Whole-node connections for the next inverse-spine synthesis

Prepared for the C1585–C1634 continuation. This note selects two finite packets from already named nodes. It does not scan for additional endpoints. The standalone target_algebra.py verifies the arithmetic.

1. The new 7000 belongs to the existing MT–LXX 910 translation

The comparative study §4.1 already appoints the pairs MT Shem/Flood 5436/4836 against restoration 536, and LXX Shem/Flood 6346/5746 against Exodus 1446. Both yield 4900/4300, and every node moves 910 years earlier. Both lower cumulative inverse legs are self-reversing: 3430 and 4340. Thus their Flood coordinates survive Conquest-held inversion, and the common Nativity extension raises both by 2700.

Adding the two completed inverse Floods therefore extends the existing three-node relation to a four-node relation:

Every adjacent edge is preserved:

The six pairwise widths in each packet are 2100, 2700, 7000, 600, 4900 and 4300, at the same respective pairs of positions. This is more informative than separate equal totals.

The 2100 has two equivalent explanations within the selected construction:

• The Nativity-stage extension is 2700; Shem stands 600 above the ordinary Flood. Hence the new inverse Flood stands 2700−600=2100 above Shem.
• In the MT–SP inverse comparison, the reversed lower legs differ by 3430−1330=2100, and the common extension preserves that gap.

These explanations agree because SP's completed inverse cumulative Flood 5436 coincides with ordinary MT cumulative Shem 5436. Thus the MT row contains a named junction with the SP family. The LXX row reproduces the entire packet under the established 910 translation. The family link is therefore a combination of one source-supported translation and one already established incidence.

Consequences are grouped as the same relationship, not independent findings:

Source basis: comparative study §4.1; C1583 MT inverse Flood construction; C1582 six primary spines; File18 cumulative Shem's serial 600-year life. No historical role is assigned to newly generated coordinates.

2. All three inverse families refine the established 12600 path

Insert the new MT inverse cumulative Flood 7536 into the previously established LXX→SP→restoration path:

Hence

This places the new 7000 and the established 7700 in one refinement:

The 5600 is the determined gap between two already supplied nodes. It is not proposed as a separately attested chronological period. The parent report can retain 5600 as an explanatory edge without adding a theological interpretation.

3. C1584's limited Rounded transfer preserves this whole path

Use the declared Rounded coordinate map $q(B\text{ BC})=1-B$, $q(\text{AD }A)=A-1$. Translate every coordinate forward 2700:

The same 5600+2100+4900 partition survives. Its three earlier nodes are now the corresponding Conquest-held inverse nodes; the common endpoint is Abram's reflected birth in the already approved Rounded display. This shows the whole named-node path, not just three detached intervals, behind the requested 12600/7000/4900 preservation.

The transformation is the inverse of the common translation used to pass from Conquest-held to completed coordinates. It performs no second decimal reversal. Deeper mirror analysis stays deferred.

The LXX target packet could also be transported algebraically, but doing so creates an unrequested AD target. Omit that extension from the reader; the existing 910 packet is sufficient for the larger argument.

4. Keep the Jubilee chain's convention explicit

The existing SP Regular completed inverse Flood remains 11206 BC. Its appointed path through MT cumulative Flood and Conquest is

This cross-axis last leg uses civil counting. The new Rounded packet uses the already declared $B+A-2$ rule. Both paths share MT inverse Flood 4836, which is enough to connect the Jubilee and Babylonian/Abrahamic explanations. There is no need to force AD65 into a Rounded companion state or open further mirror analysis.

5. Anchored Key scope

Affine Key maps are covariant when the source, result and held anchor all translate together. This fact is already established in earlier work; repeating the general conjugacy proof does not supply a new source connection. Transporting the current Covenant anchor into an unrequested AD coordinate would add complexity without improving the present explanatory packet. Retain the established Covenant result and explain the new packets through translation, cumulative life divisions and the SP/MT incidence.

Recommended reader emphasis

1. Extend the established MT–LXX 910 relation to the four named-node packets.
2. Show how the new MT Flood divides the shared three-MSS path into 5600+2100+4900.
3. Use one compact table to carry that complete path forward 2700 to the approved Rounded AD 2166 endpoint.
4. Identify the shared 4836 node joining that packet to the already verified SP Jubilee path.

These reduce several observations to a small number of transformations and named junctions. All equations are conditional on the source chronology and conventions already selected in the project.