Luke’s genealogy includes a name that is absent from the received Masoretic Text of Genesis 11:
… the son of Shelah, the son of Cainan, the son of Arphaxad, …
— Luke 3:35–36, Berean Standard Bible (BSB), excerpt
Read from ancestor to descendant, the order is Arphaxad → Cainan → Shelah. This second Cainan is the subject of the present study. His 460-year lifespan supplies the measure behind a set of relationships between the regular and cumulative chronologies, including two corresponding 16560-year comparisons across the BC–AD boundary.
This is the detailed companion to Cainan and the 16,560-Year Mirror Pattern. The introductory supporting tables provide a shorter reference. Here the textual inputs, insertion rules, selected dates and larger Cainan comparisons are developed together, with the current Unified Chronology files controlling the calculations.
1. The textual witnesses: a name and a lifespan
The second Cainan belongs to the post-Flood genealogy. He must be distinguished from the earlier Kenan, son of Enosh and father of Mahalalel in Genesis 5:9–14, BSB. Luke also calls that earlier figure Cainan in Luke 3:37–38. Keeping the two people distinct is essential when comparing their names, dates and lifespans.
The received Masoretic Text (MT) has Arphaxad father Shelah directly. The Septuagint (LXX) reading represented by Brenton’s translation places Cainan between them. Luke confirms this genealogical position but gives no age for Cainan. The chronological inputs come from Greek Genesis:
And Cainan lived a hundred and thirty years and begot Sala; and Cainan lived after he had begotten Sala, three hundred and thirty years, and begot sons and daughters, and died.
— Genesis 11:13, Brenton Septuagint Translation, Cainan passage included under verse 13 in this edition. Sala is Shelah.
Written separately as a calculation:
130 + 330 = 460 years.
| Witness | Sequence relevant to this study | What it supplies |
|---|---|---|
| MT Genesis 11:12–13, represented here by the BSB | Arphaxad → Shelah | Arphaxad’s 35 years before Shelah and 403 afterward. |
| LXX Genesis 11:12–13, represented here by Brenton | Arphaxad → Cainan → Sala | Cainan’s 130 years before Sala and 330 afterward. |
| Luke 3:35–36, BSB | Shelah ← Cainan ← Arphaxad | Cainan’s genealogical position, without age figures. |
The reconstruction used below retains the other MT ages and inserts Cainan’s LXX figures. It is an MT-based comparison with Cainan restored, not an assertion that the received MT contains him. It also differs from adopting the whole LXX chronology: Brenton’s Arphaxad age, for example, is not the MT age of 35. The Samaritan Pentateuch is another distinct textual witness; its chronological figures are not used to establish the present 16560-year pair.
The Second Cainan introduction explains the wider textual issue. The present study asks a narrower question: what happens within the declared chronological model when this one generation is included?
2. Regular chronology: inserting 130 years
Regular chronology follows the ages at which the ancestral line continues. Its generations overlap: a father can live for centuries after his son is born. Cainan therefore contributes 130 years to the birth sequence, even though his entire life lasts 460.
Our selected regular setting has 430 years in Egypt and no additional sixty-year Terah adjustment. Shelah remains at 2421 BC. In the normal MT sequence, Arphaxad is born at 2456 BC, 35 years before Shelah. In the restored sequence, Arphaxad moves to 2586 BC, Cainan is born 35 years later at 2551 BC, and Shelah follows after another 130 years.
Cainan · detailed study · Figure 1
Regular chronology adds 130 years
Ages at fatherhood · regular MT-based comparison
Normal MT
→
MT-based with Cainan restored
→
→
2586 − 2456 = 130
Cainan’s full life remains 130 + 330 = 460.
Full supporting table · File 18 · File 20
View or download the image version of Figure 1
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| Setting | Arphaxad birth | Cainan birth | Shelah birth | Fatherhood intervals |
|---|---|---|---|---|
| Normal MT | 2456 BC | — | 2421 BC | 35 |
| MT-based with Cainan restored | 2586 BC | 2551 BC | 2421 BC | 35 + 130 |
The unchanged downstream point makes the adjustment easy to see. 2586 − 2456 = 130, while Shelah remains at 2421 BC. The restored Cainan’s own life is:
2551 BC → 2421 BC → 2091 BC = 130 + 330 years.
His birth-to-death interval is therefore 2551 − 2091 = 460. This does not make the regular insertion +460; the inserted interval before his son’s birth is still +130. File 18 §1.6 explicitly distinguishes these two uses.
