This appendix gives the selected inputs and endpoint checks behind the introductory article. “Actual” means calculated from retained unrounded inputs. “Rounded” means rebuilding a chain after rounding its inputs to the nearest multiple of five. Cumulative positions are lifespan-chain coordinates. Nisan is the default frame; no +60 Terah shift is applied.
All same-era comparisons below use BC subtraction. The Mirror example explicitly uses civil elapsed years, BC + AD − 1, and the stated Protocol-1 counterpart labels. Its result is distinct from a pure rounded-width display or a seasonal phase-resolved Mirror calculation.
1. Orientation and selected states
| State | Selected coordinates | Use |
|---|---|---|
| Normal MT regular | Creation 4114; Flood 2458; Abram 2166; Exodus 1446; Conquest 1406 BC | Orientation; Gear 2 default; Arphaxad 2456 BC remains fixed |
| Rounded MT regular | Creation 4111/4106; Flood 2456 BC | Rounded inputs and stated boundary block |
| Rounded cumulative MT | Creation 14011/14006 BC | Upper Aaron / lower Moses branches |
| SP regular, own sojourn | Actual Creation week 4206–4199 BC | Canaan-and-Egypt 215+215 reconstruction |
| SP cumulative comparison | Upper rounded Creation 13406 BC | Whole-lifespan rounding and Aaron+5 |
| Native LXX | Cainan 130 regular; 460 cumulative | Retained unless a removal column is expressly shown |
The regular boundary block and the cumulative Aaron/Moses pair have different origins. An identical five-year width does not merge the two constructions. In the SP forty-year example, 4206 is an Actual regular opening and 13406 is an upper Rounded cumulative member.
2. Round parts or round whole lives
| Example | Input | Regular component method | Cumulative whole-lifespan method |
|---|---|---|---|
| Methuselah, MT/LXX | 187 +782 =969 | 185 +780 =965 | 969→970 |
| Lamech, MT | 182 +595 =777 | 180 +595 =775 | 777→775 |
| Lamech, operative LXX | Reconstructed 182 +calculated 571 =attested 753 | 180 +570 =750 | 753→755 |
| Aaron / Moses terminal | 123 /120 | — | 125 /120; difference 5 |
The regular rounded death layer is theoretical. The operative LXX lifespan is 753; 777 is an MT-derived comparison overlay and is not used here. An attested lifespan does not make every component of the combined LXX biography independently attested.
3. Compact rounded source registers
For the regular register, SP is on the equalized full-sojourn comparison plane. Its own −215 execution is used separately below. No localized Shem +2 is added to these rounded regular rows.
| Node | MT | SP, equalized | LXX, Cainan removed | Native LXX |
|---|---|---|---|---|
| Creation | 4111/4106 | 4416/4411 | 5361/5356 | 5491/5486 |
| Noah birth | 3056 | 3706 | 3706 | 3836 |
| Warning, modeled 120 before Flood | 2576 | 3226 | 3226 | 3356 |
| Shem birth, rounded comparison | 2556 | 3206 | 3206 | 3336 |
| Flood / Arphaxad comparison seam | 2456 | 3106 | 3106 | 3236 |
| Noah death, theoretical | 2106 | 2756 | 2756 | 2886 |
A rounded Flood/Arphaxad seam is a comparison convention. Actual SP Gear 2 has Flood start 2893, close 2892, and fixed Arphaxad 2891 BC in the SP’s own sojourn frame. Its Noah primary 3493→2543 and companion 3492→2542 bind 350 years to the corresponding Flood start or close. The local person-station adjustment belongs to Noah and Shem; it does not move the Flood year or the earlier ancestors.
| Tradition | Actual Creation member | Rounded Creation, upper/lower | Actual Flood member | Rounded Flood, upper/lower |
|---|---|---|---|---|
| MT | 14006 | 14011/14006 | 4831 | 4841/4836 |
| SP | 13398 | 13406/13401 | 4711 | 4721/4716 |
| LXX, Cainan removed | 14436 | 14441/14436 | 5285 | 5291/5286 |
| Native LXX | 14896 | 14901/14896 | 5745 | 5751/5746 |
MT and LXX cumulative chains terminate with Moses at 1406 BC. The SP chain includes Joshua’s 110 years and ends at 1296 BC, preserving the 1406 joint. The Actual sums are 12600, 12102, and 13490; their Rounded sums are 12600, 12105, and 13490 respectively. Upper Rounded members add the declared Aaron+5 branch. Actual seven-year envelopes remain separate: MT Creation 14011–14004, SP 13403–13396, LXX-off 14441–14434, and nativeLXX 14901–14894 BC.
4. The three overlapping Creation comparisons
The added MT Cainan is an explicit comparison state. Each row below gives four ordered coordinates and the resulting total width. The rows reuse source positions and overlap.
| Comparison | Rounded ordered coordinates, BC | Rounded width | Actual ordered coordinates, BC | Actual width |
|---|---|---|---|---|
| Native LXX → SP | 14896→14436→13861→13401 | 460+575+460 =1495 | 14896→14436→13858→13398 | 460+578+460 =1498 |
| Native LXX → MT | 14896→14466→14436→14006 | 430+30+430 =890 | 14896→14466→14436→14006 | 430+30+430 =890 |
| MT+Cainan → SP | 14466→14006→13861→13401 | 460+145+460 =1065 | 14466→14006→13858→13398 | 460+148+460 =1068 |
| Sum / arithmetic mean | 1495+890+1065 =3450 | 3450÷3 =1150 | 1498+890+1068 =3456 | 3456÷3 =1152 |
Here 13861 =13401+460 and 13858 =13398+460. The rounded outer LXX-off–SP gap is 1035; the unrounded gap is 1038. The mean equals 460 plus two-thirds of that outer gap:460 +(2/3×1035) =1150, or 460 +(2/3×1038) =1152. The three-year SP shift appears twice, so the mean changes by(2×3)/3 =2.
| Selected regular state | Shem birth, BC | Conquest, BC | Span |
|---|---|---|---|
| Gear 2, normal | 2558 | 1406 | 2558−1406 =1152 |
| Gear 1, declared alternative | 2556 | 1406 | 2556−1406 =1150 |
The aggregate pair and the Shem pair have different derivations. Their correspondence is a structural observation. It does not establish a universal conversion between every five-year rounded block and seven-year Actual envelope.
