# Branch handoff — 3+7 ×529 through Noah’s birth

**Date:** 21 September 2026  
**For:** The original 490d Strategy–Unification window.  
**Status:** Verified arithmetic and source-qualified endpoints; one interpretation of Dean’s seasonal shorthand remains unconfirmed. This is a separate report from the 11×529 Conquest handoff.

## 1. Main observation

Dean identifies a Noah-birth division of the established 5290-year cumulative-Flood-to-Christ comparison. All dates in the principal chain are BC:

\[
\boxed{5296\xrightarrow{1587=3\times529}3709
\xrightarrow{3703=7\times529}6.}
\]

Thus **1587+3703=5290=(3+7)×23²**. The intermediate coordinate is an admitted SP Noah-birth station.

The controlling source labels are **MT cumulative, second Cainan ON**, at the 5296 Flood-week opening; **SP regular, G3 companion Noah birth**, at 3709; and the project’s **6 BC Christ-birth anchor**. Regular settings are full-430, Terah +60 OFF, and second Cainan OFF. The cumulative and regular Cainan selections are deliberately distinct.

Dean’s initial wording called 5296 “LXX cumulative, Cainan OFF.” The current LXX OFF field is **5290–5283**, whereas **5296–5289** is MT cumulative ON. Likewise, the regular LXX OFF G3 Noah birth is **3710**, while **3709** is SP’s G3 −1 companion. These corrections preserve the numerical observation.

## 2. Full Nisan ladder and source membership

Each row preserves the same **3×529 + 7×529** division. Every column below is **Nisan BC**.

| MT cumulative ON Flood-week member | Regular Noah birth | Christ-period landing | SP identification | LXX OFF identification |
|---:|---:|---:|---|---|
| **5296n** | **3709n** | **6n** | G3 companion | — |
| 5295n | 3708n | 5n | G2 primary | G2 |
| 5294n | 3707n | 4n | G2 companion | — |
| 5293n | 3706n | 3n | G1 primary | G1 |
| **5292n** | **3705n** | **2n** | G1 companion | — |

SP therefore supplies five consecutive annual selections, spanning four elapsed years. The first two intervals are always **1587** and **3703**. The terminal members belong to the previously retained Christ-period field; the table does not assert five independently established historical birth dates.

Dean’s final extension “5295/3705/2” is treated as an apparent typo for **5292/3705/2**: **3705+1587=5292**. This correction is arithmetic; explicit confirmation of the typo was not received before this report was requested.

Regular LXX OFF G3 **3710n** would require **5297n→3710n→7n BC**. That cumulative member lies one year before the held MT ON Nisan field, so G3 supplies no complete Nisan chain within it.

## 3. LXX phase pairs and Dean’s overlap wording

The complete LXX-supported paired chains are:

| Gear | MT cumulative ON member — BC | LXX OFF Noah birth — BC | Terminal pair — BC |
|---|---|---|---|
| G2 | **5296t / 5295n** | **3709t / 3708n** | **6t / 5n** |
| G1 | **5294t / 5293n** | **3707t / 3706n** | **4t / 3n** |

Both same-season components preserve the stated lengths. These pairs give a possible reading of Dean’s shorthand **5296–5293 → 3709–3706 → 6–3** as outer bounds running from **Tishri to Nisan**. The outer bounds span 2½ elapsed years and contain the two admitted Gear pairs; they do not make every intervening annual coordinate an LXX Nisan birth station.

SP’s G1 companion adds the complete paired chain **5293t/5292n → 3706t/3705n → 3t/2n BC**, extending the later edge by one year. SP also has the earlier G3 companion chain shown in §2. **The phase reading of Dean’s LXX shorthand was proposed by the assistant but remains unconfirmed.**

## 4. What this adds to the earlier reports

The earlier cumulative–regular handoff already contains **5296→2651→6 BC**, a **5×529 + 5×529** partition. Dean’s new observation gives the same outer span an event-qualified SP intermediate point, **3709**, located **1058=2×529** years earlier than 2651. Hence the change from **5+5** to **3+7**.

A bounded search found no earlier explicit occurrence of this particular **5296→3709→6** partition. The total and other uses of the component numbers were already known; exhaustive historical priority is not claimed.

Source basis: the supplied **20 September MT cumulative–regular branch handoff** and **SP regular/cumulative Noah–Shem–Flood tables**, with **File_18 (20260919-141048), §§3, 4 and 6B–6D**, and the paired-phase convention of the **21 September 6877/598/299 handoff**. Arithmetic and seasonal checks were completed for the displayed chains. No canonical file was changed; the SP −1 companion remains local to SP Noah/Shem.

**Best next bounded step:** clarify the intended LXX seasonal envelope, then compare this 3+7 partition with the retained 5+5 construction through their **1058-year intermediate-point separation**. **High is sufficient.**