The main article uses Rounded cumulative coordinates compared with fixed target dates. This appendix shows their derivation and places them beside the non-rounded, or Actual, cumulative values. “Actual” here means calculation from the retained unrounded lifespans; both methods produce constructed lifespan-chain coordinates, not ordinary biographical dates.
The complete non-rounded cumulative tables remain the larger reference. Open the MT table, SP table, or LXX table directly. The canonical Markdown and amendments control the figures.
In this appendix: lifespan rounding · coordinates and foundations · endpoint ledger · non-rounded envelopes · text and conventions · sources.
1. Round the lifespans, then add them
Each retained lifespan is rounded independently to the nearest multiple of five. For example, MT Arphaxad’s 438 becomes 440, Jacob’s 147 becomes 145, and Shem’s 600 stays 600. The cumulative positions are then rebuilt from the stated terminal anchor. Rounding the final BC date alone would be a different operation.
Table A1. The lifespans below Shem
All entries are years. A dash means that second Cainan is absent from that base chain; it is not a zero-year lifespan.
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| Patriarch | MT Actual | MT Rounded | SP Actual | SP Rounded | LXX Actual | LXX Rounded |
|---|---|---|---|---|---|---|
| Arphaxad | 438 | 440 | 438 | 440 | 465 | 465 |
| Second Cainan | — | — | — | — | 460 | 460 |
| Shelah | 433 | 435 | 433 | 435 | 460 | 460 |
| Eber | 464 | 465 | 404 | 405 | 504 | 505 |
| Peleg | 239 | 240 | 239 | 240 | 339 | 340 |
| Reu | 239 | 240 | 239 | 240 | 339 | 340 |
| Serug | 230 | 230 | 230 | 230 | 330 | 330 |
| Nahor | 148 | 150 | 148 | 150 | 208 | 210 |
| Terah | 205 | 205 | 145 | 145 | 205 | 205 |
| Abraham | 175 | 175 | 175 | 175 | 175 | 175 |
| Isaac | 180 | 180 | 180 | 180 | 180 | 180 |
| Jacob | 147 | 145 | 147 | 145 | 147 | 145 |
| Levi | 137 | 135 | 137 | 135 | 137 | 135 |
| Kohath | 133 | 135 | 133 | 135 | 133 | 135 |
| Amram | 137 | 135 | 137 | 135 | 137 | 135 |
| Moses | 120 | 120 | 120 | 120 | 120 | 120 |
| Arphaxad through Moses | 3425 | 3430 | 3305 | 3310 | 4339 | 4340 |
| Joshua extension | — | — | 110 | 110 | — | — |
| Total after Shem | 3425 | 3430 | 3415 | 3420 | 4339 | 4340 |
Sources: File_18 §§2–4 and 6A–6D for retained lives and foundations; File_51a §§16.1–16.2 for rounding and cumulative addition. The native LXX chain retains second Cainan. The MT and SP base chains do not acquire him for this comparison. No +60 Terah shift or alternative sojourn operation is applied.
The SP differs from the MT by 60 at Eber and 60 at Terah. Those differences survive rounding unchanged. Joshua’s additional 110 years connect the SP’s 1296 foundation to 1406, explaining why the resulting MT/SP separation is 120, despite the different terminal ledgers.
Return to the main article’s Rounded explanation.
2. Coordinates and foundations
Table A2. Rebuilding the source coordinates
All dates are BC. Add the relevant total from Table A1 to the terminal anchor; then add Shem’s full 600 years.
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| Construction | MT | SP | LXX |
|---|---|---|---|
| Terminal anchor | Moses / Conquest 1406 | Cumulative Joshua endpoint 1296 | Moses / Conquest 1406 |
| Actual Flood/Arphaxad coordinate | 1406 + 3425 = 4831 | 1296 + 3415 = 4711 | 1406 + 4339 = 5745 |
| Rounded Flood/Arphaxad coordinate | 1406 + 3430 = 4836 | 1296 + 3420 = 4716 | 1406 + 4340 = 5746 |
| Actual Shem coordinate | 4831 + 600 = 5431 | 4711 + 600 = 5311 | 5745 + 600 = 6345 |
| Rounded Shem coordinate | 4836 + 600 = 5436 | 4716 + 600 = 5316 | 5746 + 600 = 6346 |
| Change produced by lifespan rounding | +5 | +5 | +1 |
This explains the LXX’s one-year difference precisely: 4339 years of retained lifespans become 4340 after individual rounding. The Rounded pair 6346/5746 is therefore a reproducible calculation, not a convenient selection from the Actual seven-year ranges.
