Alright - in fact, that "floating remnant" is simply what is left of the remaining character - just like the rest of the stainless that you see - after the blade is ground.
Here's how I do it, and a bit of my San Mai philosophy:
Making Stainless/Simple Carbon San Mai is a lot like trying to glue a Gummy Bear to an ice cube.
They're both happy by themselves, and would rather not be connected.
In fact, every possible variable is against that happening.
I've seen some guys start with their three components so close to their final thickness/dimension that once they get their initial weld, they do very little more forging.
I am of the opposite inclination - I want my San Mai billet to remain at welding heat as long as possible and spend as much time under the press and power hammer as I can get it to do so.
So, I start with a 3/8" thick 1095 core and .280" - well over a 1/4" - stainless jacket on each side.
When getting my initial weld - which I do twice and which must be in an oxygen free atmosphere - I soak for nearly 1/2 hour. After the weld, I want as much carbon and alloy migration as feasible. I want those components to become ONE!
And they do.
I've tried everything I can possibly do to destroy one of these blades and I can't get them to fail.
I draw out my billet almost to my final thickness incrementally by about .020" per reduction with flat dies in my press.
On the next to last pass I reduce the steel with round drawing dies. Those create those undulations you see along the bottom edge.
Often I have referred to this San Mai as a really good demonstration of what is happening inside our steel when we use drawing dies.
Them, when I flat grind it, we get to see the highs and lows of the drawing dies.
That remnant you refer to out there at the end is simply where the 420 SS was pushed into the 1095 with the drawing die. When I did the flat grind and got thinner along the distal taper, I sheared off the spot between the draw bites that was more 1095 than 420.
So, when some guys make their San Mai and start at a dimension that is already thin and near their final thickness, they don't have the time/mass to do drawing functions, so they saw-cut into the edge a lot like when making ladder Damascus.
There are things I could do with a ball peen hammer to put in more activity along the line.
Truth is, I just don't see any other San Mai out there quite like mine, so as long as it remains recognizable as mine, I think I'll just leave it like it is.