04b SP rectangle

The same located changes now supply the SP equal-gain rectangle. Starting with the selected standard MT frames and the 1446 Exodus anchor, the source construction gives two radii:

The Regular line retains the post-Flood additions, pre-Flood shortening, Sojourn choice and seven-year source opening. The Cumulative line retains the cap losses, post-Flood lifespan changes and ten-year source opening. Those openings and absolute frames remain source premises.

Both radii gain forty. Their difference stays 9200; Priestly expansion then gives $9200\times25/23=10000$.

The equal-gain condition is $R/69=C/299$, or $3C=13R$. Before the source openings, the radii are 2753 and 11950 and their balance is $3C-13R=61$. Adding seven and ten changes that balance by $3(10)-13(7)=-61$. This identifies precisely how the source packet closes the rectangle.

The advance is an explanation of where its two inputs come from. The equality of gains follows once those inputs and Keys are fixed; it is one connected family of consequences. The cap mechanism does not independently select the source openings or the Exodus anchor.

Source basis: Strategy §4.3; Report IV; C1223–C1230.