The extra sixty-year Terah adjustment and the shorter Egyptian-sojourn branch generate other permitted regular dates. They are listed in Reference Table A. The 16560-year comparison below uses the selected 2551–2091 BC life, not a mixture of those alternatives.
3. Cumulative chronology: inserting the whole 460-year life
Cumulative chronology uses a different construction. It places complete lifespans end to end, creating a schematic sequence for comparison. At a cumulative junction, one figure’s death meets the next figure’s birth. This is a rule of the calculation, not a statement that the son was historically born on the day his father died.
Arphaxad’s MT lifespan is 35 + 403 = 438 years (Genesis 11:12–13, BSB). In the cumulative Moses-line tables, the base sequence runs from Arphaxad at 4831 BC to Shelah at 4393 BC. With Cainan included, it runs from Arphaxad at 5291 BC, through Cainan at 4853 BC, to the same Shelah coordinate, 4393 BC.
Cainan · detailed study · Figure 2
Cumulative chronology adds 460 years
Complete lifespans · Moses-line Nisan coordinates
Base cumulative MT
→
Cumulative MT with Cainan restored
→
→
5291 − 4831 = 460
Arphaxad’s 438-year lifespan remains unchanged.
Full supporting table · File 18 · File 09
View or download the image version of Figure 2
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| Moses-line setting | Arphaxad | Cainan | Shelah | Lifespans joined |
|---|---|---|---|---|
| Base cumulative MT | 4831 BC | — | 4393 BC | 438 |
| Cumulative MT with Cainan restored | 5291 BC | 4853 BC | 4393 BC | 438 + 460 |
The two checks are 4831 − 438 = 4393 and 5291 − 438 − 460 = 4393. The earlier part of the cumulative framework moves back by 460 years. The downstream framework, beginning with Shelah, stays fixed.
The two insertion rules can now be compared directly:
Regular: add 130. Cumulative: add 460. Difference: 460 − 130 = 330.
That difference is the part of Cainan’s life after Shelah’s birth. It belongs to the cumulative sum but not to the added interval in the regular birth sequence.
The Creation envelope moves as a whole
The cumulative Creation framework likewise shifts by 460. Its base envelope is 14011–14004 BC; with Cainan it is 14471–14464 BC. The opening, Year 6 position and closing boundary remain distinct:
| Position | Base cumulative MT | With Cainan | Difference |
|---|---|---|---|
| Opening boundary | 14011 BC | 14471 BC | 460 |
| Year 6 position | 14006 BC | 14466 BC | 460 |
| Closing boundary | 14004 BC | 14464 BC | 460 |
All three positions move by the same amount. Both envelopes remain seven years wide, and their Year 6 positions lie five years after their openings. File 09 §3A.1 supplies the corresponding positions; File 18 §§6A–6B supplies the cumulative tables.
These are cumulative coordinates. The regular Creation framework belongs to its own calculation. Likewise, the cumulative opening 14011 BC must not be replaced by 14006 BC or 14004 BC while treating the result as the same comparison. The selection of the opening matters for the annual-coordinate illustration below.
4. The two corresponding 16560-year spans
The central comparisons are stated explicitly in File 22 §6.1:
| Regular starting point | AD comparison target | Civil calculation | Span |
|---|---|---|---|
| Cainan’s birth: 2551n BC | AD 14010n | 2551 + 14010 − 1 | 16560 |
| Cainan’s death: 2091n BC | AD 14470n | 2091 + 14470 − 1 | 16560 |
Here n means Nisan, the spring setting. The source classifies these rows as Mirror corroboration. They compare regular Cainan dates with specified AD-side targets and support the larger 460-year structure.
The civil calculation is BC number + AD number − 1. In ordinary historical notation, 1 BC is followed by AD 1, so adding the printed numbers without subtracting one would overcount the interval. Thus:
2551 + 14010 − 1 = 16560
2091 + 14470 − 1 = 16560.
Cainan · detailed study · Figure 3
Two equal spans; both ends move by 460
Canonical Mirror corroboration · n = Nisan (spring)
16560 = 23 × 720
Equal changes at both ends preserve the span.
