# Flags, levers and disclosures

Companion to `model.md`. Everything here either weakens the model, is a choice
made rather than a number computed, or is a place where the record cannot support
what a reader might want from it. Nothing is buried; each item is cross-referenced
from the main record.

Rebuilt 2 September 2026 alongside model.md.

---

## 1. The error the first draft made, and who found it

The first draft built the whole model from Israel outward: Israelite males, times
the fraction on Adam's line, times a multiple covering Edom, Ishmael, Midian,
Moab, Ammon and Aram. Every one of those is a descendant of Terah. So it counted
one narrow twig of Noah's line and gave every other branch zero.

Genesis 10 and 11 put about eighty founder lines outside Terah's, forking six
hundred to a thousand years earlier. The undercount runs between two and fourteen
times, about five and a half at the centre.

**Mike found it, on 2 September 2026**, from the observation that Abraham had
other sons and that Noah's family had many other lines before Israel exists.

The draft also framed the Genesis 10 question as a choice between two ends: either
the nations descend biologically from Noah's sons, giving five to twenty million
males, or only Terah's line counts. That is a false pair. The institutional
reading says the nations are not biologically Noah's; it does not say Noah's sons
had no descendants. The truth is a dial, and the draft sat at one end of it while
naming the other end as the only alternative.

The dial now appears as A5, the ceiling in model.md §5. It is the largest single
lever in the model.

## 2. What the census reading does and does not decide

**It does not decide footprint size.** Israel's own term is 8% of N, and Terah's
whole cluster is 28%. The first draft said the census page was load-bearing on
this flank. That was wrong.

**It calibrates the model.** Terah's cluster is the one countable Noahic house.
It is what shows that a flourishing line doubles every 39 years, and therefore
what shows that the eighty side lines cannot have grown at anything like that
rate without Noah's descendants outnumbering the world before Moses.

**It carries the whole of model.md §11**, the question of whether the Bible's own
account of Israel in Egypt holds together, which needs no genetics at all.

**And it now has a fourth leg.** Counting the side branches, the face-value
reading of Numbers puts Terah's descendants alone at about 3.4 million men, half
of every man in the world Genesis 10 describes, before one of Noah's other eighty
lines is counted. The face-value reading of Numbers and the institutional reading
of Genesis 10 cannot both stand.

## 2a. A2 is applied more harshly than the reading requires

model.md §2 treats every man entering Israel through the mixed multitude, through
bought slaves, or as a captive as though he were off Adam's male line. That is
right for most of them on this site's reading, since the peoples of Egypt and the
Levant were here before Noah crossed. It is wrong for any who came from a kin
nation, and those men are on the line. The error runs against the argument.

The fraction is applied uniformly to Israel and to Terah's other houses, and it
should be. Two reasons. Israel's reputation for endogamy rests on rules about
wives, which do not touch the male line at all. And the sister peoples took over
lands with people already in them, the same absorption channel, so there is no
ground for giving Israel a higher fraction. Deuteronomy 23:3-8 shows male
admission to Israel was governed rather than absent, with the wrinkle that
Ammonites, Moabites and Edomites are Terahite and on the line anyway.

Scholarship reads Israel as more permeable to male incomers than its reputation
suggests. Christine Hayes (*Gentile Impurities and Jewish Identities*, 2002)
treats Ezra's ban on all Gentile marriage, grounded in a "holy seed" idea of
inherited impurity, as an innovation against an older and more permeable
background rather than the baseline.

## 3. Three central values are chosen, not computed

- **c = 3.0** (model.md §1), from the household reading of "firstborn". See §17.
- **A3 = 2.5** (§3), below the 2.9 the midpoints give. The reason is textual: each
  sister people took over a land that already had people in it, so their
  biological share of their own nation is lower than Israel's.
- **S = 479,000** (§4), the side branches. The floor and ceiling are argued; the
  point between them is a choice, and the flattering direction is low.
- **The quarter share** in the ceiling (§5). Note that the ceiling does not bind
  on any row: the largest N is 1.44 million against a ceiling of 1.73 million. Its
  work is indirect, as the reason the side-branch bracket stops where it does. An
  earlier draft of this record called it the largest single lever, which its own
  arithmetic does not support.

## 4. The side-branch growth rate is the free parameter

S is set by a doubling time that nothing measures. Across the range that could
still be called spreading out, 150 years down to 100, S swings from about 90,000
to about 3.2 million, three orders of magnitude on the low side and past the
ceiling on the high side.

