490d C340 — Noah death refinement of the double-E ladder
24 September2026. Step7 of10 in the C334–C343 authorization.
The primary Noah-held ladder has a single source-labelled refinement:460+490+108+92+100=1250. The existing950+108 reading occupies its first1058; the later92 and100 reach the actual MT Shem and base-Flood endpoints.
In the order SP Noah N → same-Gear restored MT Noah M → matched SP Noah death D → next-Gear restored MT Flood R → base MT Shem H → base MT Flood F, the source comparisons give:
| Valid source state | Consecutive legs N,M,D,R,H,F | N−H | D−H | D−F |
|---|---|---|---|---|
| Primary, same-Gear Shem: i3 andi5 | 460 +490 +108 +92 +100 | 1150 | 200 | 300 |
| SP companion, actual MT Shem: i2 andi4 | 459 +491 +108 +91 +101 | 1149 | 199 | 300 |
| G2 primary, named502/98 Shem binding | 460 +490 +108 +94 +98 | 1152 | 202 | 300 |
For the primary state, the successive totals are 1058=950+108, 1150=950+200, and 1250=950+300. The300 tail from SP death to base MT Flood is shared by all five tested chains. The interior200 is specific to the primary same-Gear Shem state; the companion and502/98 controls give199 and202.
A compact formula makes the dependence visible. Let e=1 for an SP companion, otherwise0, and let σ be the selected Shem displacement from the same-Gear base-MT Shem (0 ordinarily;−2 in the named502/98 control). The last two legs are 92−e−σ and 100+e+σ. Their sum is always192. The108 tail is held, so the complete post-death tail remains300.
All dates are existing source endpoints used in a comparison coordinate chain, not one historical biography spanning traditions and contexts. SP primary Noah death retains File_18 §3.2.1's inclusive/harmonic qualification; the matched companion uses its ordinary-companion qualification. Both retain the950 subtraction.
These decompositions do not mean E leaves950 fixed while expanding only its remainder. E multiplies the complete source interval. The next step will make that map distinction exact, including the inherited seasonal components.
Verification and limits
36 main checks and 17 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.
Five existing comparison chains only. Equal durations and their refinements are dependent source arithmetic, not independent witnesses or a prescribed global map.
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
C341, proposed and unexecuted: Verify the exact phase and map conditions for the Noah-held duration ladder: use only existing quarter-year components, test mismatched-component controls, and determine whether one affine map can preserve the source Noah lifespan or both seasonal Noah components.
C340 unifies the death partition and expansion ladder, but its additive950 terms could be misread as a fixed biography under E. An exact map audit will distinguish duration identities, componentwise comparison and a whole-time-axis transformation.