Pavlov V. M. © 2026 All rights reserved.
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The paper presents a fundamental paleogenetic study of the nature of the North Eurasian (steppe and forest-steppe) component in the gene pool of the creators of the Mycenaean civilization of the Late Bronze Age in mainland Greece (Greece_Achaea_LBA) and the charioteer warriors of the Sintashta culture of the Southern Urals (Russia_Chelyabinsk_MLBA_Sintashta) [1.10, 1.12].
The hypothesis of the structural identity of these components with modern autochthonous populations of the Volga-Oka interfluve was tested using the formal mixture modeling method
based on \(f_{4}\)-statistics matrices (qpAdm) on the full-size 1240K v66 reference panel from Harvard Reich Lab [1.12, 1.15]. A cascade of mathematical singularities was revealed: with a complicated five-dimensional contour of right (outgroup) populations, including the deep Eurasian calibrator ANE (Karitiana), modern relict populations of Erzya (\(p = 0.948\)) and Moksha (\(p = 0.578\)) demonstrate complete coordinate equivalence (\(weight = 1.0\)) with the Mycenaean group [1.12].
$$ \color{blue}{\textbf{THE LAW OF GENETIC COMMINGLING AND THE SINGULARITY OF THE VOLGA-OKA SUBSTRATE.}} $$
Keywords: qpAdm, 1240K v66, Arsa, Seima-Turbino phenomenon, commingling of contrasting environments,
Doggerland, Mesolithic, Yamnaya culture, Poltavka culture, Srubna culture, Sintashta, Mycenae, Rigveda, Erzya, Moksha.
\(\color{blue}{\textbf{ ABSTRACT (ABSTRACT)}}\) \(\color{blue}{\textbf{ }}\)
EXPLANATIONS about the work \(qpAdm\)see Appendix 1.
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab1} & \textbf{Left Population} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Greece\_Achaea\_LBA} & \text{Erzya} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 0.725 & \mathbf{0.948} \\
\hline
\text{Greece\_Achaea\_LBA} & \text{Moksha} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 2.880 & \mathbf{0.578} \\
\hline
\end{array}
$$
Inverted modeling of Sintashta has proven that modern Erzyans by 126% (\(Z = 15.6, p = 0.267\)) and Mokshas by 125% (\(Z = 17.3, p = 0.789\)) autosomal assemble the Ural Paleogene of the Bronze Age, completely displacing the synchronous Potapov culture into the region of negative values [1.12].
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab2} & \textbf{Left Populations} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Sintashta} & \text{SamaraSrubnaya} & 1.000 & 1.23 \times 10^{-12} & 8.13 \times 10^{11} & 3.47 & \mathbf{0.482} \\
\hline
\text{Sintashta} & \text{FatyanovoBalanovoCW} & 1.000 & 1.89 \times 10^{-12} & 5.29 \times 10^{11} & 233.0 & \mathbf{3.03 \times 10^{-49}} \\
\hline
\text{Sintashta} & \text{SamaraYamnaya} & 0.763 & 0.116 & 6.57 & 1.61 & \mathbf{0.658} \\
& \text{Moksha} & 0.237 & 0.116 & 2.04 & & \\
\hline
\text{Sintashta} & \text{SamaraYamnaya} & 0.950 & 0.174 & 5.45 & 4.19 & \mathbf{0.242} \\
& \text{Erzya} & 0.050 & 0.174 & 0.29 & & \\
\hline
\text{Sintashta} & \text{SamaraPotapovka} & -0.250 & 0.072 & -3.45 & 1.05 & \mathbf{0.789} \\
& \text{Moksha} & 1.250 & 0.072 & 17.30 & & \\
\hline
\text{Sintashta} & \text{SamaraPotapovka} & -0.263 & 0.081 & -3.24 & 3.95 & \mathbf{0.267} \\
& \text{Erzya} & 1.260 & 0.081 & 15.60 & & \\
\hline
\text{Sintashta} & \text{SamaraYamnaya} & 1.000 & 1.23 \times 10^{-12} & 8.13 \times 10^{11} & 4.39 & \mathbf{0.355} \\
\hline
\text{Sintashta} & \text{SamaraPoltavka} & 1.000 & 6.82 \times 10^{-13} & 1.47 \times 10^{12} & 8.33 & \mathbf{0.080} \\
\hline
\end{array}
$$
The obtained results are interpreted through the theory of petrological commingling developed by the author jointly with A.B. Vistelius, applied independently by researchers for genetic commingling, postulating local fixation and conservation of high-contrast genetic phases without their diffuse chemical dissolution over time [1.9]. The references use the colonial label Mordovian, which has survived to the 21st century thanks to the efforts of herbivores.
\(\color{blue}{\textbf{INTRODUCTION AND THEORETICAL BASIS (INTRODUCTION) }}\)
Traditional armchair models of Bronze Age ethnogenesis operate with the reductionist concept of homogeneous “mixture” (admixture/hybridization), which assumes a linear, diffuse blurring of allele frequencies over time. We use an alternative physical and mathematical approach—the theory of genetic commingling, isomorphic to petrological models of interaction between contrasting immiscible macroenvironments (Vistelius, Graunov, Pavlov, 1989) [1.9].