5. The SP shared-forty construction
| Comparison mode | Selected source, BC | To Exodus 1446 BC | Conversion | To Conquest 1406 BC | Gain |
|---|---|---|---|---|---|
| Regular, Actual Creation-week opening | 4206 | 2760 =69×40 | ×70/69 | 2800 =70×40 | 40 |
| Cumulative, upper Rounded Creation | 13406 | 11960 =299×40 | ×300/299 | 12000 =300×40 | 40 |
| Difference between modes | 13406−4206 =9200 | 11960−2760 =9200 | Two different ratios | 12000−2800 =9200 | 0 change |
The endpoints 4206 and 13406 remain fixed; the converted spans move the target from 1446 to 1406 BC. This is not one common multiplier applied to the 9200 separation. The separate established comparison 13398−4198 =9200 uses an internal Actual cumulative member and a selected regular Gear 1 coordinate; it does not reset the preferred regular Creation boundary 4199.
The regular/cumulative triplet comparison is 13406/13401/13396 minus 4206/4201/4196 =9200 in each position. These triplets assemble Actual and Rounded coordinates for comparison. They are not single transmitted envelopes.
6. The native/generated LXX Flood Mirror
| Construction | BC start | AD end | Civil span | Role |
|---|---|---|---|---|
| Rounded LXX, Cainan removed | 5291 | 5290 | 5291+5290−1 =10580 | Input; 23×460 |
| Expand that span by 25/23 | — | — | 10580×25/23 =11500 | Generated output; gain 920 |
| Rounded native LXX | 5751 | 5750 | 5751+5750−1 =11500 | Native-Cainan input |
| Declared onward conversion | — | — | 11500×25/23 =12500 | Generated output; gain 1000 |
Cainan adds 460 to each side of the civil comparison, producing 920 additional years. The sequence can be written 23×460 →25×460 =23×500 →25×500. The native and generated 11500 share data, so they are not statistically independent witnesses. The 12500 result is a converted span. A bilateral realization, if chosen, must state its generated endpoints; no ancient event is inferred merely from that total.
7. A bounded SP–Book of Jubilees companion
These coordinates use the adopted reconstruction of the Book of Jubilees. They establish the following comparisons within that reconstruction, without proving direct literary dependence on the extant SP.
| Comparison | Coordinates, BC | Result |
|---|---|---|
| SP Creation → BJ Creation, corresponding week openings | 4206−3863 | 343 =7×49 |
| SP Creation → BJ Creation, corresponding week closes | 4199−3856 | 343 =7×49 |
| SP Creation → BJ Eve/Fall, corresponding openings | 4206−3856 | 350 =5×70 |
| SP Creation → BJ Eve/Fall, corresponding closes | 4199−3849 | 350 =5×70 |
| SP G 2 Flood start → BJ Flood | 2893−2549 | 344 |
| SP G 2 Flood start → BJ Ark-building year | 2893−2550 | 343 =7×49 |
| Rounded SP → rounded BJ Fall, upper / lower | 4201−3856 =4196−3851 | 345; ×70/69 =350 |
BJ Creation is 3863–3856 and its Eve/Fall week 3856–3849 BC. Both weeks span seven elapsed years. The 343/344 Flood distinction concerns different event boundaries; it is not a discrepancy in the uniform 343 Creation translation. A proposed deliberate Ark-year compensation remains interpretation.
Sources and further reading
| Source | Relevant use |
|---|---|
| File 18: chronological data | §§3, 4 A, 6 A–6 D: source inputs, SP event/person distinctions, operative LXX Lamech, cumulative tables |
| File 51 a: rounded scaffold | §§3.4, 16.1–16.2, 17.4, 23.7: rounding methods, Aaron+5, adopted SP boundaries |
| File 11: gear protocol | §9.1: established Actual SP 9200→10000 construction |
| File 56: SP Creation decade | §§5–7:11960→12000, 1495→1500, restored-Cainan 12420→12600 |
| File 46: harmonic expansion | §§6 A.3, 6 A.5: bounded repeated expansion and 430/30/430 field |
| File 09: cumulative architecture | §§0.5–0.6, 3 A: Actual envelopes, seasonal Mirror, and foundations |
| File 20: Jubilees witness | BJ source framework and SP affinity; event boundaries remain typed |
| File 53: Jubilees Creation and genealogy | BJ Creation/Fall comparison, seven-year fields, and Jubilee-scaled interpretation |
Read the earlier Shem and the Flood article and its supporting tables for the 120–480–120 and 4300/4900 comparison. The 9900-year bridge article explains the 1650 backbone; the sojourn article explains the 430/215 distinction.
The preserved ReportIV records the longer research discussion. This article follows the current source inputs where a later correction affects that original edition. The full discussion is useful for following the derivations and unresolved proposals; it is not required before reading the introduction.
The arithmetic and comparisons are conditional on the stated source inputs and frames. Providential coherence, ancient intention, and the theological force of an analogy are interpretive questions. These tables do not supply a statistical significance test.