These are the selected base Rounded lines. The separate Rounded Aaron branch and its five-year displacement are not being added to this article’s figures. The previous cumulative appendix explains the underlying Moses/Aaron foundation in greater detail.
Return to the main coordinate table.
3. Endpoint ledger for the Rounded comparisons
All calculations below are same-side BC subtraction. The source coordinates are Rounded cumulative values; the named historical targets belong to the stated normal MT comparison framework.
Table A3. Retained spans
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| Comparison | Calculation | Result |
|---|---|---|
| MT Shem → SP Shem | 5436 − 5316 | 120 |
| SP Shem → MT Flood/Arphaxad | 5316 − 4836 | 480 |
| MT Flood/Arphaxad → SP Flood/Arphaxad | 4836 − 4716 | 120 |
| Combined MT/SP extent | 5436 − 4716 | 720 |
| MT Flood/Arphaxad → Conquest | 4836 − 1406 | 3430 = 70 × 49 |
| SP Shem → Conquest | 5316 − 1406 | 3910 = 170 × 23 |
| SP Flood/Arphaxad → Conquest | 4716 − 1406 | 3310 |
| SP Shem → MT entry into Egypt | 5316 − 1876 | 3440 = 8 × 430 |
| SP Shem → Exodus | 5316 − 1446 | 3870 = 9 × 430 = 3 × 1290 |
| LXX Shem → Exodus | 6346 − 1446 | 4900 = 10 × 490 |
| LXX Flood/Arphaxad → Exodus | 5746 − 1446 | 4300 = 10 × 430 |
| LXX Flood/Arphaxad → SP Shem | 5746 − 5316 | 430 |
| LXX Flood/Arphaxad → MT entry into Egypt | 5746 − 1876 | 3870 = 9 × 430 = 3 × 1290 |
| MT entry into Egypt → Exodus | 1876 − 1446 | 430 |
| MT Shem → restoration | 5436 − 536 | 4900 |
| MT Flood/Arphaxad → restoration | 4836 − 536 | 4300 |
| LXX versus MT corresponding coordinates | 6346 − 5436 = 5746 − 4836 = 1446 − 536 | 910 |
The shared 4300-year span has two complementary divisions: 5746→5316→1446 = 430 + 3870, through Rounded SP Shem, and 5746→1876→1446 = 3870 + 430, through the fixed MT Egypt-entry target. Showing both intermediate nodes gives 430 + 3440 + 430, where 3440 = 8 × 430 and each longer span is 3870 = 9 × 430 = 3 × 1290.
The SP 3910 starts at Shem 5316, not Flood 4716. Likewise, its 3440/3870 comparisons start at Shem; starting at 4716 gives 2840/3270. These start points matter even when the desired factors recur elsewhere. Comparing a cumulative SP or LXX coordinate with MT 1876/1446 does not assert an Egypt-only 430-year reading in the SP or LXX text.
Return to the main deliverance comparison.
4. The related non-rounded comparisons
The Actual tables include a seven-year starting envelope associated with the cumulative Moses/Aaron and Shem allowances. Its whole-year width 2 + 3 + 2 = 7 remains distinct from the separately phase-resolved 2 + 3.5 + 2 = 7.5. The main article does not substitute either envelope for its selected Rounded coordinates.
Table A4. Actual cumulative ranges
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| Tradition | Primary Nisan Shem coordinate | Shem envelope | Primary Nisan Flood/Arphaxad coordinate | Flood/Arphaxad envelope |
|---|---|---|---|---|
| MT | 5431 BC | 5436–5429 BC | 4831 BC | 4836–4829 BC |
| SP | 5311 BC | 5316–5309 BC | 4711 BC | 4716–4709 BC |
| LXX, native Cainan | 6345 BC | 6350–6343 BC | 5745 BC | 5750–5743 BC |
The MT/SP 120–480–120 arrangement also holds in this unrounded frame. Its corresponding upper members give 5436→5316→4836→4716; its lower members give 5429→5309→4829→4709. The MT and SP Rounded coordinates happen to match the upper Actual members, but their derivations remain different.