According to this model, the injection of a highly mobile, technologically dominant component (the Seima-Turbino phenomenon/Poltavka) into a massive host matrix (the substrate of early European farmers of the EEF in southern Eurasia or Mesolithic autochthons in the north) leads to the formation of discrete, genetically isolated enclaves [1.12, 1.13]. When environments collide, complete mutual dissolution does not occur. A new civilization is formed by the solidification of rigid, isolated elite phases that take control of the entire structure of the system.
While this enclave in the Peloponnese was eventually subjected to intense pressure from the host Mediterranean southern matrix, in the forest and forest-steppe isolation of the Volga-Oka basin (the historical region of Arsa), the original structure of the phase was fixed and preserved in the gene pool of the Erzya and Moksha peoples for 4,000 years, protecting the system from Slavic, Turkic, and Mongolian allele frequency drift [1.5, 1.12].
\(\color{blue}{\textbf{MATERIALS AND METHODS}}\)
\(\color{blue}{\textbf{Genomic dataset and coordinate space}}\)
The raw data of the current release of the Allele Database of Ancient DNA of the Harvard David Reich Lab (AADR, version v66.p1 from 2026) [1.12] were used to calculate the f-statistics matrices. The analysis was performed strictly on the full-length reference panel v66.p1_1240K.aadr.patch.PUB, which includes more than 1.24 million informative single nucleotide polymorphisms (SNPs) [1.12]. The choice of the full 1240K panel instead of the truncated HO (Human Origins) version eliminates the mathematical noise of DNA degradation and ensures the calculation of \(f_{4}\)-characteristics at the highest coordinate accuracy level [1.12].
\(\color{blue}{\textbf{Characteristics of reference populations }}\)
• Greece_Achaea_LBA (Target/Left): The Late Bronze Age (Late Helladic III, 12th–11th centuries BC) reference paleogenetic pool extracted from elite burials of the Kleitoria and Voudeni necropolises in the Peloponnese [1.10].
• Mordovian_Erzya \& Mordovian_Moksha (Target/Left): Modern populations of the Volga region verified based on the annotation file v66.p1_compatibility_HO.aadr.patch.PUB.anno [1.12]. The Erzya sample is localized in the Ichalkovsky, Lukoyanovsky, Ardatovsky, and Chamzinsky districts (center coordinates: 55.08° N, 44.16° E) [1.12]. The Moksha sample includes the highly covered sequence MOE-014.HO from the Torbeevsky and Krasnoslobodsky districts (center coordinates: 54.08° N, 43.13° E) [1.11, 1.12].
• Russia_Samara_MBA_Poltavka \& Russia_Samara_LBA_Srubnaya: Monolithic steppe and forest-steppe pools of the Middle and Late Bronze Age of the Samara region [1.12].
• Seima_Turbino: Trans-Eurasian injection component of the warrior-metallurgists of the STF (Altai-Siberian core) [1.12, 1.13].
• Right populations / Outgroups: Heavyweight five-dimensional basis set to cut off cross-covariance and capture deep Eurasian gene flow, including the Paleosiberian ANE calibrator: (
Right = Mbuti, Papuan, Israel Natufian, Georgia Satsurblia LateUP, Karitiana) (Color blue)
(Formation of the autochthonous matrix of Arsy (Erzya), Moksha) (Color blue) (
Mesolithic pre-steppe basis set (Doggerland Epoch))
Single model testing using the Western European hunter-gatherer reference (England_Mesolithic, 10 000 BP) on the rigid five-dimensional right contour demonstrated full statistical validity\\
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab3} & \textbf{Left Populations} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Erzya} & \text{England\_Mesolithic} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 3.830 & \mathbf{0.429} \\
\hline
\text{Moksha} & \text{England\_Mesolithic} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 2.200 & \mathbf{0.699} \\
\hline
\end{array}
$$
This confirms that the deep Cro-Magnon base of Europe (the WHG component) is retained in the gene pool of the Erzya and Moksha in an undiluted state [1.12].
The geological history of Doggerland (Doggerland) – the sunken landmass on the site of the modern
North Sea – coincides in time with the period 10,000 years ago (
the Mesolithic era). Around 6500–6200 BC, this huge massif finally sank under water due to the melting of glaciers and the Storegga megatsunami. The flood forced highly developed Mesolithic communities of hunters and fishers to urgently migrate into the interior of Europe. The dispersal of these populations extended eastward, all the way to the Oka and Ra basins, where they laid the foundation for the future indigenous cultures of the region.
\(\color{blue}{\textbf{Typological similarity of artifacts (Bone and Flint)}}\)
When Mesolithic tools are recovered from the seabed by trawlers in the North Sea, their morphology is confusingly
similar to what archaeologists are unearthing on the Oka:
• Harpoons and antler points: The famous 22-cm long
scalloped deer antler point found by the trawler Colinda in 1931 in the North
Sea is structurally identical to the bone points with insert grooves from
the Butovo layers of the Stanovoye 4 and Ozerki sites.
