# Paternal nesting: first result

7 September 2026. Exploratory secondary analysis, not preregistered. Website pages have not been changed for this test.

## Calculation

Hammer et al. (2009), Figure 1, reports 215 self-identified Cohanim. I transcribed its Cohanim column and grouped the entries into deep paternal branches. The complete transcription and reproducible calculation are in `run.py` and `results.json`.

| Deep branch | Sampled men |
|---|---:|
| E | 15 |
| G | 7 |
| H | 4 |
| I | 1 |
| J1 | 99 |
| J2 | 63 |
| L | 1 |
| Q | 2 |
| R | 20 |
| T | 3 |
| Total | 215 |

A single recent paternal founder cannot span these branches under ordinary Y inheritance. Even allowing every member of the largest branch to belong to that founder gives:

**215 − 99 = 116 men, or 54.0%, necessarily outside that proposed single-founder lineage.**

This is a lower bound on exclusions. Finer resolution might exclude more; it cannot establish that the remaining 99 are Aaronic. Source: [published Figure 1](https://link.springer.com/article/10.1007/s00439-009-0727-5/figures/1).

## What is tested

The strict identification of all sampled modern Cohanim with one biological paternal founder in Aaron's period is incompatible with these assignments under ordinary inheritance. This is not the same as testing whether some Cohanim descend from Aaron. That weaker proposition remains unidentified.

The fraction describes this sample only. It is not a worldwide estimate, a probability the hypothesis is false, a per-generation paternity error rate, or evidence that any named person has a particular ancestry. It also does not imply that these excluded men lack descent from Noah: exclusion from Aaron's line is a different claim. Nor does it establish the mechanism by which multiple paternal ancestries came to share priestly status.

The biological assumption concerns ancestry after Aaron, in our world. Unknown mutation rates before Noah's crossing cannot remove this later incompatibility. Nevertheless, the result uses the established deep phylogeny and ordinary mutation process; it is not independent of all evolutionary assumptions. Arbitrary chromosome replacement or radically different post-Aaron mutation processes would require a different, specified model.

## Implications for the proposed nesting test

The required relationship is between biological descendant sets: Aaron's descendants are a subset of Levi's, and Levi's a subset of Noah's. It does not require the sampled social categories called Cohen and Levite to form those sets, nor three visibly distinct named haplogroups. A sampled family can have a younger common ancestor than its biblical founder when earlier branches leave no sampled descendants.

We have not obtained an independent identification of the Aaronic or Levitic genetic set. Selecting the most frequent lineage and naming its ancestor Aaron would build the answer into the test. Likewise, choosing whatever subset fits the genealogy and then treating the fit as evidence is circular.

The prominent J1 Cohen lineage and R1a Ashkenazi Levite lineage cannot both identify biological Aaron and biological Levi under ordinary inheritance. Their deep separation conflicts with that joint identification, not with every possible identification. The existing results do not determine which, if either, carries those ancestries. The relevant Levite evidence is [Rootsi et al. 2013](https://www.nature.com/articles/ncomms3928) and [Behar et al. 2017](https://www.nature.com/articles/s41598-017-14761-7).

This limits the bridge from the biblical census to modern sampling. The conditional count of 4,363 ancient priests and Levites is not overturned by modern diversity, but modern membership cannot automatically identify their biological descendants.

## Audit trail and limits

An initial calculation using only consistent rounded prose percentages gave a weaker bound of 59 exclusions. The reported 6.1% for one category did not reconcile with n=215 under standard rounding. Figure 1 supplies its actual count, 13, and the complete remaining counts, superseding that provisional calculation. The 21 positive categories sum exactly to 215. Grouping J2 subcategories together deliberately avoids overstating incompatibility among every published category.

This analysis reuses published assignments; it is not a new sequence analysis. It does not estimate a likelihood allowing genotyping errors, an adoption process, differential reproductive success or ascertainment. Consequently no posterior odds for Noah candidates are reported. No YFull website access was used.

One search excerpt discussing the R1a/J1 discrepancy came from a reader comment on the 2017 article, not its authors. That comment is not evidence for the historical mechanism and has not been used as such.

## Conclusion

The test produces a real negative result for using modern priestly status as a universal biological ancestry label. It cannot yet test the necessary biblical nesting itself, because the required genetic family identities are not independently established. A further candidate ranking would not repair that missing identification. Evidence linking a specific paternal pedigree to independently contextualised ancient samples would materially improve the test; another census total alone would not.