Source choices behind the SP Flood construction

The Flood-cap model now has a clearer source explanation. Its age input is not an unstructured list: the supplied sources relate Adam’s130 to the two65 ages, preserve the first-five460 span, and explicitly align the MT/LXX Methuselah death with the Flood. Those relations connect the genealogy’s internal age measurements to the lifespan quantities used by the cap.

They do not determine every number. After the three source age relations are retained, six age freedoms remain. Holding the three clipped-life measurements gives three more conditions. One shared age scale and two interior ages then reconstruct the complete nine-age packet. Using the output of the cap to recover its own input is consistency, not an additional independent constraint.

The five-year grid and descending first-five order leave ten allocations for the three interior ages. Retaining the actual Seth105, Enosh90 or Kenan70 separately leaves2,3 or5 possibilities. For this actual tuple the grid does not reduce the retained-coordinate count: both this grid comparison and the rational model still use the shared65 scale plus two interior ages. This clarifies C1139’s broad wording about different identification costs.

The strongest new local relation is the capacity/slack explanation. MT and SP source birth intervals differ at the located rows by100,120 and130 completed units. Their ordered accumulation lowers capacities by350,250 and130 at the relevant stages. A life is shortened exactly where that loss exceeds the original slack. This generates Jared115, Methuselah249 and Lamech124 without separate fitted lifespan adjustments.

The MT capacities in that comparison use the same inclusive capacity convention as the SP calculation; they do not change ordinary MT death counting. Methuselah’s ordinary MT death-at-Flood relation gives969 from187+182+600. Comparing the SP path adds one inclusive unit, explaining why its lifespan reduction is249 rather than250.

The resulting grammar has two parts: source-labelled local row changes create an ordered capacity field, and the minimum rule determines which lifespan changes follow. The next useful extension is to post-Flood rows, where different preserved components can be identified directly. The sources still supply exact interior ages and selected baseline biographies; this study has not established their historical origin.