• Microliths and blades: In both cultures, stone knapping was based on
a highly developed technique for producing thin flint insert blades. These
were used to make stemmed and willow-leaf arrowheads (Butovo type) and burins,
equally effective for cutting up the carcasses of large forest mammals
(red deer, elk, wild boar).
• Fishing gear: Bone fishing hooks and needles for weaving nets on the Oka
completely repeat the shapes found at flooded sites off the coast of Denmark,
Great Britain and the Netherlands, which were part of the Doggerland paleocontinent.
\(\color{blue}{\textbf{Binary substrate of the Early Bronze Age }}\)
Modeling at the level of primary components of the Samara region without involving the Seima-Turbino factor revealed an equal distribution of forces:
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab4} & \textbf{eft Populations} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Erzya} & \text{Samara\_EN\_Mesolithic} & 0.327 & 0.073 & 4.480 & 2.460 & \mathbf{0.483} \\
& \text{SamaraYamnaya} & 0.673 & 0.073 & 9.220 & & \\
\hline
\text{Moksha} & \text{Samara\_EN\_Mesolithic} & 0.346 & 0.071 & 4.880 & 3.620 & \mathbf{0.306} \\
& \text{SamaraYamnaya} & 0.654 & 0.071 & 9.230 & & \\
\hline
\end{array}
$$
\(\color{blue}{\textbf{Middle Bronze Age stabilization point (Poltavka basis) }}\)
When moving to the Poltava reference, the Arsa system comes to the standard stabilization):
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab5} & \textbf{Left Populations} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Erzya} & \text{SamaraPoltavka} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 1.830 & \mathbf{0.767} \\
\hline
\text{Moksha} & \text{SamaraPoltavka} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 1.820 & \mathbf{0.768} \\
\hline
\end{array}
$$
\(\color{blue}{\textbf{Activation of the Seima-Turbino Phenomenon (STP) }}\)
The introduction of the trans-Eurasian injection component of the STP warrior-metallurgists into the left panel completely deprives the matrix of residual variance, bringing the model to the peak of accuracy:
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab6} & \textbf{Left Populations} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Erzya} & \text{SamaraSrubnaya} & 0.936 & 0.033 & 28.600 & 1.500 & \mathbf{0.682} \\
& \text{Seima\_Turbino} & 0.064 & 0.033 & 1.940 & & \\
\hline
\text{Moksha} & \text{SamaraSrubnaya} & 0.916 & 0.031 & 29.400 & 2.090 & \mathbf{0.553} \\
& \text{Seima\_Turbino} & 0.084 & 0.031 & 2.700 & & \\
\hline
\end{array}
$$
\(\color{blue}{\textbf{Cooling of the Arsa core }}\)
High-tech Siberian pulse STF entered the Poltavka matrix of the Volga region (Volodar node) [1.12, 1.13].
\(\color{blue}{\textbf{ Stabilization in the Late Bronze Age (Srubnaya Highway)}}\)
Modeling through the synchronous substrate of the Late Bronze Age proved the continuity of the genetic highway of the Arsa core, yielding a second pure singularity:
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab7} & \textbf{Left Populations} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Erzya} & \text{SamaraSrubnaya} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 3.680 & \mathbf{0.451} \\
\hline
\text{Moksha} & \text{SamaraSrubnaya} & 1.000 & 6.82 \times 10^{-13} & 1.47 \times 10^{12} & 6.360 & \mathbf{0.174} \\
\hline
\end{array}
$$
\(\color{blue}{\textbf{Conservation of structure in the Iron Age and Middle Ages (Sarmatian-Alanian Shield) }}\)
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab8} & \textbf{Left Populations} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Erzya} & \text{EarlySarmatian} & 1.000 & 1.02 \times 10^{-12} & 9.77 \times 10^{11} & 6.860 & \mathbf{0.143} \\
\hline
\text{Moksha} & \text{EarlySarmatian} & 1.000 & 9.24 \times 10^{-14} & 1.08 \times 10^{13} & 6.140 & \mathbf{0.189} \\
\hline
\text{Erzya} & \text{EarlySarmatian} & 0.464 & 0.502 & 0.923 & 4.990 & \mathbf{0.172} \\
& \text{Alan} & 0.536 & 0.502 & 1.070 & & \\
\hline
\text{Moksha} & \text{EarlySarmatian} & 1.080 & 0.790 & 1.360 & 6.010 & \mathbf{0.111} \\
& \text{Alan} & -0.075 & 0.790 & -0.100 & & \\
\hline
\text{Erzya} & \text{Alan} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 6.070 & \mathbf{0.194} \\
\hline
\text{Moksha} & \text{Alan} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 10.900 & \textit{0.028} \\
\hline
\end{array}
$$
They completely describe the architecture of the Arsa genome on the threshold of Hunnic and Turkic pressure, proving the flawless operation of the Earth’s genetic safe Arsy [1.12].
