# How the chronological families fit together

**Reading guide · C632–C731 research cycle · 28 September 2026**

The families fit together through a small set of operations on the same kinds of structured source data. A chronology carries more than dates: it also carries a source tradition, a measurement rule, subdivisions, event roles, an anchor and a calendar or phase convention. Many apparent mismatches become understandable once those pieces remain visible.

| Question | What the research shows |
|---|---|
| Why do MT, LXX and SP move differently? | Regular chronology measures selected begetting intervals; cumulative chronology measures lifespans. A source change can affect those two measurements differently. |
| What makes Round distinctive? | Its admitted scaffold and subdivisions matter. Reversing the two supplied spans can produce a result that reversing their combined total does not. Latest File52c remains the controlling draft. |
| Why do different calculations meet? | Calendar calibration or a supplied partial expansion can give equal totals. The held anchors and direction determine whether endpoints also meet. |
| Why do whole families resemble one another? | Translation, reflection, indexed units or a repeated refinement can generate every member from a few parameters. |
| What still comes from the sources? | Absolute placement, selected roles, phase choices and authorized subdivisions. Arithmetic explains their consequences; it does not independently establish their historical origin. |

The strongest connection to Round remains the Actual cumulative path **14004→1929→1446**. Its two parts are 12075 and 483. Expanding just the final 483 by the Priestly Key gives 525; expanding the whole 12558 by the Enochian Key gives the same total, **12600**. Both reach generated 1404 with Creation held, although they place the internal junction differently. Translating the endpoint pair by +2 gives the Rounded **14006/1406** pair. This connects the families through explicit operations while preserving their distinct event roles.

Here E=25/23 is the Priestly Key, P=70/69 the Prophetic Key, and J=300/299 the Enochian Key.

The new work explains that connection at another scale. A phase scalar of 34.5 has calibrated calendar volume

$$
336E(34.5)=360P(34.5)=364J(34.5)=12600.
$$

Its ordinary 364-volume is 12558. The same conversion structure therefore appears in the small calendar calculation and the large Actual span. The units remain different. A supplied macro partition makes the relationship concrete: retain the lower **2940** and convert only the upper **9660**. The native, Prophetic and Priestly cases produce **12600, 12740 and 13440**. One retained-component construction explains all three.

Two other advances show why working with whole families is productive:

- **Creation–Terah refinement:** one five-position template turns Creation’s **6|1|6|1** into Terah’s **60|10|60|10**. Jacob and Joseph share its simpler three-position form, without requiring unsupplied inner events.
- **Creation–Joseph calendar rails:** two equal 7+7 rails generate all nine cross-spans. With the source’s 14- and 26-year offsets fixed, simultaneous half-calendar divisibility makes **2366**, with counts **13/14/13**, the smallest positive compatible span. This is a conditional mathematical result, not a proof of historical selection.

The 4346 hinge also has a clear explanation. Two supplied regular-MT routes use different source states, anchors and Keys. Their source states differ by 190; their expansion gains differ by exactly 190. That balance makes the generated heads agree. The surrounding 1470-step ladder and refined 4900 path then fit around the shared hinge.

The resulting picture is a common grammar with local realizations. Some operations preserve lifespan, some preserve center, some preserve a weighted point, and some preserve only a final total. The next historical question is which source evidence supports the selected placements and subdivisions. The research no longer needs to treat every repeated number as a separate discovery.

**Read next:** the integrated draft develops these connections with source tables and equations. The accompanying diagram shows the rail, micro-calibration, retained macro partition and Actual–Rounded endpoint bridge. The complete record preserves all 100 sequential steps, reassessments, corrections and verification evidence. The previously deferred work remains outside this cycle.