Rectangle Decomposition

Multiple independently changing histories cannot be projected into one row without temporal alignment.

An entity can have many independently historized attributes stored as attribute rows. Each attribute can have its own valid-time and visible-time history.

When independent histories are combined, simple joins can create overlapping combinations that never existed as a real business state.

When those attributes are projected into one reporting row, the result needs one shared bitemporal interval. Without decomposition, the output can contain overlapping or ambiguous historical states.

Two independently historized attributes are decomposed into stable bitemporal rectangles.

Turning independent attribute histories into one consistent bitemporal representation.

Rectangle decomposition resolves independently historized attributes into stable bitemporal regions.

Instead of joining overlapping histories directly, the pattern extracts real temporal boundaries, creates atomic rectangles and assigns one resolved attribute combination to each region.

The result is a structure that can be validated, queried and consumed by reporting systems without ambiguous historical states.

Analyze this Rectangle Decomposition example

Use these sample target tables to test the validator:

1. Copy one of the target tables below.
2. Start an investigation with this example data.
3. Paste the copied table as your target output.
4. Check whether overlapping attribute projections were decomposed.

entity_id,valid_from,valid_to,visible_from,visible_to,risk_code,coverage_code,decomposition_status
P1,2024-01-01,2024-03-31,2024-01-01,9999-12-31,R1,C1,decomposed
P1,2024-04-01,2024-06-30,2024-01-01,9999-12-31,R2,C2,decomposed
P1,2024-07-01,2024-12-31,2024-01-01,9999-12-31,R2,C2,decomposed

entity_id,valid_from,valid_to,visible_from,visible_to,risk_code,coverage_code,decomposition_status
P1,2024-01-01,2024-06-30,2024-01-01,9999-12-31,R1,C1,not_decomposed
P1,2024-04-01,2024-12-31,2024-01-01,9999-12-31,R2,C2,not_decomposed

Independent attributes create independent temporal boundaries.

Different source systems capture changes at different moments. Each attribute therefore represents a partial view of the same entity with its own valid-time and visible-time history.

When these histories are combined directly, overlapping projections can create combinations that never existed as a real business state.

Rectangle Decomposition reconciles these independent histories by creating deterministic temporal regions with one resolved attribute combination per region.

Validate that the projected output is bitemporally stable.

Rectangle Decomposition turns independent attribute history into one reportable history.

Without Rectangle Decomposition, the same entity and reporting date can produce multiple possible attribute combinations.

With decomposition, each output row represents one entity, one bitemporal rectangle and one stable historical truth.

How this pattern relates to other temporal models

Rectangle decomposition does not replace temporal models. It prepares complex histories by resolving overlapping temporal regions before reporting and analytical models consume the data.

This pattern is especially useful when corrections arrive frequently, attributes change independently or reporting requires one consistent historical truth.