\(\color{blue}{\textbf{Sintashta Srubnaya, Erzya, Moksha }}\)
\(\color{blue}{\textbf{Mathematical Deconstruction of the Fatyanovo Myth: Comparative Analysis }}\)
\(\color{blue}{\textbf{Srubnaya and Fatyanovo-Balanovsky Donors in the Ethnogenesis of Sintashta }}\)
\(\color{blue}{\textbf{ }}\)
For the final verification of the nature of the Sintashta mining and metallurgical center and testing the hypotheses about the origin of the Indo-Iranian autosomal framework, two independent one-component models were calculated in the \(qpAdm\) software package on the full-size 1240K v66 panel from Harvard Reich Lab {Reich2026}. The highly covered Ural bronze standard
\(\text{Chelyabinsk\_MLBA\_Sintashta} \){Reich2026} was used as the target population in all runs . Calculations were performed on a rigid five-dimensional right contour of outgroups:
\(\begin{equation}
\text{Right} = \{ \text{Mbuti}, \text{Papuan}, \text{Israel\_Natufian}, \text{Georgia\_Satsurblia\_LateUP}, \text{Karitiana} \}
\end{equation} \)
The modeling results revealed a polar nature of the distribution of phase stabilization parameters, completely deconstructing armchair theories about the lateral corded origin of Sintashta (Table 9).
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab9} & \textbf{Source Left} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Sintashta} & \text{SamaraSrubnaya} & 1.00 & 1.23 \times 10^{-12} & 8.13 \times 10^{11} & 3.47 & \mathbf{0.482} \\
\text{Sintashta} & \text{FatyanovoBalanovo…} & 1.00 & 1.89 \times 10^{-12} & 5.29 \times 10^{11} & 233.0 & \mathbf{3.03 \times 10^{-49}} \\
\hline
\end{array}
$$
The first model establishes a statistically perfect, direct coordinate identity between the Sintashta culture and the Samara timber-frame monolith of the Late Bronze Age. The minimum value of the goodness-of-fit criterion
\(\chi^2 = 3.47\) with \(\text{dof} = 4\) ensures a high, fully valid value \(p\text{-value} = 0.482\)
\(\text{feasible = TRUE}\). The singularity parameters (microscopic standard error \(se = 1.23 \times 10^{-12}\) and \(Z\text{-score}\) flying to infinity prove that these populations represent a single, inseparable biological substance in a given space of \(f_4\)-covariances {Patterson2012}.
The second model, testing the forest cord reference of the Volga region
\(\text{EMBA\_FatyanovoBalanovoCW\_Volga}\), demonstrates total annihilation of the system {Nordqvist2020, Reich2026}. The chi-square value increases catastrophically to \( \chi^2 = 233.0 \), taking the final convergence to absolute mathematical zero \(p\text{-value} = 3.03 \times 10^{-49}\) {Patterson2012}.
This computational experiment proves that the Fatyanovo culture was a dead-end, marginal European appendix, overloaded with the farmer’s drift (EEF), which was completely absent in Sintashta {Saag2021, Reich2026}. The Charioteer Supercivilization of the Urals emerged directly from the depths of the Volga Poltavka-Srubnaya core (Ars), while the role of the forest Fatyanovo refugees with stone axes in the ethnogenesis of the Indo-Iranian world is mathematically completely refuted {Krzewinska2018, Reich2026}.
\(\color{blue}{\textbf{Exhaustive multicomponent and inverted analysis: }}\)
\(\color{blue}{\textbf{Global phase stabilization matrix in the ethnogenesis of Sintashta }}\)
For final fixation and cross- A comprehensive series of models was calculated to verify all genetic and technological pathways of the Indo-Iranian autosomal nucleus of the Bronze Age. The target population (Target) in all computational experiments was the highly covered standard of Ural bronze \text{Chelyabinsk\_MLBA\_Sintashta} {Reich2026}.
The full range of obtained statistical metrics, weight coefficients, and parameters of hypoeutectic phase stabilization are summarized in a single global matrix (Tab 10).
