490d C339 — Double-E ladder under the two named Shem bindings
24 September2026. Step6 of10 in the C334–C343 authorization.
The endpoint relation1058×E²=1250 survives both valid Shem bindings. The complete intermediate1150 requires the Noah-bound500/100 choice in the named G2 control. This qualifies the ladder without treating502/98 as an error.
Hold SP G2 primary Noah N=3708, restored MT G3 Flood start R=2650, and base MT G2 Flood start F=2458. Use the two Shem bindings already retained in C329, retrieving their base-MT counterparts from C286.
| Valid binding | Base MT Shem H | Base MT Noah→H / H→F | N−R, N−H, N−F | R−H / H−F |
|---|---|---|---|---|
| Noah-bound, Shem G2 | 2558 | 500 /100 | 1058,1150,1250 | 92 /100 |
| Arphaxad-bound, Shem G1 | 2556 | 502 /98 | 1058,1152,1250 | 94 /98 |
Both1058 and1250 are unchanged because their endpoints do not depend on the Shem binding. The first expansion predicts1150; the second expansion of the actual alternate1152 exceeds1250 by50/23. Thus the alternative remains a valid source comparison but is not a two-stage E ladder through its selected Shem endpoint.
This control uses the explicit G2/G1 comparison. It does not invent Gear0 to impose an analogous lower-Gear binding on G1. C338's companion limitation also remains: the one-year MT intermediate needed there is absent, regardless of the numerical appeal of1150.
The next useful step is to insert the already source-qualified SP Noah death. That will show how the newly matched92/100 increments relate to the retained950+108 dissection, and how the actual companion and alternate Shem records modify that interior reading.
Verification and limits
13 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.
Two named valid bindings, not all conceivable modal combinations. Conditional fit does not prescribe or canonize the500/100 mode. No missing Gear or companion is created.
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
C340, proposed and unexecuted: Insert the matched SP Noah death into the verified interval ladder. Resolve the primary, companion and named502/98 interior partitions from existing records, retaining the primary-death qualification and forbidding imported MT companions.
C339 separates invariant outer endpoints from a modal interior. The previously established950+108 relation can now connect directly to the verified92/100 gains and reveal their dependence.