Named partitions distinguish the three Regular inverse spines

Research support for C1433–C1482. All coordinates below are BC. This note uses single reversal of original durations only.

Strongest new finding: MT and LXX retain their heads when Noah replaces the Flood partition, for different reasons

File52c already establishes the MT alternatives through Flood, Noah, or both. The LXX supplies a new comparison: its two coarse partitions also yield the same head, but retaining both named nodes adds 990 to the transformed total. The SP accepted Fall construction changes its result under either refinement. This comparison explains the role of the partition; it does not replace the accepted primary Flood spines.

The selected Regular source paths, processed away from the later anchor, are:

The LXX Noah coordinate 3836 is already reconstructed inside Moses_LXX_native_complete_path.json, alongside Rounded Creation 5486, Shem 3336 and Arphaxad 3236. The SP node 3706 follows from its selected lower Rounded Flood 3106 and the retained 600-year Noah–Flood leg; File47 §6.1 independently corroborates the local relation. No new +215 variant is applied in this comparison, and it does not transport gears into Adam–Lamech. MT Noah 3056 is explicit in File51a §3.1 and File52c §§3.3–3.4.

Thus LXX Noah-only still gives 10436 from held Conquest and 13136 after prepending the reversed Nativity leg. Its both-node refinement gives 11426 and 14126. The SP alternatives give different outputs and remain diagnostic comparisons, with the accepted Flood-only heads 11606/14306 unchanged.

The exact explanation uses two merging defects

For original source legs $a,b,c$, with $b=600$ from Noah to Flood, define

This uses each original duration once; neither argument is a previously reversed output. Let

Then

For MT the two refinements are individually additive. For LXX both lose the same 990 when merged, so the coarse totals agree despite nonadditivity. SP uses different decimal registers: its 1700 + 600 merge becomes 2300, while its 600 + 700 merge becomes 1300. The unequal defects preserve the importance of its chosen Flood partition.

The result warrants a short addition to the reader: a common terminal head can arise either from exact additive refinement (MT) or from balanced nonadditivity (LXX); SP demonstrates why the named partition must remain part of the chronological construction.

Other explanatory results and their prior status

1. The three Regular/Cumulative head separations 0, +500 and −190, and their reversed-leg decompositions, are already in the reader. Do not count these as new discoveries.
2. The cumulative contractions 1980, 3960 and 1980 are also already in the reader.
3. The 610 MT–SP cumulative head separation in all three states is already in C1432's supporting algebra notes, although absent from its main report. It can be promoted as an explanatory synthesis: the −1980 contraction changes position from MT upper leg to SP lower leg. Source differences (120,490) become inverse differences (2100,−1490), preserving their total 610.
4. A compact digit mechanism explains all current contractions: for abc0, $I(n)-n=990(c-a)$; for ab00, $I(n)-n=900(b-a)$. The four MT/LXX original legs and both cumulative SP legs use the first register; SP Regular uses the second. This is an explanation of existing results, not a new harmonic occurrence.
5. The LXX–MT cumulative reversal changes an original head difference +890 to −1090. The fixed lower-leg difference +910 survives, but upper legs 9150 versus 9170 differ by −20, which becomes −2000 after reversal. Thus +910−2000=−1090. The accepted SP cumulative source head is 1500 later than LXX's; the additional LXX contraction 1980 changes that order by 480. These are source-dependent reversal mechanisms, not arbitrary fitted date maps.

Files actually inspected

• Supplied September 28 LXX/SP study, §§2–7: six accepted primary source paths.
• File52c frozen C1432 source, §§3.3–3.4: MT Noah/Flood refinements.
• File51a mounted source, §3.1: rounded MT Noah.
• File18 mounted September 19 source, §§2.2.1 and 3.2.1: LXX Noah member, SP primary Noah member and comparative +215.
• C1431 reader §§10–13 and technical companion: existing claims and novelty check.
• C1432 main report and support note bridge_algebra_findings.md: existing 610 relation and reciprocal head closure.

No canonical source was edited; no second reversal, broad scan, or new statistical claim was made.