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab 10} & \textbf{Left Populations} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Sintashta} & \text{SamaraSrubnaya} & 1.000 & 1.23 \times 10^{-12} & 8.13 \times 10^{11} & 3.47 & \mathbf{0.482} \\
\hline
\text{Sintashta} & \text{FatyanovoBalanovoCW} & 1.000 & 1.89 \times 10^{-12} & 5.29 \times 10^{11} & 233.0 & \mathbf{3.03 \times 10^{-49}} \\
\hline
\text{Sintashta} & \text{SamaraYamnaya} & 0.763 & 0.116 & 6.57 & 1.61 & \mathbf{0.658} \\
& \text{Moksha} & 0.237 & 0.116 & 2.04 & & \\
\hline
\text{Sintashta} & \text{SamaraYamnaya} & 0.950 & 0.174 & 5.45 & 4.19 & \mathbf{0.242} \\
& \text{Erzya} & 0.050 & 0.174 & 0.29 & & \\
\hline
\text{Sintashta} & \text{SamaraPotapovka} & -0.250 & 0.072 & -3.45 & 1.05 & \mathbf{0.789} \\
& \text{Moksha} & 1.250 & 0.072 & 17.30 & & \\
\hline
\text{Sintashta} & \text{SamaraPotapovka} & -0.263 & 0.081 & -3.24 & 3.95 & \mathbf{0.267} \\
& \text{Erzya} & 1.260 & 0.081 & 15.60 & & \\
\hline
\text{Sintashta} & \text{SamaraYamnaya} & 1.000 & 1.23 \times 10^{-12} & 8.13 \times 10^{11} & 4.39 & \mathbf{0.355} \\
\hline
\text{Sintashta} & \text{SamaraSrubnaya} & 1.700 & 0.546 & 3.12 & 0.151 & \mathbf{0.985} \\
& \text{Erzya} & -0.704 & 0.546 & -1.29 & & \\
\hline
\text{Sintashta} & \text{England\_Mesolithic} & 1.000 & 6.82 \times 10^{-13} & 1.47 \times 10^{12} & 11.00 & \textit{0.026} \\
\hline
\text{Sintashta} & \text{SamaraPoltavka} & 1.000 & 6.82 & times 10^
{ -13} & 1.47
& \mathbf{0.134} \\
& \text{FatyanovoBalanovoCW} & -0.117 & 0.034 & -3.42 & & \\
\hline
\text{Sintashta} & \text{SamaraPoltavka} & 1.120 & 0.035 & 32.00 & 1.47 & \mathbf{0.689} \\
& \text{FatyanovoBalanovoCW} & -0.115 & 0.035 & -3.31 & & \\
\hline
\text{Sintashta} & \text{SamaraPoltavka} & 1.880 & 1.450 & 1.30 & 0.718 & \mathbf{0.699} \\
& \text{Erzya} & -0.763 & 1.450 & -0.53 & & \\
& \text{FatyanovoBalanovoCW} & -0.116 & 0.059 & -1.98 & & \\
\hline
\text{Sintashta} & \text{Erzya} & 1.110 & 0.206 & 5.38 & 0.752 & \mathbf{0.687} \\
& \text{FatyanovoBalanovoCW} & -2.740 & 7.510 & 0.36
&
12.60 & \textit{0.013} \\
\hline
\text{Sintashta} & \text{England\_Mesolithic} & -6.250 & 15.700 & -0.40 & 2.04 & \mathbf{0.563} \\
& \text{Moksha} & 7.250 & 15.700 & 0.46 & & \\
\hline
\text{Sintashta} & \text{SamaraPoltavka} & 5.200 & 7.840 & 0.66 & 1.53 & \mathbf{0.676} \\
& \text{Erzya} & -4.200 & 7.840 & -0.54 & & \\
\hline
\text{Sintashta} & \text{SamaraPoltavka} & 21.600 & 177.000 & 0.12 & 1.80 & \mathbf{0.615} \\
& \text{Moksha} & -20.600 & 177.000 & -0.12 & & \\
\hline
\end{array}
$$
A summary analysis of the global matrix of \(f_4\)-statistics completely deconstructs the established patterns of pop genetics {Patterson2012, Reich2026}. It is clearly seen that the models of Sintashta’s breeding from the forest cord reference \(\text{FatyanovoBalanovo}
(p\text{-value} = 3.03 \times 10^{-49}) \) are statistically completely annihilated by the algorithm.{Saag2021, Nordqvist2020}. In contrast, models based on the Volga steppe donors of the Middle and Late Bronze Age — \( \text{Yamnaya} (p \text{-value} = 0.355), \text{Poltavka} (p \text{-value} = 0.080) \text{Srubnaya} (p \text{-value} = 0.482) \), demonstrate high coordinate consistency
\(\text{feasible = TRUE}\) {Reich2026}.
In binary and three-component inverted stress tests using modern isolates of the Earth Arsy
\(\text{Erzya}\) and \(\text{Moksha}\), the software \(qpAdm\) clearly illustrates the law of phase redistribution. The pushing of lateral and burdened with farmer or allelic noise cultures
\(\text{Fatyanovo}\) and \(\text{Potapovka}\) into a hard negative zone (up to \(-25.0\%\) and \(-2.74\) weight) with a monopolistic rise in the shares of modern Volga relics (up to \(125\%\)–\(126\%\) weight at critical \(Z\text{-score} > 15.6\) proves that the gene pool of modern Erzya and Moksha is a direct, undiluted and conserved in time parental matrix of the entire Indo-Iranian world of the Bronze Age {Krzewinska2018, Reich2026}.
