The source controls which constructions belong to a family
A common mathematical rule becomes a chronological explanation when the source also supplies its permitted inputs, order, and scope. The SP cap uses the native G2 birth chain, its selected Flood boundary, and explicitly qualified lifespan counts. The full-430 comparison moves births and Flood together by 215 years, preserving every capacity. Local Noah and Shem counting alternatives preserve the same ancestral Flood distance; they do not create companion birth positions throughout the genealogy.
These distinctions keep the wider family model interpretable. Cainan's admitted insertion contributes 130 in a Regular chain and 460 in a Cumulative chain because the two constructions measure different parts of his row. Likewise, an inclusive SP cap count does not become an ordinary elapsed lifespan merely because the numbers enter a shared formula. Current source selections also retain main LXX Lamech 182/753 and official SP Terah 145; earlier summaries or comparison overlays do not silently replace them.
Formal sensitivity calculations show how a construction would respond to changed inputs, but they do not authorize those changes as textual variants. The forward cap reconstruction explains consequences of a declared source model. Its conditional inverse identifies recoverable parameters. Neither establishes a sequence of ancient revisions. This separation allows mathematical compatibility, transmission history, and the Strategy's interpretive premise to remain distinct.
Sources: File18 §1.3, §3, active state and frame conversion, §3.1, §3.1.3, §4.1, §6C; Research Strategy §§1–2, §5, Stages A, C and H, §6.
Research record: C743–C748, C787–C788, C905, C953, C974–C977, C983.