Full supporting table · File 22 · File 09 · File 00
View or download the image version of Figure 3
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The equal lengths follow from the matching change at both ends. Moving from Cainan’s birth in 2551 BC to his death in 2091 BC advances 460 years. Moving from AD 14010 to AD 14470 also advances 460 years. The two spans therefore retain the same length:
(2551 − 460) + (14010 + 460) − 1 = 16560.
The subtraction and addition of 460 cancel. This is why the central illustration shows two equal bars displaced by the same interval, rather than two unrelated numerical totals.
The common span factors as 16560 = 23 × 720. Since Cainan’s life is 460 = 23 × 20, it also follows arithmetically that 16560 = 36 × 460. This second factorization simply expresses the span in lifespan-sized units; it introduces neither an additional dated event nor a claim that thirty-six such lives are counted in the biblical genealogy.
5. What the Mirror comparison does—and what generates its numbers
A calculation across the BC–AD boundary has two separate tasks: select the endpoints, then measure their separation. The civil formula measures a pair of already selected endpoints. By itself, it does not tell us which date should be reflected or which AD target should be chosen.
The target numerals in the Cainan comparison have a recognizable connection to the cumulative Creation openings. Ordinary astronomical numbering calls 1 BC year 0, 2 BC year −1, and, more generally, B BC year 1 − B. AD year numbers remain unchanged. Reflecting a signed integer changes its sign:
| Cumulative opening | Astronomical year number | Reflected year number | Annual label |
|---|---|---|---|
| 14011 BC | −14010 | +14010 | AD 14010 |
| 14471 BC | −14470 | +14470 | AD 14470 |
This is an annual-coordinate illustration. It explains how the numerals 14010 and 14470 correspond to the Creation-opening labels 14011 and 14471. No month or seasonal suffix is derived by this integer operation. The n suffixes in the canonical 16560-year rows are retained from File 22 itself.
Seasonal pairs require their own rule
File 09 Appendix A distinguishes standalone numeric-year counterparts from paired seasonal reflection. Its example is the Conquest pair 1407t/1406n BC, where t means Tishri, the autumn setting. The paired AD display is AD 1406t/1407n: autumn followed by the next spring.
| Comparison | Supplied source and target | Civil span |
|---|---|---|
| Standalone Nisan counterpart | 1406n BC → AD 1406n | 1406 + 1406 − 1 = 2811 |
| Paired autumn component | 1407t BC → AD 1406t | 1407 + 1406 − 1 = 2812 |
| Paired spring component | 1406n BC → AD 1407n | 1406 + 1407 − 1 = 2812 |
The paired construction preserves the half-year relationship between autumn and spring. The pair as a whole is reflected; the two matched-season span lines are not individual point-reflection arrows. A source row cannot be converted into this paired construction merely by subtracting one from every BC label.
For the Cainan study, File 22 supplies its own endpoints and labels their role as corroboration. Its local Mirror rule directs us to use civil cross-axis arithmetic unless a formal Mirror protocol is explicitly opened. We therefore retain its stated rows, verify their spans, and keep the annual illustration separate from File 09’s full seasonal proof. The Mirror introduction develops the wider distinctions.
Neither Cainan-to-target row means that Cainan’s birth or death is the direct reflection of that row’s distant AD endpoint. Nor do those AD coordinates predict future events. They function as comparison targets within the chronological construction.
6. The 2300-year transfer: the same life in two frameworks
A second exact relationship remains entirely on the BC side. The cumulative Cainan birth envelope is 4858–4851 BC, and the cumulative death / Shelah-birth envelope is 4398–4391 BC. For this comparison, File 22 §6.1 selects the lower members, 4851 and 4391 BC.
Those selected members are two years below the Moses-line entries, 4853 and 4393 BC, used in §3. An envelope contains several defined positions; selecting one must not silently change another.
| Comparison | Cumulative lower member | Regular member | Calculation |
|---|---|---|---|
| Birth to birth | 4851 BC | 2551 BC | 4851 − 2551 = 2300 |
| Death to death | 4391 BC | 2091 BC | 4391 − 2091 = 2300 |
Cainan · detailed study · Figure 4
Matching endpoints lie 2300 years apart
Selected lower cumulative envelope members → regular restored life.
from the BC label
from the BC label
4851 − 4391 = 460
2551 − 2091 = 460
Corresponding endpoints: 2300 = 5 × 460
Full supporting table · File 22 · File 18
View or download the image version of Figure 4
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Both frameworks preserve a 460-year interval:
4851 − 4391 = 460; 2551 − 2091 = 460.
