Explorer

Watch the K4 control grammar come into existence.

This path starts with a bare graph and earns each word: incidence, conservation, cycle, cut, orthogonality, geometry, field, symmetry, and control. The field visualizers become evidence later, not the first thing you are asked to trust.

Lesson frameone concept, one claim, one interaction

Static saga lenses are preserved as an atlas after the derivation.

step 1 of 10[A]algebraic

Four points, six connections

What can K4 say before geometry or physics exists?

K4 has 4 vertices and 6 oriented edges.
E01E02E03E12E13E230123
vertices4
connections6
physical changenone

The arrow is a sign convention. Reversing it changes how a signed edge value is recorded, but the connection itself is unchanged.

E01 value = + E01 value

algebraic: Graph identity. No geometry or field model is needed for this step.

Earned concept

An oriented graph can encode relationships before geometry or physics exists.