### Separate constraints from their consequences

A constraint states something additional about the source packet. A consequence follows once the existing constraints and construction rules are supplied. This distinction matters because a compact family can produce many exact equations from relatively few relationships.

For example, the selected Covenant claim list has nine equations but only eight independent rows when its source quantities are treated as variable. One household-middle equality follows from the second 147 rail, equal lifespans, the twin death arms and Joseph’s double span. It adds no further condition after those are retained.

The count also depends on which values are already fixed. The centred 147–161–175 progression and the Priestly completion of 161 to 175 are distinct equations while the relevant lifespans vary. Once the source 147 and 175 are supplied, either radius condition implies the other.

Even prominent pattern totals leave some source data unidentified. Formal sensitivity calculations can change local ages while preserving those selected totals. These directions demonstrate a limit of the pattern description; they are not admitted chronological alternatives.

Accordingly, algebraic rank explains information requirements rather than probability or historical independence. The useful result is a dependency map: what is supplied, what is generated automatically, and which further joins require an additional source relationship.

*Sources:* C1039; C1042–C1047; C1053–C1057; File60 §§2–6; File61 §§6–8.

*Research record:* C1039, C1042–C1047, C1053–C1057.