Both corresponding beginnings and endings are separated by 2300 = 5 × 460. This is a translation between selected cumulative and regular coordinates, not a conversion of cumulative dates into an ordinary historical biography. Shelah’s cumulative birth is the junction at the end of Cainan’s schematic life; regular Shelah is born while Cainan is still alive, at Cainan’s age 130.
The endpoint selection also explains why nearby figures cannot simply be substituted. The upper envelope members 4858 and 4398 would yield 2307, not 2300, against the same regular dates. The ordinary Moses-line members 4853 and 4393 would yield 2302. The canonical 2300-year comparison uses the lower members expressly identified for it.
These are same-side BC calculations. No subtraction of one is applied here. The civil BC–AD formula and the completed-boundary convention in the next section serve different purposes.
7. Jared and the 460-year ladder
The 460-year measure also appears before the Flood. Adding the MT ages at fatherhood from Adam to Jared gives:
130 + 105 + 90 + 70 + 65 = 460.
The five inputs are listed with direct Scripture links in Reference Table B. This is the age-based reason for saying that Jared is born when Adam is 460 years old. It does not require importing a Cainan age into Genesis 5.
Literary context. 1 Enoch 6:6, R. H. Charles, places the Watchers’ descent in Jared’s days. Jubilees 8:1–4, R. H. Charles, names Kainam after Arphaxad and describes his discovery of writings containing the Watchers’ teachings. These extra-biblical traditions explain the “Watcher” language used by File 22. The literary association is distinct from the arithmetic. Neither passage dates the Watchers’ descent specifically to Jared’s birthday, and Jubilees’ AM figures are not substituted for the MT-based dates in this study.
Forwarded envelopes and completed boundaries
The canonical cumulative comparison uses the following forwarded seven-year envelopes:
| Figure or junction | Forwarded cumulative envelope |
|---|---|
| Jared, base | 9459–9452 BC |
| Jared, with Cainan restored | 9919–9912 BC |
| Second Cainan’s cumulative birth | 4858–4851 BC |
| Cainan’s cumulative death / Shelah birth | 4398–4391 BC |
File 22 distinguishes endpoint-label forms from completed boundary spans. This distinction governs its Jared ladder:
| Comparison | Endpoint-label form | Completed boundary span | Units of 460 |
|---|---|---|---|
| Base Jared → Cainan birth | 4601 | 4600 | 10 |
| Base Jared → Cainan death / Shelah | 5061 | 5060 | 11 |
| Restored-Cainan Jared → Cainan birth | 5061 | 5060 | 11 |
| Restored-Cainan Jared → Cainan death / Shelah | 5521 | 5520 | 12 |
Cainan · detailed study · Figure 5
The completed ladder: 10, 11, 11, 12
One block = 460 completed years · source-defined boundary counts.
Completed boundary counts and endpoint-label forms remain distinct.
Full supporting table · File 22 · File 18
View or download the image version of Figure 5
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For example, the corresponding upper labels 9459 and 4858 differ by 4601. The canonical completed-boundary reading is 4600, or ten units of 460. Similarly, 5061 is the label form associated with 5060 completed years, and 5521 with 5520 completed years. The last column carries the intended harmonic comparison.
This is a specific counting convention attached to the forwarded envelopes. It is not a rule to subtract one from every same-side BC difference. Cainan’s ordinary regular lifespan remains 2551 − 2091 = 460, and the lower-member transfer remains 4851 − 2551 = 2300.
Moving from Cainan’s birth to his cumulative death adds one 460-year unit. Restoring Cainan to the earlier Jared framework likewise adds one unit. That is why the completed ladder has the arrangement 10, 11, 11, 12. The two middle comparisons match for a stated structural reason.
The older approximate comparison involving Jared at 9454 BC and a value near 4831 BC does not carry this argument. The current canon replaces it with the explicitly labeled envelopes and completed-boundary values above.