Terah's own rate cannot be borrowed for it, and model.md §4 says why: the tracked
line is tracked because it flourished. That is a selection effect, and using the
survivor's rate for the lines nobody wrote about would be the error the whole
model exists to avoid.

## 5. Cain's line is unconstrained, and so is carried the same way as the side branches

K, Cainite males at 1266 BC, is bracketed 5,000 to 450,000, and the bracket is not
informative: no ancient DNA exists from Mesopotamia in the window 5000 to 1266 BC.

K and S are the same kind of quantity, lines the text says are there that no text
counts. One rule covers both: carry them as brackets or carry neither. Excluding
them is now the choice that flatters the argument rather than the cautious one.

## 6. G: which reconstruction of ancient population, and the disclosure

Settled 2 September 2026: **HYDE, giving G = 82**, with the Census Bureau
compilation's G = 207 printed alongside in every table. The reasoning and the
disclosure are in `sources.md` §1.1. The short form: HYDE is the only series that
can supply the ceiling as well as G and s, and mixing series is what broke the
first draft.

HYDE is also the series that flatters this reading. At G = 82 the central
prediction stays below the size at which a branch would be hard to miss; at
G = 207 it does not. That is why both columns are printed.

## 7. The house-size distribution is censored, and the correction runs against the argument

The 1,091 houses are those that both survived and were sampled. Small surviving
houses that were missed are absent, so the measured spread is shifted toward large
houses and its middle overstates the true middle. Against the true spread, the
predicted branch sits at a **higher** rank than model.md §8 reports, which makes
it more conspicuous, not less. The correction is not applied.

## 7a. The leaf calibration assumes even testing, and testing is not even

One sampled leaf standing for 230,000 living men holds only if testing were spread
evenly across the world's men. It is not. Testing is project-driven, and Near
Eastern and Jewish lineages are heavily over-represented while much of Asia and
Africa is thin.

This flatters exactly the branches the prediction is compared against, since they
are Near Eastern. Taken literally the rate gives J-Z1884 520 million living men,
one man in eight on earth, which is the bias showing. The record therefore
compares leaf counts with leaf counts and prints no men-count for any named
branch.

## 7b. The N men are treated as independent, and they are not quite

P(extinction) = e^(-sN) treats the N men as independent lines. They share ancestry
within the previous sixteen hundred years, so they are not. With N spread across
Israel, Terah's other houses and eighty founder lines in different lands the
correlation is weak, and the conclusion, that survival is certain, does not turn on
it. A reader should still know the form assumes what it does.

## 8. s is anchored, not fitted, and the anchor is loose

s divides 1,091 surviving houses by an estimate of the male population at 5100 BC.
Two features push the true value higher than the figures used: the anchor is
measured over 7,120 years and applied over 3,200, and 1,091 is a sampled floor
rather than a full count. Neither is adjusted for. Both make the survival result
conservative, which now matters little, since survival is certain on every row.

## 9. Where the prediction sits among the houses is read between frozen points

The frozen quantiles are median 1, p75 = 4, p90 = 14, p95 = 31, p99 = 155, largest
3,599. Anything finer is interpolation.

## 10. The visibility mark is a chosen round number

A branch of 10^8 living men is 435 sampled leaves, which would rank in the top
fifteen or twenty of the 1,091. It marks a change in what could be tested, not a
cliff in the data. A reader who prefers 5 x 10^7 moves the line and changes no
conclusion.

## 11. What this record does not claim

It says what a reading of Genesis predicts about the measured male family tree. It
does not say the reading is true, and no figure in it is a probability that the
reading is true. Everything is conditional on the reading throughout.

## 12. Cain's line is in our world, and the ark is not the narrowest point

`pages/can-ancient-dna-test-cains-arrival.html` puts Cain in our world from about
5000 BC; `pages/nations-after-noah.html` says "the flood destroyed the ancient
world, not ours". So Cain's line passes the flood untouched.

Three surviving lines at the ark is the narrowest point of Noah's channel, not of
Adam's line in our world. Figure 2 and the journey counter both need this said, or
the counter dropping to three will read as a claim this site does not make.

