qector-space-timelisted

# QECTOR Space-Time and Streaming Source of authority: v1.0.0 reference manual, chapter 10. ## Why space-time Physical measurements are noisy, so a detector event must be attributable either to a data fault or to a measurement fault. The space-time approach builds a `(2+1)`-dimensional detector lattice over `T` rounds and solves a single matching problem on it, with anisotropic edge weights. ## Detector formulation (manual 10.1) d_{c,t} = s_{c,t} xor s_{c,t-1} - A data error in round `t` flips the same checks in round `t` and `t+1`, producing two detection events in consecutive layers. - A measurement error flips one detector in a single layer. The lifted matrix `H_ST` contains data columns and measurement columns, with: - **Spatial weights** derived from the data-error probability. - **Temporal weights** derived from the measurement-error probability. ## Theorem 13 (space-time lifting faithfulness, manual 10.2) > Let `H_ST` be the lifted parity-check matrix with data and > measurement columns. A correction `c_ST` whose boundary in the > detector graph equals `d` satisfies `H_ST c_ST = d (mod 2)`; > projecting the measurement columns away yields a spatial > correction whose syndrome differs from the final raw round only > by the final-round measurement error term. The proof sketch: the lifted matrix is a chain complex whose boundary operator applies the spatial syndrome to each time layer and the difference operator across layers. Any matching whose paths p