490d C361 — Shem600/650 rectangle and squared-E endpoints
24 September 2026. Step 8 of 10 in the C354–C363 authorization.
The600 and650 branches fit one exact Shem birth/death rectangle. At the first primary placement:
| Source event | BC coordinate | Next gap |
|---|---|---|
| SP Shem birth | 3206 | 600 |
| SP Shem death | 2606 | 50 |
| MT Shem birth | 2556 | 600 |
| MT Shem death | 1956 | — |
The second placement adds2 throughout. Both biographies have600 years; corresponding SP/MT endpoints differ by650. The50-year gap between SP death and MT birth is therefore650−600. It is also the difference between expanding598 by25/23 to650 and by300/299 to600.
From the retained SP Noah fixed point, these alternatives give1100 to SP Shem death and1150 to MT Shem birth. From SP Shem birth to MT Shem death, the source span is 600+50+600=1250.
There is a second connection to the retained529 grammar. Translating the existing Noah-held squared-E endpoints by−500 yields:
| Fixed SP Shem birth | Input: restored next-Gear MT Shem death | Output: base MT Shem death | Widths |
|---|---|---|---|
| 3206 | 2148 | 1956 | 1058→1250 |
| 3208 | 2150 | 1958 | 1058→1250 |
The source roles themselves supply the500 moves: SP Noah birth→Shem birth, and each MT Flood start→same-Gear Shem death. Thus 3206+(625/529)(2148−3206)=1956. The192-year death-endpoint difference is the existing130+60+2 context/Gear difference.
However, a single E step lands at2056/2058, absent from the frozen528-record register. The squared-E endpoint comparison is exact, but it is not a composable path of two source-qualified E edges. The formal intermediate is recorded only as a diagnostic coordinate. C356’s failed−500 single-E transport and this successful squared-E endpoint transport are consistent.
These constructions reconnect source endpoints using the same inherited650 offset,600 lifespan, E ratio and529 widths. They do not add independent historical witnesses or new source nodes.
Verification and limits
16 main checks and 16 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. These checks and the source interpretation were performed by the root agent; no new independent-agent review is claimed. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.
A sourced direct squared-E endpoint relation does not establish a two-edge source path through an absent intermediate. The50 and1250 identities share the same source constants.
Mirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct.
Decision after this result
C362, proposed and unexecuted: Stress-test the Shem-held squared-E endpoint comparison across the fixed C319 menu and test both new constructions against the inherited seasonal-component choices. Keep Flood-close transport distinct from SP person companions and from MT person states.
The new endpoint realization needs its source-domain and phase limits stated before synthesis. In particular, a Flood close translated by500 must not manufacture an MT companion death.