For the thing about public proof, I'd go with the facts: they're legitimate times. I get that there are no solutions mentioned, but the times are legit.

What facts?

A quick update: I've gotten into contact with Archanfel, and he has given me the solutions to the improved puzzles. However, it seems that the 6-9 puzzle solution does not work (it eventually leads to the character hitting a wall). Currently waiting on Archanfel to clarify this oddity.

Archanfel got back to me, and it turns out the puzzles they have on their site are mirrored vertically compared to the GB version, so that was why their solutions were not working right away. Fixing that, I now have a movie implemented both new solutions, movie file to replace this submission: http://tasvideos.org/userfiles/info/75103587700952367

Just for case if someone would like to also update TAS for sequel of this game (http://tasvideos.org/3620M.html) I found new better solution for 08-06 level. Here it is: Solution: 260 Moves, 90 Pushes* uuuuullDDllllllUdrUdrUdrUdrDDllUdrUruUdrrDDLUruLUrurrd LrdddddddddllllllllllUUrrDurDurDurDuruuLLDurUdDrdDlllluUURDluUU RDuUrrrrrdDDDDLDlllllullUURDldRDluuuURlURlUUUdRUdDDDDDldddll uuuuuuuuuRldRldRldRldRldRldRldRDldRurrrrrrrruruLruLUUUruUrrdLrd LrdLrdLrdLrdLrdLDrdL *Flip vertically if necessary

I don't know if I'm doing this correctly, but I see that this movie is longer if I only compare gameplay durations, both with and without lag. Per-level differences are all over the place: sometimes much longer, sometimes much shorter.

----------------------------
|      |   lag   | lagless |
----------------------------
| old  | 1014230 |  375224 |
| new  | 1014714 |  375787 |
| diff |    +484 |    +563 |
----------------------------

Download leveltimes.lua

Language: lua
gameplay = false
lastgameplay = false
timer = 0
while true do
	local first  = memory.readbyte(0x385, "WRAM")
	local second = memory.readbyte(0x387, "WRAM")	
	gameplay = first == 3 and second == 3	
	if gameplay and not lastgameplay then
		timer = 0
	elseif gameplay and lastgameplay and not emu.islagged() then
		timer = timer + 1
	elseif lastgameplay and not gameplay then
		print(timer)
	end	
	lastgameplay = gameplay	
	emu.frameadvance()
end

Figuring out if something is a legitimate improvement or not is not only the judge's job, but also something the author needs to prove. Reapplying the same strats on the old publication is a sensible way to check improvement validity, but not when there's 100 levels and level durations differ in both directions. I can't do this automatically, and I can't do this manually. I can't do this partially either, because improvement is not uniform here: if it makes some levels longer in the old emulator version too, I wouldn't know until I tweak and check them all. On top of that, more accuracy leading to more lag doesn't automatically mean solutions for less accurate version also make sense for more accurate version even if they take longer. Maybe more accurate version needs different solutions that also save some lag. Maybe those new solutions cause too much lag compared to old solutions. I'm leaning towards rejecting this movie until times become more comparable. Easiest way out is incorporating those strats into the old movie, checking if they save time in every level they appear in, and submitting that. Until then, it's unclear if the new methods are still more optimal with more accurate emulation.

Does this movie sync on real console?