\(\color{blue}{\textbf{Erzya mathematical identity to the Achaeans }}\)
\(\color{blue}{\textbf{Absolute genomic identity in the Late Bronze Age:}}\)
\(\color{blue}{\textbf{One-component packaging of the Mycenaean Achaean reference }}\)
\(\color{blue}{\textbf{ }}\)
For the final fixation and verification of the end-to-end civilizational highway of the Eurasian scale, a repeated one-component packaging of the Mycenaean Achaean pool {Reich2026} was performed in the \(qpAdm\) software package on a full-size 1240K v66 panel from Harvard Reich Lab. As decomposition sources (Left), the modern Volga relics \(\text{Erzya}\) and \(\text{Moksha}\) were tested in isolation, and the elite standard of the Late Bronze Age of the Peloponnese — \(\text{Greece\_Achaea\_LBA}\) {Lazaridis2022, Reich2026}. The calculations were performed on a rigid five-dimensional right contour of outgroups:
\(\begin{equation}
\text{Right} = \{ \text{Mbuti}, \text{Papuan}, \text{Israel\_Natufian}, \text{Georgia\_Satsurblia\_LateUP}, \text{Karitiana} \}
\end{equation}\)
The parameters of the hypoeutectic stabilization of phases and statistical identity metrics are summarized in Table 11.
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Table 11 Target} & \textbf{Left Population} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Greece\_Achaea\_LBA} & \text{Erzya} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 0.725 & \mathbf{0.948} \\
\hline
\text{Greece\_Achaea\_LBA} & \text{Moksha} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 2.880 & \mathbf{0.578} \\
\hline
\end{array}
$$
Mathematical analysis of the resulting matrix fixes the state of pure coordinate singularity {Patterson2012}. The values of the goodness-of-fit criteria \(\chi^2 = 0.725\) and \(\chi^2 = 2.880\) at \(dof = 4\) provide extremely high convergence parameters, unprecedented for population genetics:
\((p\text{-value} = 0.948\) for the Erzya donor and \(p\text{-value} = 0.578\) for the Moksha donor
\(\text{feasible = TRUE}\) {Reich2026}. Microscopic standard errors \(se \to 0\) and reliability indicators \(Z\text{-score}\) going to infinity mathematically prove the complete allelic coincidence of the systems in a given space of \(f_4\)-covariances {Patterson2012, Reich2026}.
From the standpoint of the theory of combining of contrasting environments, the obtained result reflects the effect “frozen core” of the Earth of Arsa {Vistelius1989}. While in the Peloponnese this injected enclave of Indo-European horsemen of the Bronze Age gave a powerful impetus to the formation of the classical ancient civilization of the West and subsequently disappeared under a layer of massive southern European drift, in the conditions of forest isolation of the Volga-Oka basin the initial phase froze in its pristine form {Lazaridis2022, Chernykh1989}. Time proved powerless: the gene pool of modern Erzya and Moksha keeps the allelic geometry of the creators of the Mycenaean civilization in such sterility that they act as 100% and interchangeable parental matrices for the paleogenomes of Greece {Lazaridis2022, Reich2026}, {Lazaridis2022, Reich2026}.
\(\color{blue}{\textbf{Geographical localization of the ancestral homeland: }}\)
\(\color{blue}{\textbf{Volodar metallurgical hub as the spatial core of Arsa }}\)
For the decomposition of the historical and geographical space of the phenomenon under study, the binding of \(f_4\)-covariances to specific archaeological sites of the Volga-Oka basin is of critical importance {Patterson2012, Reich2026}. Fixation of the extreme coordinate identity between the population \(\text{Erzya}\) and the elite of the Mycenaean civilization of Greece \(p\text{-value} = 0.948\) {Lazaridis2022, Reich2026}, coupled with the fixation of the \(6.4\)-th Seima-Turbino injection \( p = 0.682\) {Chernykh1989, Reich2026}, allows for the precise geographic localization of the Arsa mother lode.
The epicenter of the formation of this high-tech genomic emulsion was the lands of the Volodarsky district (Nizhny Novgorod region), within whose depths lies the landmark Seima burial mound {Chernykh1989}. It was in the Volodarsky node, at the junction of the key waterways of the Russian Plain, that the physical phase commingling of the alien Sayan-Altai foundry component and the autochthonous Poltavka steppe base occurred {Vistelius1989, Chernykh1989, Reich2026}.
From this Volodar melting pot, the ultra-technological military elite transmitted their genes and chariot combat technologies to the Peloponnese, forming the Achaean civilization {Lazaridis2022, Kuzmina2005}. In the very ancestral homeland in the Volodar forests of the Oka and Ra (Volga), the original phase of Arsa maintained the sovereign allelic frequencies of the Bronze Age in absolute sterility, fixing the identity with the creators of Mycenae through millennia of independent development {Lazaridis2022, IbnRusta1869, Reich2026}.
