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The crux is all about getting off of the ground, and while there appear to be several ways to do this, none seemed easy. The route is height-dependent (to reach the first hold) and also weight-dependent (to pull up on the first hold).
With a foot on the rock behind you, and hands on the good slopers right of the crack, reach up into a little seam in the offset and get into it. Match hands and shoot for the obvious "jug" at the top of the crack. I found a few consecutive heal-hooks in slopers to the right to be key. YMMV. Once on the jug, protect again and climb up into a crack on vertical rock to low angle stone- then make your way up and over to join "Inner Sanctum."
Arrive at the Upper South face of the 3rd Flatiron in the vicinity of the "S.W. Chimney" and "S. Chimney". Just downhill from the SW chimney, perhaps 50 meters and just 15 meters right of the pocketed dihedral that is the start of the South Chimney, there is a shallow, blocky, left-facing dihedral starting at the ground and rising up over a lower angle section to a right-facing steep corner. This is the start of "Inner Sanctum." Just right of this is the offset overhanging seam and flake start to "Thin Crack" which after the initial steep section (a few meters) goes up vertical rock for a total of 20 meters and then joins "Inner Sanctum"
Wisdom is required in placing pro on this route- be mindful that the starting flake may be questionable for smaller pieces and stick a fat one behind it... After that, take a standard light rack to 3".
I was able to "toss" a stopper into the crack from below and clip it before climbing the route, and then shot directly for the first jug before placing more protection.