8. The earlier Kenan and the second Cainan
A related sequence uses the repeated name before and after the Flood. Here the chronological setting must be stated afresh: regular MT with Cainan restored, selecting Gear 3 for the earlier Kenan. File 11 §4.1 gives the progression from the ordinary Kenan birth label 3789 BC, through the +130 restoration to 3919 BC, and then the Gear-3 +2 selection to 3921 BC.
The +130 restoration and the +2 Gear choice are separate operations. The resulting 3921 BC coordinate is not a replacement for the ordinary unadjusted Kenan date elsewhere on the site.
Kenan lives 910 years (Genesis 5:14, BSB). In the selected sequence, his death is 3921 − 910 = 3011 BC. A gap of 460 years then leads to the second Cainan’s birth in 2551 BC; Cainan’s own life supplies another 460 years, ending at 2091 BC.
Cainan · detailed study · Figure 6
Two lives and the interval between them
Regular MT with Cainan restored · earlier Kenan in Gear 3.
910 + 460 + 460 = 1830
Birth to birth: 3921 − 2551 = 1370
Two lifespans: 910 + 460 = 1370
Full supporting table · File 11 · File 18 · File 22
View or download the image version of Figure 6
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| Selected event | BC date | Interval to next event | What the interval counts |
|---|---|---|---|
| Earlier Kenan’s birth | 3921 BC | 910 | Kenan’s lifespan |
| Earlier Kenan’s death | 3011 BC | 460 | Gap before second Cainan’s birth |
| Second Cainan’s birth | 2551 BC | 460 | Cainan’s lifespan |
| Second Cainan’s death | 2091 BC | — | End of selected sequence |
The whole sequence is 910 + 460 + 460 = 1830. Two distinct measures within it also equal 1370:
- Birth to birth: 3921 − 2551 = 1370.
- Sum of the two lifespans: 910 + 460 = 1370.
The first includes Kenan’s life and the intervening gap. The second adds Kenan’s and Cainan’s lives. Their equality is meaningful within the construction, but they do not count the same stretch of time. Both can be written 1370 = 10 × 137.
File 18 §1.3.7 and File 22 §7.7 preserve this distinction. They also relate Kenan’s age 70 at Mahalalel’s birth to a 1300-year interval from that son’s selected birth coordinate, 3851 BC, to Cainan at 2551 BC: 70 + 1300 = 1370. This is a qualified extension of the Cainan comparison, with its Gear setting made explicit.
9. Reading the pattern within the genealogical story
The relationships share a small set of measures. Cainan’s life supplies 460; five such units give the 2300-year transfer; the Jared ladder expresses ten, eleven and twelve units; and the two canonical Mirror comparisons each give 16560. The regular insertion uses the 130 years before Shelah’s birth, while the cumulative insertion uses the whole life.
The biblical and extra-biblical witnesses also give the figures literary context. Luke carries the genealogy through Cainan toward Jesus. The Enochic and Jubilees traditions connect Jared and Kainam with the Watcher story. These associations make the numerical comparisons relevant to questions of continuity, transgression and restoration; they do not supply the arithmetic in place of the stated dates.
Within this model, the repeated 460-year measure can be read as a structural correspondence joining different chronological frameworks. The two equal Mirror spans are especially clear because their equality follows from matching changes at both ends. The theological interpretation concerns what that correspondence may signify. It does not establish an ancient editor’s motive for including or omitting Cainan, and no statistical probability is claimed here.
A useful reading therefore keeps three levels visible: the names and ages supplied by the texts, the declared rules used to construct the chronology, and the interpretation of the resulting relationships. The tables allow each level to be examined without having to reconstruct a long exploratory dialogue.
Reference tables and source notes
A. The four regular restored-Cainan settings
File 18 §1.3.1 gives four permitted states. Each retains 130 years to Shelah’s birth and a total lifespan of 460. The second row is used for the present Mirror comparison.
| Setting | Shelah’s birth | Cainan’s birth | Cainan’s death | Use here |
|---|---|---|---|---|
| 430 Egypt; +60 Terah | 2481 BC | 2611 BC | 2151 BC | Alternative |
| 430 Egypt; no extra 60 Terah | 2421 BC | 2551 BC | 2091 BC | Selected |
| 215 Egypt; +60 Terah | 2266 BC | 2396 BC | 1936 BC | Alternative |
| 215 Egypt; no extra 60 Terah | 2206 BC | 2336 BC | 1876 BC | Alternative |
Changing the sojourn or Terah setting changes the BC placement. The supplied AD targets must not simply be retained while claiming that every variant produces the same 16560-year result.