## 13. The claim about what the tree shows has inverted

The first draft said the tree's silence is what this reading predicts. On the
rebuilt numbers that holds for the low row only. The central prediction is above
p99 on either reconstruction of ancient population, and crosses the visibility
mark on one of them.

The claim is now that this reading predicts a large branch, forking about 2900 BC,
inside a house of Adam's era. Section 8.1 of the record found three houses on the
whole tree with that shape. This is a harder claim than the one it replaces, and
a more checkable one. It is also a different claim from the one currently on
`pages/can-genetics-find-noahs-family-line.html`, which needs rewording.

The sentence on that page saying the line reaches the present "in a few men no
database has noticed, or in daughters only" is contradicted by the model at every
value of G. It reaches the present with probability indistinguishable from 1 and
in tens of millions of men.

## 14. "No such lineage exists" was too strong

Large young branches are not absent from the tree. R-L151 holds 3,143 of the
17,611 sampled leaves, about 720 million living men, forking at 2850 BC. What is
nearly absent is that size with the predicted structure: 114 branches qualify on
size and date, 13 on nesting, in 3 houses. The structural claim is the one that
survives, and it is stronger than the one it replaces.

## 15. The undersampling escape is gone

A small branch can hide if its region is undersampled. Genesis 10 puts Noah's side
branches in Anatolia, the Aegean, Iran and Egypt, among the better-sampled
populations on the tree. And absorption spread these lines widely: Edom's men were
circumcised into Judea about 125 BC and Herod's house was Idumean; Midian's Kenite
branch settled inside Judah; Aramean and Arab populations absorbed the rest. The
prediction is a line spread across many present-day peoples.

This is also why the T11-F sweep found no Jewish patterning at any lead, and why
none should have been expected.

## 16. The structural count is a filter, not a test, and no size criterion can now be set honestly

The 114 / 13 / 3 count in model.md §8.1 is a filter over node ages, reproduced
against the published T9 diagnostics. It identifies nobody and it is not
preregistered.

**No size criterion is set here, and none can be set honestly at this point.** The
candidate sizes were read before the rebuilt range existed: J-Z1884 at 2,259
leaves, J-Y2919 at 124, J-Z640 at 121. Any criterion chosen now would be chosen
knowing which candidates it admits. On the first draft's numbers a criterion would
have called J-Y2919 a fit and J-Z1884 a refutation; on the rebuilt numbers
J-Z1884 becomes a strain, and the reversal would rightly be read as fitting.

What can be done instead: publish the range, label it as computed after the
candidates were seen, and in the detectability study inject test branches across
the whole span rather than testing a threshold. A sweep fits nothing.

Two things the count does not establish. The corridor geography rule has not been
applied to N-M2126 or E-M4694 at all. And whether T9 and T11 could have seen a
branch of this size and shape is unknown to this record; that is the question that
decides whether the reading is under pressure or merely untested.

## 17. What "firstborn" counts

HALOT on בְּכוֹר: "first-born, oldest offspring... of men and women, first of the
mother, later of the father", citing Hempel and Mendelsohn, and listing Numbers
3:40 and 3:12 among its examples (Koehler et al., Brill, 1994-2000, 131). The
sense the lexicon puts first, and calls the earlier one, is the mother's.

Against it, TDOT (Tsevat, vol. II, 125) holds the womb definition "could not have
been the predominant one", because Israel reckoned primogeniture through the
father, "especially in the case of contemporary (occasional) polygamy".

| reading | firstborn males equal | c is | c comes to |
|---|---|---|---|
| the mother's first child | about half the mothers | twice the sons per mother | 5 to 7 |
| every household has one | the households | the sons per household | about 3 |

**Mike's ruling, 2 September 2026:** the household reading, from Exodus 12:30,
"there was not a house without someone dead". The alternative is offered as a
toggle rather than argued away.

The ruling was made on the text, before any footprint had been computed from it
and before any candidate branch had been compared against a range. The record
notes the sequence because the sequence is what makes the later comparison worth
anything.

Two points against interest. Numbers 3:40-43 does not itself use "opens the womb";
it inherits that definition from 3:12-13, and the NIV of 3:12 reads "in place of
the first male offspring of every Israelite woman", which is the mother
formulation, two verses before the count. And Philip Budd's Word Biblical
Commentary holds that the 22,273 is not a count of living people at all but a
figure worked backward from the redemption price to make a post-exilic argument
about funding the priesthood. That is the modern critical reading and this record
does not answer it.