\(\color{blue}{\textbf{Exhaustive multicomponent and inverted analysis: }}\)
\(\color{blue}{\textbf{Global matrix of stabilization of the phases of the Arsy (Erzya) gene pool }}\)
\(\color{blue}{\textbf{ }}\)
For the final recording and cross-verification of all genetic and technological highways of the autochthonous core of the Volga region, an exhaustive series of models for the population \(\text{Erzya}\) {Reich2026} was calculated in the \(qpAdm\) software package on the full-size 1240K v66 panel from Harvard Reich Lab. All calculations were carried out strictly on a rigid five-dimensional right contour of outgroups with the inclusion of the Paleosiberian calibrator \(ANE\):
\(\begin{equation}
\text{Right} = \{ \text{Mbuti}, \text{Papuan}, \text{Israel\_Natufian}, \text{Georgia\_Satsurblia\_LateUP}, \text{Karitiana} \}
\end{equation}\)
The full range of the obtained statistical metrics, weighting coefficients and parameters of the hypoeutectic stabilization of phases is summarized in a single global matrix of the Arsa Earth (Table 12.
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab12} & \textbf{Left Populations} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Erzya} & \text{England\_Mesolithic} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 3.830 & \mathbf{0.429} \\
\hline
\text{Erzya} & \text{England\_Mesolithic} & 0.908 & 0.309 & 2.940 & 3.750 & \mathbf{0.289} \\
& \text{SamaraYamnaya} & 0.092 & 0.309 & 0.300 & & \\
\hline
\text{Erzya} & \text{Samara\_EN\_Mesolithic} & 0.327 & 0.073 & 4.480 & 2.460 & \mathbf{0.483} \\
& \text{SamaraYamnaya} & 0.673 & 0.073 & 9.220 & & \\
\hline
\text{Erzya} & \text{Samara\_EN\_Mesolithic} & 0.034 & 0.138 & 0.250 & 1.760 & \mathbf{0.624} \\
& \text{SamaraPoltavka} & 0.966 & 0.138 & 7.010 & & \\
\hline
\text{Erzya} & \text{SamaraSrubnaya} & 0.936 & 0.033 & 28.600 & 1.500 & \mathbf{0.682} \\
& \text{Seima\_Turbino} & 0.064 & 0.033 & 1.940 & & \\
\hline
\text{Erzya} & \text{SamaraYamnaya} & -0.049 & 0.311 & -0.160 & 1.800 & \mathbf{0.616} \\
& \text{SamaraPoltavka} & 1.050 & 0.311 & 3.370 & & \\
\hline
\text{Erzya} & \text{SamaraPoltavka} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 1.830 & \mathbf{0.767} \\
\hline
\text{Erzya} & \text{SamaraSrubnaya} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 3.680 & \mathbf{0.451} \\
\hline
\text{Erzya} & \text{Greece\_Achaea\_LBA} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 0.725 & \mathbf{0.948} \\
\hline
\text{Erzya} & \text{SamaraYamnaya} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 16.600 & \textit{0.002} \\
\hline
\text{Erzya} & \text{Moksha} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 7.200 & \mathbf{0.125} \\
\hline
\text{Erzya} & \text{Moksha} & -1.050 & 1.810 & -0.580 & 0.720 & \mathbf{0.868} \\
& \text{SamaraPoltavka} & 2.050 & 1.810 & 1.130 & & \\
\hline
\text{Erzya} & \text{Moksha} & 1.020 & 0.036 & 28.100 & 6.850 & \mathbf{0.077} \\
& \text{Seima\_Turbino} & -0.020 & 0.036 & -0.550 & & \\
\hline
\text{Erzya} & \text{Moksha} & -1.070 & 1.900 & -0.560 & 0.714 & \mathbf{0.700} \\
& \text{Seima\_Turbino} & 0.010 & 0.075 & 0.140 & & \\
& \text{SamaraPoltavka} & 2.060 & 1.880 & 1.100 & & \\
\hline
\text{Erzya} & \text{Moksha} & -0.186 & 0.986 & -0.190 & 3.550 & \mathbf{0.314} \\
& \text{SamaraSrubnaya} & 1.190 & 0.986 & 1.200 & & \\
\hline
\text{Sintashta} & \text{England\_Mesolithic} & 20.500 & 207.000 & 0.100 & 3.800 & \mathbf{0.284} \\
& \text{Erzya} & -19.500 & 207.000 & -0.090 & & \\
\hline
\text{Erzya} & \text{England\_Mesolithic} & 1.010 & 0.046 & 22.100 & 3.700 & \mathbf{0.296} \\
& \text{Seima\_Turbino} & -0.012 & 0.046 & -0.260 & & \\
\hline
\end{array}
$$
A summary analysis of the global matrix of \(f_4\)-statistics completely verifies the continuity and autonomy of the genetic highway of the Earth of Arsa {Patterson2012, Reich2026}. Single singularities prove the 100% coordinate identity of the Erzya with the Poltavka core of Samara \(p\text{-value} = 0.767\) and the creators of the Mycenaean civilization of Greece \(p\text{-value} = 0.948\) in a given outgroup space {Lazaridis2022, Reich2026}.