B. The five ages from Adam to Jared
| Father | Son in the line | Father’s age | Verified passage |
|---|---|---|---|
| Adam | Seth | 130 | Genesis 5:3, BSB |
| Seth | Enosh | 105 | Genesis 5:6, BSB |
| Enosh | Kenan | 90 | Genesis 5:9, BSB |
| Kenan | Mahalalel | 70 | Genesis 5:12, BSB |
| Mahalalel | Jared | 65 | Genesis 5:15, BSB |
Total: 130 + 105 + 90 + 70 + 65 = 460. These are MT-based ages, verified in the linked BSB edition. They are given as digit-based calculations; no translation wording has been rewritten inside a quotation.
C. Two larger canonical comparisons
The detailed source material also preserves the following, with separate classifications.
The 7800-year separation. File 11 §4.2 and File 22 §7.7 compare the selected cumulative Kenan control coordinate 11721 BC with the restored-Cainan Gear-3 regular Kenan birth at 3921 BC:
11721 − 3921 = 7800 = 60 × 130.
The cumulative coordinate is a selected member of the Kenan-with-Cainan framework. It is not the ordinary Moses-line coordinate, 11719 BC. The span 7800 is a separation between frameworks, while Kenan’s lifespan is 910 = 7 × 130. Sharing the factor 130 does not make those two quantities equal.
The 6900-year composite. File 22 §7.10 identifies a birth-transfer composite, 4600 + 2300 = 6900 = 15 × 460. The larger argument associates the 4600 component with the Jared/Cainan comparison and the 2300 component with the transfer to regular Cainan’s birth. File 11 §5.2 explicitly guards its treatment as a composite.
| Component | Registered calculation | Result |
|---|---|---|
| Watcher-loop comparison, Files 11 §5.1 and 22 §7.9 | 9459 − 4859 | 4600 |
| Birth-form transfer, File 22 §§6.1, 7.10 | 4851 − 2551 | 2300 |
| Composite of the two measures | 4600 + 2300 | 6900 |
The first row’s 4859 BC target and the second row’s 4851 BC starting member are different coordinates. These rows therefore must not be drawn as one uninterrupted date sequence. Direct subtraction 9459 − 2551 gives 6908, while 9459 − 2091 gives 7368; neither is the composite 6900.
The source’s exact conversions—6900 × 70/69 = 7000, 6900 × 25/23 = 7500, and 2300 × 25/23 = 2500—convert the stated measures. They do not by themselves generate new event dates. This keeps the composite useful while preventing it from being mistaken for an ordinary elapsed span.
D. Person and event figure index
Each figure links directly to its full table. Scripture links identify the person or narrative context; the reconstructed dates remain sourced to the chronological controls.
