What the common explanation achieves
The work now gives a connected construction for several families that previously appeared as separate numerical displays. Two local row changes explain why Regular and Cumulative chronology respond differently. Ordered accumulation carries them into complete fields. SP birth capacities connect its shorter birth path to its lifespan reductions. Row rounding generates the Moses blocks and cycles; the reconstructed coordinates supply the Regular duration words in File52c. Anchored Keys connect declared measures. Covenant joins arise from local paths, repeated lifespans and one further 147 relation. Lists and NT show which parts of ordered measurement survive a change of labels or grouping.
The compact presentation has four parts: a primitive-data register, an operation inventory, a relation ledger and a complete-family reconstruction ledger. “Compact” here means that the same rules explain multiple outputs. It is not a proof that no smaller source model exists. Source ages, named supports, cuts, terminals and calibration choices remain visible in the registers.
Some striking equalities are now accounted for as consequences of one construction. The three Moses cycles share one path. The SP rectangle’s equal gains follow from its two selected radii. The Covenant’s first two clutch joins follow from the shift definition and equal lifespans, while the third uses a further source relation. The NT’s two Key equations express one scale relation. These distinctions strengthen the explanation by identifying the information each family actually uses.
The inherited Sothic and BJ results retain their place in the larger project. Shared operation grammar is broader than exact common calibration: the Sothic factor H differs from the exact-K 365-day extension G. The SP-derived BJ bridge is not an independent witness. The prior bounded symmetry and comparison results remain established at their declared scope; no remote SKL source-chain theorem or historical priority is added here.
The next discriminating research question is whether a frozen subset of this grammar can reconstruct another complete, source-appointed family with fewer fresh choices than a direct restatement of its data. Before that test, choose the family and permitted inputs, identify anything already used in fitting, and specify every expected output. A known family can still challenge transfer, but cannot be represented as untouched evidence.
The present mathematical result is already substantial: it explains how the selected chronological families fit together through shared source information, different measurements, and explicitly connected operations. Historical transmission and theological interpretation can now be discussed against that concrete structure.