## 18. The Levite count does not fit c, and this site's own test is what resolves it

Numbers 3:39 gives 22,000 Levite males; 3:43 gives 22,273 firstborn of the other
tribes. At c = 3 that makes Levi about a quarter of all Israel. For Levi to be one
tribe in twelve, c would have to be about 11.

This site's own fingerprint test resolves it. 22,000 ends in three zeroes, the
mark `numbers/census.html` uses to identify a booked figure, shared by 22 of the
24 tribal totals. 22,273 is jagged and the text says "listed by name". So the
firstborn figure is a count and the Levite figure is not, and the Levite number
cannot calibrate c.

That is the fingerprint argument doing work on a case it was not built for, which
is worth stating. A reader who notices the ratio without knowing the test will
think the arithmetic has broken.

## 19. What c does to the face-value reading, on any of its readings

With 22,273 firstborn males and 1,207,100 males of every age, c would be 54.2:
one firstborn for every 54 males, or 54 sons per household. No fertility regime
and no amount of polygamy reaches it. Jamieson, Fausset and Brown registered the
same puzzle in the nineteenth century and offered two rescues the text does not
support.

## 20. The Exodus anchor and the sojourn

The record uses 1266 BC, this site's appendix figure, and a sojourn of 215 years,
following Glen Fritz on the LXX and Samaritan reading of Exodus 12:40. The site's
prose sometimes rounds the Exodus to 1270 BC; the data layer carries 1266.

## 21. What the tree cannot settle

No ancient DNA has been recovered and attributed to Edom, Moab, Ammon, Aram or
Midian. That is a limit of the evidence rather than a gap more work closes.

## 22. A prediction nobody has looked for

If the whole genome was copied and not the Y chromosome alone, then Adam's
mitochondrial DNA is the donor's mother's. Eve was made from Adam, so she carries
it too, and so does every woman of the ancient world descended from her. That is a
prediction on the maternal line, and no study on this site has looked at it. It
dissolves if the wives who boarded the ark were of our world rather than Adam's
line, and this site has not said which they were.

## 23. Section 11.2 was overstated in an earlier draft

The first version of §11.2 read the priestly and Levite haplogroup discordance as
setting a floor under A2, meaning the fraction of Israelite males on Adam's line
could not be near 1. It does not. The discordance bounds admixture accumulated
across three thousand three hundred years, and ordinary unrecorded paternity alone
accounts for most of it. Modern Jewish Y data cannot separate the Exodus era from
the two thousand years after it, so it neither confirms nor constrains A2.

## 24. Mike's rulings on the copy claim, 2 September 2026

**Wording.** "Took from", not "copied", in page prose. This record keeps "copy"
because it is the precise term and because the proposal is named that elsewhere on
the site.

**Pre-matching.** A chromosome created already matching a haplotype our world
would produce later is not excluded by any observation. Mike's ruling, in his own
words: "it is not as fitting as contemporary matching. I don't think it's
impossible, but I think it is less likely. Because of the risk of implying God has
been deceptive." So the road is left open and ranked below contemporary matching,
on a theological ground rather than an empirical one, and the page says which.

**The category.** Grafting, not adoption. A branch grafted into a stock truly
carries the stock's history and is not the stock's offspring. This is the answer to
the objection that the copy road makes Adam's chromosome testify to a quarter of a
million years of descent Adam did not have: every event the chromosome records
happened, in real men, and the only thing misattributed is Adam's own descent.
Eve is the scriptural instance, her body made from Adam without her being his
daughter.

## 25. The Genesis 10 control was removed from the page, 3 September 2026

The page's controls no longer offer "founded the nations biologically". On this
site's reading the peoples of the Genesis 10 lands were already there, so the
only question the model can ask is how large a share of them Noah's lines had
become by Moses' day, and the side-branch control already carries that, capped
where they would outgrow the world Genesis 10 describes (§4, §5). Reading
Genesis 10 as biological descent is the traditional reading that goes with a
global flood and an empty world; on the page it belongs with the global flood's
point, not among the assumptions of this reading. The "largest lever" wording
in §1 above refers to that reading and stands as history.