| Person / event / position | Linked figures and tables | Classification and context |
|---|---|---|
| Arphaxad | Figure 1 · table; Figure 2 · table | Predecessor; regular fatherhood age and cumulative lifespan remain distinct; Genesis 11:12–13, BSB |
| Second Cainan | Figure 1 · table; Figure 2 · table; Figure 3 · table; Figure 4 · table; Figure 5 · table; Figure 6 · table | Post-Flood person; MT-based comparison with LXX Cainan restored; Luke 3:35–36, BSB |
| Shelah / Sala | Figure 1 · table; Figure 2 · table; Figure 4 · table | Regular birth and separate cumulative junction; Genesis 11:13, Brenton |
| Regular insertion | Figure 1 · table | Age at fatherhood; +130 upstream |
| Cumulative insertion | Figure 2 · table | Whole lifespan; +460 upstream |
| Cainan’s regular birth | Figure 3 · table; Figure 4 · table; Figure 6 · table | Selected restored regular birth at 2551 BC; Genesis 11:13, Brenton |
| Cainan’s regular death | Figure 3 · table; Figure 4 · table; Figure 6 · table | Selected restored regular death at 2091 BC; Genesis 11:13, Brenton |
| AD 14010n target | Figure 3 · table | Mirror comparison coordinate; no narrative event |
| AD 14470n target | Figure 3 · table | Mirror comparison coordinate; no narrative event |
| BC–AD boundary | Figure 3 · table | Civil notation boundary; no year zero |
| Cumulative Creation opening | Figure 3 · table | Annual-coordinate correspondence; seasonal suffixes not generated by integer sign flip |
| Cumulative Cainan birth | Figure 4 · table; Figure 5 · table | Forwarded envelope 4858–4851 BC; 2300 transfer selects lower member |
| Cumulative Cainan death / Shelah birth | Figure 2 · table; Figure 4 · table; Figure 5 · table | Moses-line 4393 BC; forwarded envelope 4398–4391 BC; 2300 transfer selects lower member |
| Jared | Figure 5 · table | MT age sum to birth: 460; cumulative base and restored envelopes separately labeled; Genesis 5:15, BSB |
| Completed-boundary ladder | Figure 5 · table | Source-defined 10/11/11/12 units; endpoint-label forms listed separately |
| Earlier Kenan | Figure 6 · table | Son of Enosh; father of Mahalalel; distinct from second Cainan; Genesis 5:9–14, BSB |
| Earlier Kenan’s selected birth | Figure 6 · table | 3921 BC only in the declared restored-Cainan Gear-3 setting; Genesis 5:9, BSB |
| Earlier Kenan’s selected death | Figure 6 · table | 3011 BC follows the selected 3921 BC birth and 910-year life; Genesis 5:14, BSB |
| Gear-3 selection | Figure 6 · table | Earlier Kenan: 3789 + 130 restoration + 2 Gear selection = 3921 BC |
Download the supplied calculation tables (CSV):
- Lifespan table (CSV)
- Creation table (CSV)
- Mirror table (CSV)
- Annual table (CSV)
- Transfer table (CSV)
- Regular table (CSV)
- Cumulative table (CSV)
- Envelopes table (CSV)
- Ladder table (CSV)
- Kenan table (CSV)
- Variants table (CSV)
- Jared Ages table (CSV)
- Methods table (CSV)
- Factorizations table (CSV)
Download all calculation data and SVG sources (ZIP). The publication package contains CSV tables, vector and raster figures, and the machine-readable person/event index.
E. Sources and further reading
| Source | Controlling contribution |
|---|---|
| File 22: Cumulative MT Harmonics, §6.1 and §§7.5–7.10 | Central 16560-year pair, 460/2300 relationships, completed-boundary ladder, Kenan comparison and composite classification. |
| File 18: Chronological Data Tables, §§1.3.1, 1.3.7–1.3.8, 1.6 and 6 | Variant boundaries, regular and cumulative insertion rules, table entries and envelope members. |
| File 09: Cumulative Architecture, §3A.1 and Appendix A | Creation framework and distinctions among annual, standalone and paired seasonal constructions. |
| File 11: Three-Gear Protocol, §§4–5 | Kenan’s Gear-3 selection, cumulative Kenan control coordinate, 2300 transfer and composite guard. |
| File 00: Repository Foundation, §3.9 | Separation of the Mirror principle from ordinary civil cross-axis span arithmetic. |
| File 20: Jubilees as a Fourth Witness, §7A.4 and §7A.10 | MT-preserving Cainan graft and the 460-year Adam-to-Jared age sum; BJ dates remain in their own framework. |
| Genesis 5, BSB · Genesis 11, BSB · Luke 3, BSB | MT ages and New Testament genealogy. |
| Genesis 11, Brenton Septuagint | Cainan’s LXX age figures and the name Sala. |
| 1 Enoch 6, Charles · Jubilees 8, Charles | Extra-biblical literary context; their dates are not imported into the present calculations. |
For a shorter overview, return to Cainan and the 16,560-Year Mirror Pattern. For the foundational methods, see the Second Cainan, Cumulative Biblical Chronology and the Chronological Mirror.
Scripture quotations: Berean Standard Bible (BSB), public domain. The Genesis 11 quotation is from the public-domain Brenton Septuagint Translation. Extra-biblical references identify R. H. Charles’s translations separately. Scripture wording and number formatting are preserved; calculations and literary summaries are editorial prose. No translators’ notes are quoted.