Resolution & grid properties

LocateTile level L partitions the world into a uniform 2^L × 2^L grid.

Angular dimensions

• Longitude span is 360°
• Latitude span is 180°

So each tile has:

• width: 360° / 2^L
• height: 180° / 2^L

Approximate linear dimensions

The table below includes approximate linear sizes computed using a WGS‑84 equatorial radius for the east–west size at the equator, and a half-circumference for north–south size.

These are approximate linear distances intended for intuition. LocateTile itself is defined in geodetic degrees with the v1 boundary semantics.

Table (levels 0–16)

Level	Tiles per axis	Total tiles	Tile width (deg)	Tile height (deg)	Width @ equator (km)	Height (km)	Max error radius (km)
0	1	1	360.000000	180.000000	40075.017	20037.508	22402.615
1	2	4	180.000000	90.000000	20037.508	10018.754	11201.308
2	4	16	90.000000	45.000000	10018.754	5009.377	5600.654
3	8	64	45.000000	22.500000	5009.377	2504.689	2800.327
4	16	256	22.500000	11.250000	2504.689	1252.344	1400.163
5	32	1024	11.250000	5.625000	1252.344	626.172	700.082
6	64	4096	5.625000	2.812500	626.172	313.086	350.041
7	128	16384	2.812500	1.406250	313.086	156.543	175.020
8	256	65536	1.406250	0.703125	156.543	78.272	87.510
9	512	262144	0.703125	0.351562	78.272	39.136	43.755
10	1024	1048576	0.351562	0.175781	39.136	19.568	21.878
11	2048	4194304	0.175781	0.087891	19.568	9.784	10.939
12	4096	16777216	0.087891	0.043945	9.784	4.892	5.469
13	8192	67108864	0.043945	0.021973	4.892	2.446	2.735
14	16384	268435456	0.021973	0.010986	2.446	1.223	1.367
15	32768	1073741824	0.010986	0.005493	1.223	0.611	0.684
16	65536	4294967296	0.005493	0.002747	0.611	0.306	0.342

Choosing a level

• Higher level → smaller tiles → higher spatial precision
• Higher level may also reduce privacy (less ambiguity within a tile)
• In ZK settings, higher level can increase constraint costs if region compilation expands tile counts

For protocol use, treat level as part of the execution format and bind it in transcripts/manifests.