## 26. The Cainite bracket on the page runs to the ceiling, 4 September 2026

Section 9 of model.md brackets K, Cainite males in 1266 BC, at 5,000 to
450,000, carried on the same footing as the side branches. Mike observed on
4 September that the upper end is inconsistent with the model's own growth
yardstick: 450,000 from one man over 3,700 years is a doubling every 197 years,
slower than the floor the page allows Noah's other lines, while Genesis 4
describes Cain's line as prolific from the start. The page's control for Cain's
line therefore runs to the same ceiling as the side branches, about 1.73
million, the quarter of the Genesis 10 horizon past which Adam's descendants
together stop being a minority, and the readout turns red when the total passes
it. The model's central and low values are unchanged, and the line is still left
out by default. Whether God altered Cain's Y chromosome at the curse is not
settled here; if he did, Cain's descendants form a second bare stalk of their
own, and the count is unaffected.

## 27. The quarter-share ceiling is withdrawn; the check is at Babel

Section 5 of the 2 September record set a ceiling of a quarter of the Genesis
10 horizon on the ground that Noah's descendants had to stay a minority among
the peoples nationhood spread through. On 4 September 2026 Mike observed that
the site nowhere claims that: its reading of Genesis 10 is about the founding of
nations among peoples already there, about 2800 BC, and says nothing about
proportions in Moses' day. The quarter was the record's judgment and is
withdrawn. Section 5 now carries the hard cap only, everyone in the horizon,
and a check at Babel: the people of Sumer at Babel are the site's best estimate
of the numerical extent of Adam's descendants in our world, so Adam's line then is at
most Sumer's population, about 275,000 men on Adams's survey figures. The check passes on
every setting the page allows, by a wide margin, and section 5 records what that
margin implies about who the people of Sumer were.

Three further points from the same conversation are recorded for the model
rather than acted on. Cain's line married into our world's peoples from the
first generation, so on the site's own inheritance result its lifespans and
generation lengths fell to ordinary within a few generations, while Noah's line
kept long generations until Babel; Genesis 10 credits Noah's three sons sixteen
sons between them, ordinary family sizes, so the long generations governed
growth and Cain's line could grow like any settled people. The date this site
gives Lamech's sons, about 4300 BC, is Mike's estimate of the length of Cain's
generations, not a figure from the text, which gives no ages for Cain's line;
the record uses only what the text fixes, that the line was one clan at that
generation. And Sumer at Babel is an upper bound on Adam's line, not an
equality, in Mike's words "the best we have".


## 28. Two ceilings, because Cain's line is not confined to the Genesis 10 lands

Recorded 4 September 2026, evening. Section 5 applied one ceiling to N, the whole
of Adam's line: the 6.9 million men of the Genesis 10 lands. Mike observed on
4 September that this silently confines Cain's descendants to those lands, which
neither the text nor this site's reading requires. Cain crossed into our world
about 5000 BC and had some thirty-seven centuries before the Exodus; his line
could have reached anywhere in the Old World in that time, and the site's own
reading of Genesis 10 is about nationhood spreading through peoples already
present, not about where anyone's descendants lived.

The ceiling is therefore split.

The families Genesis 10 places in those lands keep the old cap, 6.9 million men,
because that is what the lands held.

The whole of Adam's line is capped instead by the measured tree, which is a
stronger and more honest constraint than any population estimate. On this site's
reading Adam's branch sits inside a family of his own era. It cannot be larger
than the family that holds it. The tree carries 1,091 such families and the
largest holds 3,599 of its 17,611 sampled lineages. At 229,970 men per sampled
lineage that is about 828 million men today, so N cannot exceed about 10,093,000
men at 1266 BC on the HYDE growth factor, or about 3,998,000 on the other. The
page computes this at run time from the growth factor a reader has chosen.

Direction: this raises the reachable ceiling on Cain's line from 6.9 million to
about 10.1 million on the site's own settings, which widens the model's upper end.
It is recorded as a widening made at Mike's direction after the question was
raised in conversation, not as a correction of an error.

Two things this does not do. It does not change the model's central or low values,
and Cain's line is still left out by default. And it does not touch the bracket on
K itself, 5,000 to 450,000 men, which section 9 sets and which flags 26 already
records as arguably too low against the model's own growth yardstick.

A note against interest, from the same conversation. Raising this ceiling does not
help the site identify any particular branch. The branch it would most obviously
admit, J-Z1884, was withdrawn on 29 August on separate and better grounds: for it
to be Noah's chromosome, Adam's copy would have had to match two thousand years of
changes that had not yet happened.