Why the regular kernel has two layers

The Strategy’s compact1250/650/405 formulas summarize two different source constructions.

First, the ordered MT–LXX row differences generate a complete Regular comparison field. Six pre-Flood century changes and six post-Flood century changes, plus Nahor’s half-century, give1250 at Creation. The post-Flood contributions alone give the650 plateau. Keeping their positions reconstructs every intermediate boundary. Native Cainan adds130 upstream, producing1380 and780 in the native comparison.

Second, the permitted Terah60, Cainan130 and Sojourn215 choices generate a finite placement field. Its offsets are0,60,130,190,215,275,345,405. Their gaps are60|70|60|25|60|70|60. The190 Terah/Cainan field and275 Terah/Sojourn field are different restrictions of this same construction.

The compact fivefold relation joins these layers: 12.5u=5(C+2T) and6.5u=5C. It holds exactly when C=13u/10 and T=3u/5. The source values u100,C130,T60 satisfy those conditions. The row support pattern does not itself generate the ratios; they are observed cross-source scale relations. The independently supplied Sojourn215 is not constrained by them.

Likewise,1250/650 can be written950±300. The midpoint equals Noah’s separately supplied lifespan950, but this rewriting does not replace the ordered row explanation.

SP retains its own mechanism. Its post-Flood650 is reduced by100 at Jared,120 at Methuselah and130 completed units at Lamech, giving the300 Creation difference. The counted53rd year contributes52 completed units; the nominal129 difference receives that one-unit correction once.

The resulting explanation is constructive and bounded: source row changes generate the baseline comparison, finite source choices generate its allowed placements, and the fivefold formula expresses the received calibration between the two. It does not establish a historical rule that created the ancestral ages from Terah or Cainan.