Paradigm · Data
Lane Databases
The gosdb "lanes" database stores each Laegna Ten by its axes — UnSignedTen I=1, O=2, A=3, E=4 — and projects every number to X/Y lanes at a radius R. Here that structure is extended into a live mathematical engine: pick any range and watch decimals become Laegna words, two-band binaries, signed values and geometric lane points.
Records32
| # | Laegna | Two-band | Signed | lane x,y |
|---|---|---|---|---|
| 1 | I | 00 | -2 | 42,18 |
| 2 | O | 01 | -1 | 33,33 |
| 3 | A | 10 | +1 | 18,42 |
| 4 | E | 11 | +2 | 0,46 |
| 5 | OI | 01 00 | -6 | 25,45 |
| 6 | OO | 01 01 | -5 | 12,51 |
| 7 | OA | 01 10 | -3 | -2,52 |
| 8 | OE | 01 11 | -2 | -16,49 |
| 9 | AI | 10 00 | +2 | 6,52 |
| 10 | AO | 10 01 | +3 | -8,51 |
| 11 | AA | 10 10 | +5 | -22,47 |
| 12 | AE | 10 11 | +6 | -34,40 |
| 13 | EI | 11 00 | +6 | -14,50 |
| 14 | EO | 11 01 | +7 | -27,44 |
| 15 | EA | 11 10 | +9 | -38,35 |
| 16 | EE | 11 11 | +10 | -46,24 |
| 17 | OII | 01 00 00 | -26 | 18,55 |
| 18 | OIO | 01 00 01 | -25 | 7,58 |
| 19 | OIA | 01 00 10 | -23 | -4,58 |
| 20 | OIE | 01 00 11 | -22 | -15,56 |
| 21 | OOI | 01 01 00 | -22 | 3,58 |
| 22 | OOO | 01 01 01 | -21 | -9,57 |
| 23 | OOA | 01 01 10 | -19 | -19,55 |
| 24 | OOE | 01 01 11 | -18 | -30,50 |
| 25 | OAI | 01 10 00 | -14 | -13,56 |
| 26 | OAO | 01 10 01 | -13 | -24,53 |
| 27 | OAA | 01 10 10 | -11 | -34,47 |
| 28 | OAE | 01 10 11 | -10 | -42,40 |
| 29 | OEI | 01 11 00 | -10 | -28,51 |
| 30 | OEO | 01 11 01 | -9 | -37,44 |
| 31 | OEA | 01 11 10 | -7 | -45,36 |
| 32 | OEE | 01 11 11 | -6 | -51,27 |
Axes
I, O, A, E order the base-4 alphabet (1..4). Two digits give 1..16, three give 1..64 — the exact UnSignedTen table shipped in gosdb.
Signed lanes
Zero is omitted: I=−2, O=−1 fall below, A=+1, E=+2 rise above. Signed and unsigned lanes are two projections of one Ten.
Geometric lanes
Each word maps to a lane (x, y): angle accumulates by digit, radius by depth — the same X/Y lanes gosdb persists per radius R.