continu.ax

Between one point and the next, there is always room for another breath.

axiom i · no gap survives attention

the axiom

Continuity begins as restraint: a refusal to leap, a discipline of touching every value on the way through.

A line is not drawn. It is remembered without interruption.

construction α

Every proof is a current; every current chooses the long way around the stone.

construction β
lemma

What seems discrete is often only an instrument panel: plates separated by luminous seams, the ocean continuous behind them.

definition · ε follows δ into the dark

the rupture

Assume a jump.

For 800 milliseconds the argument fractures, coral light overruns the glass, then the line repairs itself.

The discontinuity arrives as noise. It leaves as evidence.

therefore

The modules converge. The particles dim. The axis holds its lavender pulse.

Continuity is proven when nothing needs to be crossed.