Noah subsection

Noah's lifespan explains a second common refinement

The cumulative extension uses Noah's 950-year lifespan, followed by Shem's 600-year lifespan in the serial stack. These common source rows give the original word

where $a$ runs from held Conquest to the Flood seam and $c$ is the remaining prefix from cumulative Noah to Creation or accepted Fall.

The MT nodes are explicit in File51a; the LXX and SP nodes follow the same cumulative rule from their declared Flood seams. The source lives remain cumulative measurements, distinct from the Regular Noah age of 600 at the Flood. [File18 §6; File51a §16.2; C1533–C1536]

Retain Flood and Noah but combine the two lives into the original 1550 interval. Then restore the Shem boundary and reverse the two original lives separately:

Thus the explicit life division lowers the inverse head by 4320 in every tradition:

Every other segment remains fixed, so the same local split explains all three changes. Adding the Nativity leg raises every listed head by 2700 and preserves the comparison. Noah-only and Flood-plus-Noah also agree in all three: $I(a+1550)=I(a)+5510$ for the three declared lower legs. Their significant digits add without a carry and remain in the same trailing-zero register. These are specific additive cases of an operation that is not generally additive. [C1541–C1544]

The differing starting heads have a source explanation. Splitting 1550 from the primary upper leg adds 990 in MT, 7020 in LXX and zero in SP. Subtracting the common 4320 gives the fully refined changes from the primary heads: −3330, +2700 and −4320. The SP primary, Shem-only, Noah-only, Flood-plus-Shem and Flood-plus-Noah constructions therefore share 11416; separately retaining both lives exposes the 4320 change. Its previously established intact Shem edge remains intact, while the extension through Noah changes the rest of the upper branch. [C1545–C1552]

The large LXX response comes from a small, located source difference. MT and LXX share the first eight rounded pre-Noah lives; selected Lamech rounds to 775 in MT and 755 in LXX. Hence their prefixes are 7620 and 7600. Placeholder-preserving reversal gives 2670 and 6700, so the 20-year source difference crosses a decimal register and becomes a 4030-year inverse-prefix difference. Their lower Noah branches retain a 910-year separation; together these explain the 4940-year separation of their Noah-partition heads. No fitted head adjustment is needed. [File18 selected 753 decision; C1535, C1547–C1550]

LXX's fully refined change of +2700 also equals the shared Nativity-stage change. It therefore connects two different constructions at 13636 BC:

The first retains the named Flood, Shem and Noah divisions from Conquest; the second is the accepted primary cumulative spine extended to Nativity. Their internal paths differ, while the source-selected heads agree. MT and SP do not satisfy this particular equality. This is a relation between refinement and completion in the LXX construction, alongside the common 4320 law across all three. [C1553–C1556]

MT's secondary 13016 branch was already established in Files52a–52c. The comparative extension explains the LXX/SP responses and the common local cause; the continuation record supplies all seven named selections of Flood, Shem and Noah for each manuscript.