Range measured: longest strictly-ascending u32 run (delta under 65536) in each
level's collision payload, levels 0 to 5.
Level 4 is the clean case. Grid 3x25, payload 2660608, and at payload +5932 a
run of 19 entries whose values are all inside the payload, starting at 146012:
deltas 204, 212, 216, 224, 224, 228, 228
The deltas grow monotonically, which is the signature of a prefix sum over
records of increasing size -- what a per-cell offset table looks like when cell
contents vary.
The others are not:
level 0 11x33 +21232 17 8193, 24575, 8192, 8192 multiples of 8192,
coincidental on
dense data
level 1 24x16 +41452 29 32771, 57339, 24575 wild, no trend
level 2 1x53 +13752 49 24, 64, 396, 104 in-region but
irregular
level 3 19x31 +667152 18 769, 257, 257, 257 values ~5.2e8, far
outside the payload
level 4 3x25 +5932 19 204, 212, 216, 224 growing, in-region
Only level 4's run has both properties a prefix sum needs: values inside the
payload, and deltas that grow.
What this does not give: level 4's run is 19 entries against 75 grid cells, so
it is not one offset per cell -- either most cells share an offset, are empty,
or the table covers something other than the grid. Nothing measured picks between
those.
Next to check: whether 19 relates to 3x25 by any arithmetic, and whether the
same offset at +5932 exists in other levels at a position given by their leading
counts. Neither has been tried.
ReaperOfVeriod
b66e77855c