Exact rational coordinates — the kernel's only number.

Coordinates appear wherever an anchor references a position rather than an identity: Anchor.Metric intervals, Anchor.Relative offsets, Op.Retime spans, and every Tamale.Warp endpoint. The kernel interpolates and composes those values (Warp.at/2, Warp.compose/2), so the coordinate type must be closed under scaling by rationals — a requirement integers and floats both fail: integers cannot represent frame 3 stretched by 4/3, and floats smear it into rounding dust that no conformance vector can pin.

The kernel's answer is the rational pair {num, den}, normalized so that den > 0 and gcd(|num|, den) == 1. Normalization makes the representation canonical: two equal coordinates are always ==-equal structs of the same shape, so plain term equality is exact equality.

Boundary rules

• Integers are accepted everywhere and promoted to {n, 1}.
• Floats are rejected. cast/1 reports them as {:error, {:invalid_coordinate, value}}; cast!/1 raises. This is the same doctrine as the canonical digest (docs/decisions/0005): normalizing domain floats into exact values — seconds as microseconds, frames as integers — is the channel adapter's job, with a declared resolution.
• Kernel outputs are always normalized rationals.

Wire form

In conformance vectors and any JSON interchange a coordinate is:

• a JSON integer when den == 1 — 4 means {4, 1}
• a "num/den" string otherwise — "4/3" means {4, 3}

Floats are not representable on the wire; decode/1 rejects them.