The related MT 3430 result preserves corresponding boundaries:
4836 − 1406 = 3430, and 4829 − 1399 = 3430.
Here 1406–1399 is the Conquest/rest envelope; 1399 is the first rest year. Both Flood boundaries are not 3430 years before the single date 1406. File_09 §4.1 controls the full-envelope comparison.
For the LXX, the distinction is especially important. Translating the Actual Shem envelope 6350–6343 by 4900, or its Flood envelope 5750–5743 by 4300, produces 1450–1443. Neither operation collapses the full envelope to the fixed Exodus date 1446. The primary Actual Nisan coordinates give 6345−1446=4899 and 5745−1446=4299. The main article’s exact 4900/4300 to 1446 uses the independently derived Rounded pair.
The original discussion explores the seasonal and half-week comparisons in greater detail. Read those alongside the current canonical controls; this appendix supplies the precise convention used in the streamlined article.
Return to the main Flood-to-land comparison.
5. Text and conventions
Shem’s lifespan and Flood age. Genesis 11:10–11 gives 100 at Arphaxad’s birth and 500 afterward. Its direct elapsed reading places the age-100 statement two years after the Flood, giving 98 at the Flood. The canonical framework also retains the named Noah/Flood-bound age-100 state. Neither is a 600-year Flood age. The complete 600-year lifespan is what the cumulative comparison adds.
The Flood/Arphaxad boundary. This is a cumulative table convention joining the next ancestral lifespan to the Flood-related marker. File_18 §6D distinguishes the death-side conventions by tradition and retains the Arphaxad marker across them. It does not override the ordinary historical two-year relationship in Genesis 11:10.
Forty-nine and the jubilee. Leviticus 25:8 counts seven sabbaths of years, totaling 49; verses 9–10 continue to the proclamation and sanctification of the fiftieth year. The equation 3430 = 70 × 49 counts seventy 49-year units. It does not decide every question about the fiftieth year’s calendar placement.
Calendar and variant scope. Nisan is the default frame. Tishri labels enter the fuller source comparisons only when stated. No regular +60 Terah, alternate sojourn, inserted MT Cainan, or BC/AD Mirror operator is used in the main article. Its BC-to-BC differences use ordinary subtraction; the September 25 Rounded BC/AD display distinction is not needed for these same-era spans.
Interpretation. The calculations are exact under their declared inputs and operations. Connections with warning, jubilee, Exodus, and restoration are the theological reading of those calculations. The several related equations share inputs and are not presented as independent statistical proofs.
Sources and further reading
On a narrow screen, scroll the table sideways to see every column.
| Source | Relevant sections and purpose |
|---|---|
| Non-rounded cumulative tables | Full retained lifespans, three-year tracks, and seven-year starting envelopes |
| File_18: Chronological Data Tables | §§2–4,6–6D: lifespans, anchors, cumulative coordinates, and current corrections |
| File_51a: Rounded Scaffold | §§16.1–16.3: individual lifespan rounding, cumulative propagation, and 3430 |
| File_09: Cumulative Architecture | §§3A.4.2,4.1: cumulative foundation and matched-boundary 3430 comparison |
| File_02: Flood/Sumerian Integration | §6: Shem allowance and cumulative envelope conventions |
| File_22: Cumulative MT Harmonics | §§0.1,1.2,3.3: coordinate states and seasonal comparison controls |
| File_30: The 4900/4300 Master Cycle | §§0.7,1: dual-deliverance interpretation and its source dependencies |
| Report III | §§5,19,21–22: supporting research for the Actual envelopes, MT/SP arrangement, and SP 3910 |
| Rounded comparative study | §§2.1,4.1: explicit Rounded three-tradition inputs and MT/LXX 910 translation |
| Original Synergy discussion | Broader exploration and historical derivations, read under the current canonical controls |
The canonical files govern the chronological inputs. The supporting studies preserve fuller comparisons without replacing those controls.