Geometry and Phase Ledgers

Phase Encode Row Ledger

position to phase

A phase-encode row is a deterministic position ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A phase scale turns position into phase

The training phase scale is 2 per metre. Each row position is multiplied by that scale.

ϕ/x=2 per metre\phi/x=2\ \text{per metre}
Phase encodingA per-metre training index maps position to dimensionless phase.phasephasephasezero phase

Four rows make four exact phase values

Positions 0 m, 1 m, 2 m, and 3 m give phases 0, 2, 4, and 6.

ϕ=0,2,4,6\phi=0,2,4,6
Phase encodingA per-metre training index maps position to dimensionless phase.phasephasephasezero phase