# Decompose the original overlap error by logical cell identity

Registered after the two native horizons and original comparisons complete,
before computing this decomposition. Both time pairs pass; same-dx field
comparison fails. At200us original displacement RMS difference~25.11nm,
reference~45.7nm; only~1.69%of its squared difference is in x<200um.
This differs from the old coarser-background cases (~65-67%in that region).
Do not assume identical causes or divide55%by96%to claim causal attribution.

Use the already verified INITIAL logical map, without changing any node or
cell. At10/50/200us, retain the original moving-cell overlap pairs/areas.
Partition the full squared difference numerator into pairs with corresponding
logical identity and pairs with different identities. Their sum must reproduce
the exact original numerator; report each area and squared-error fraction.
Use the unchanged FULL denominator for component ratios and unchanged FULL
10%gate. This is not a restricted easier pass criterion.

Separately compare displacement along logically corresponding material-node
trajectories, weighting by reference initial film-cell area. This is a different
diagnostic (different initial sample locations and cell masses), not continuum
truth, not the original Eulerian overlap criterion, and never an alternative
qualification. Report it only to distinguish trajectory sensitivity from
discontinuous cell-field representation effects.

This decomposition can locate how an overlap norm arises; it cannot prove
physical continuum accuracy, erase undersampling of sharp fields or establish
that the actual coarser-background error is a representation artefact.