A phase index is a small exact ledger, not a full reconstruction. 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 index can pin position

The phase index is 2 per metre. Positions 0, 1, 2 metres give ticks 0, 2, 4.

22=42\cdot2=4
MRI encodingA magnetic gradient makes position-specific frequency addresses.fieldfreqfieldfreqphasefieldfreqphasezero phase

This is an address ledger, not reconstruction

The checked claim is the position-to-phase ledger. Fourier reconstruction stays outside this toy model.

address first, reconstruction later\text{address first, reconstruction later}
MRI encodingA magnetic gradient makes position-specific frequency addresses.fieldfreqfieldfreqphasefieldfreqphasezero phase