Original duration words and the inverse backbone
File52c’s decimal operation reverses the significant digits of each original span while retaining its trailing-zero places. Thus 1650 becomes 5610, 1050 becomes 5010, and 1400 becomes 4100. A source-appointed partition is part of the operation: the regular 2700-year Creation-to-Conquest span, treated whole, produces 7200; its 1650+1050 partition produces 5610+5010=10620. The named Flood division therefore carries information that the total alone omits. [File52c §§1.2,3.3–3.4]
With Conquest 1406 BC held, the regular primary path gives
The cumulative primary path uses Creation 14006 and Flood 4836, giving 9170+3430. Its one-pass images are 7190+3430, also totaling 10620 and rebuilding 12026 BC. This convergence concerns the specified primary paths; their source breakpoints remain distinct. [File52c §3.3]
A decimal-register calculation explains the two-component convergence. Under the declared trailing-zero register, a Regular total 2700 forces transformed total 10620. A Cumulative total 12600 allows two carry branches; its actual 917 and 343 cores select the 10620 branch. The source supplies the named split. The technical companion retains the proof and the alternative branch. [C938–C947]
The continuation to 14726 BC supplies an additional original interval: Conquest 1406 to Nativity 6 is 1400 years, whose one-pass image is 4100. Moving the held anchor from 1406 to 6 and including this leg changes the rebuilt endpoint by 4100−1400=2700. Therefore 12026 becomes 14726. The explanation retains both the original tail and the anchor change. [File52c §3.4; C952]
All four admitted completed paths can be compared compactly. The divisions are listed outward from the held 6 BC anchor toward earlier source dates:
| Source path after Nativity | Original spans | One-pass spans |
|---|---|---|
| Regular: Conquest–Flood–Creation | 1400 + 1050 + 1650 | 4100 + 5010 + 5610 |
| Regular: Conquest–Noah–Creation | 1400 + 1650 + 1050 | 4100 + 5610 + 5010 |
| Regular: Conquest–Flood–Noah–Creation | 1400 + 1050 + 600 + 1050 | 4100 + 5010 + 600 + 5010 |
| Cumulative primary: Conquest–Flood–Creation | 1400 + 3430 + 9170 | 4100 + 3430 + 7190 |
Every transformed row totals 14720 and therefore ends at 14726 BC. The Noah alternatives preserve the regular result through their particular component relations. The new genealogy interface matches the first three original rows exactly and reuses their established images; the cumulative row retains its own source measurement. The first transformed leg ends at 4106 BC, numerically equal to original regular Creation, but it remains the generated endpoint of the Conquest leg. This preserves the distinction between a shared coordinate and a shared chronological role. [File52c §3.4; C1274–C1276]
The same 12026 anchor also divides the selected Actual Creation bridge. Its cumulative and regular completion endpoints are 14004 and 4114 BC, respectively. Their 9890-year separation splits into
Priestly expansion by 25/23 gives 2150 and 8600, preserving 1:4 and totaling 10750. These expanded parts belong to the expanded total. The Rounded endpoints 14006/4106 instead divide into 1980+7920=9900, again 1:4. Both selected pairs satisfy
where C,R are their cumulative and regular Creation coordinates. Moving Rounded→Actual changes them by −2 and +8, preserving the weighted value because 4(−2)+8=0. The regular +8 combines the six-year row residual with the separate standard Shem +2 convention; selecting the cumulative completion endpoint supplies its −2. The matching weight is derived from these selected values. It expresses their compatibility without making the state selections disappear. [File52c §3.14; C932–C948]
The same division is visible in the original one-pass convergence. The regular span grows from 2700 to 10620, gaining 7920; the cumulative span falls from 12600 to 10620, losing 1980. The gain is four times the loss. Thus the weighted coordinate and the inverse construction express a shared relation among these source values. Once the inputs are fixed, the two descriptions belong to one connected calculation. The historical significance rests on why those particular intervals and their named divisions occur in the source family. [C937–C948]
The completed backbone also has a 9890-year interval to the Conquest-held cumulative Flood companion at 4836 BC: 14726−4836=9890=23×430. The Flood companion retains the 1406 anchor and unchanged 3430 span; it is a separate anchored comparison from the completed Nativity-held path. Its interval matches the Actual Creation bridge in magnitude, while the original Rounded Creation gap stays 9900. The correspondence links declared measurements without replacing their endpoints or chronological roles. [File52c §3.6]