry,
Now just replace the letters with numbers.
Ooooh - was that a C in the corner? ;-)

Proof of uniqueness
-------------------
https://sigh.github.io/Interactive-Sudoku-Solver/?q=.Whisper%7E5%7ER3C1%7ER2C1%7ER1C1%7ER1C2%7ER1C3%7ER2C3%7ER3C3.Whisper%7E5%7ER1C7%7ER1C8%7ER1C9%7ER2C9%7ER3C9%7ER3C8%7ER3C7.Whisper%7E5%7ER7C9%7ER8C9%7ER9C9%7ER9C8%7ER9C7%7ER8C7%7ER7C7.Whisper%7E5%7ER9C3%7ER9C2%7ER9C1%7ER8C1%7ER7C1%7ER7C2%7ER7C3.BlackDot%7ER5C8%7ER5C9.BlackDot%7ER5C7%7ER5C6.WhiteDot%7ER5C8%7ER5C7.WhiteDot%7ER5C6%7ER5C5.X%7ER8C6%7ER9C6.X%7ER6C3%7ER6C2.X%7ER5C9%7ER4C9.X%7ER2C5%7ER3C5