Number, glyph, lane

Eight digits, four poles. Each digit is a station of a single octave, and each pair of digits names an interval on it. Nothing here is positional in the decimal sense: the pair is a range, and ranges compose by intersection and union rather than by carry.

The four poles I, E, O, A recur across the whole ecosystem: they are the truth values of Logecs, the inner/outer channels of Laegna Physics, and the affirm/negate structure of spiritual reasoning. Number, logic and meaning share one skeleton — that is the point of the system.

The base glyphs are not arbitrary strokes. Each is the octahedral square with a number of its folds inked: the outline, the two axes, the two diagonals, the two arcs, the centre. Writing a Laegna letter is drawing a state of the quilt.

Image sources live in LaegnaBaseAlphabet; the text-based source is at laegna.notaku.site/laegna-base-alphabet.

Log space, linear space and exponential space are not three worlds; they are three tunings of one lane. LaeLane is the operator that straightens them, so that a step of size one means the same kind of step at every magnitude. Straighten the lane and you straighten the ball: the collapsing sphere becomes addressable, and infinity becomes walkable.

Every number carries a curve. In LaeLane a value is never only a position — it is a position plus the bend of the lane it sits on, which is what lets a single coordinate mean "here, at this magnitude, in this regime".

The LaneDatums tables give the coordinate convention: a quilt cell, its spherical bearing, and the Laegna slice-lane that names it. Because the quilt cell and the sphere triangle are in bijection, a lane label is simultaneously a texture address and a direction in space.