# From source rows to the SP equal-gain rectangle

The Strategy’s rectangle now connects directly to the reconstructed genealogies. The same local operations that explain the SP Regular and Cumulative differences supply its two measured radii.

| Stage | Regular route | Cumulative route |
|---|---|---|
| MT supplied baseline | Creation4114 | Completion14004 |
| Pre-Flood source change | Begetting ages reduce the chain by350 | Shared Flood cap removes488 |
| Post-Flood source change | Six centuries plus half-century add650 | Eber and official Terah remove120 |
| Declared placement | Native SP frame subtracts215 | Completion endpoint remains the selected type |
| Resulting endpoint |4199 |13396 |
| Source opening | Seven-year wrapper gives4206 | Ten-year decade gives13406 |
| Distance to Exodus1446 |2760=69×40 |11960=299×40 |
| Declared Key |70/69 gives2800 |300/299 gives12000 |
| Generated target |1406 |1406 |

The cap’s488 is no longer an unexplained aggregate: capacity loss exceeds baseline slack at Jared, Methuselah and Lamech by115,249 and124. The separate120 comes from two post-Flood lifespan changes. On the Regular side, the located late-age losses sum to350, while the shared post-Flood begetting operations sum to650.

Both Keys add40, preserving the difference9200; its25/23 expansion is10000. These values were already established. The new gain is their source-mechanism provenance, not an additional independent numerical occurrence.

The whole equality still requires the source-appointed frames and node roles. Before the seven- and ten-year openings are included, the equal-gain balance3C−13R is61. Their contributions remove that61. The cap and row laws therefore explain the genealogical components; they do not independently generate the wrappers, the MT absolute baselines, or the historical role of Exodus1446.

This provides a useful model for the wider project: derive as much of the input field as the sources permit, show exactly how it enters a common operator, and keep the remaining source choices visible.