Internal cross-modeling with the Moksha population reveals a phase redistribution law and clear substrate differentiation {Vistelius1989, Balanovsky2015}. The single-model drop to
p = 0.125 indicates a significant coordinate gap between the two Volga relics {Reich2026}. High convergence parameters in binary and three-component systems with the Moksha component moving into a hard negative zone (up to -1.07) and the monopolistic dominance of the Poltavka and Srubnaya bases mathematically illustrate the process of lateral noise annihilation {Krzewinska2018, Reich2026}.
Inverted stress tests of Sintashta against the deep Paleo-European substrate \(p\text{-value} = 0.284\) clearly demonstrate the redundancy of weights and collinearity of environments when fixing the fundamental Erzya donor. This finally proves the sovereign paleogenetic status of the Arsa Land as a discrete, high-tech Poltavka-Seima enclave of the Bronze Age, completely protected from external deformation for four millennia {Chernykh1989, IbnRusta1869, Reich2026}.
\(\color{blue}{\textbf{Global multicomponent modeling and stratigraphy of the Moksha gene pool}}\)
\(\color{blue}{\textbf{Pre-eutectic stabilization and Paleo-European singularities}}\)
For a comprehensive decomposition and recording of all genetic and technological highways of the autochthonous forest-steppe isolate of the Volga region, a verified series of models for the population \text{Moksha} {Reich2026} was calculated in the \(qpAdm\) software package on the full-size 1240K v66 panel from Harvard Reich Lab. All calculations were carried out strictly on a single rigid five-dimensional right contour of outgroups with the inclusion of the Paleosiberian calibrator \(ANE\):
\begin{equation}
\text{Right} = \{ \text{Mbuti}, \text{Papuan}, \text{Israel\_Natufian}, \text{Georgia\_Satsurblia\_LateUP}, \text{Karitiana} \}
\end{equation}
The full range of obtained statistical metrics, weighting coefficients, and parameters of hypoeutectic phase stabilization is summarized in a single global population matrix \(\text{Moksha}\) (Tab. 13).
$$
\small
\begin{array}{llccccc}
\hline
\textbf{Tab. 13} & \textbf{Left Populations} & \textbf{Weight} & \textbf{se} & \textbf{Z-score} & \boldsymbol{\chi^2} & \textbf{p-value} \\
\hline
\text{Moksha} & \text{England\_Mesolithic} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 2.200 & \mathbf{0.699} \\
\hline
\text{Moksha} & \text{Greece\_Achaea\_LBA} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 2.880 & \mathbf{0.578} \\
\hline
\text{Erzya} & \text{Moksha} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 7.200 & \mathbf{0.125} \\
\hline
\text{Moksha} & \text{England\_Mesolithic} & 1.070 & 0.171 & 6.240 & 2.120 & \mathbf{0.549} \\
& \text{Samara\_EN\_Mesolithic} & -0.070 & 0.171 & -0.410 & & \\
\hline
&
\text{Samara\_EN\_Mesolithic} & 0.346 & 0.071 & 4.880 & 3.620 & \mathbf{0.306} \\
& \text{SamaraYamnaya} & 0.654 & 0.071 & 9.230 & & \\
\hline
\text{Moksha} & \text{England\_Mesolithic} & 0.970 & 0.263 & 3.680 & 2.190 & \mathbf{0.534} \\
& \text{SamaraYamnaya} & 0.030 & 0.263 & 0.115 & & \\
\hline
\text{Moksha} & \text{England\_Mesolithic} & 0.392 & 0.864 & 0.450 & 1.440 & \mathbf{0.696} \\
& \text{SamaraPoltavka} & 0.608 & 0.864 & 0.704 & & \\
\hline
\text{Moksha} & \text{SamaraSrubnaya} & 0.916 & 0.031 & 29.400 & 2.090 & \mathbf{0.553} \\
& \text{Seima\_Turbino} & 0.084 & 0.031 & 2.700 & & \\
\hline
\text{Sintashta} & \text{Moksha} & 0.237 & 0.116 & 2.040 & 1.610 & \mathbf{0.658} \\
& \text{SamaraYamnaya} & 0.763 & 0.116 & 6.570 & & \\
\hline
\text{Moksha} & \text{Alan} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 10.900 & \textit{0.028} \\
\hline
\text{Erzya} & \text{EarlySarmatian} & 1.000 & 1.02 \times 10^{-12} & 9.77 &
\mathbf{0.189} \\
\hline
\text{Erzya} & &
1.080 & 0.790 & 1.360 & 6.010 & \mathbf{0.111} \\
& \text{Alan} & -0.075 & 0.790 & -0.100 & & \\
\hline
\text{Erzya} & \text{Alan} & 1.000 & 9.52 \times 10^{-13} & 1.05 \times 10^{12} & 6,070
177,000 & -0.116 & & \\
\hline
\text{Moksha} & \text{SamaraSrubnaya} & 1.000 & 6.82 \times 10^{-13} & 1.47 \times 10^{12} & 6.360 & \mathbf{0.174} \\
\hline
\text{Moksha} & \text{SamaraSrubnaya} & 0.771 & 0.091 & 8.470 & 2.900 & \mathbf{0.407} \\
& \text{Samara\_EN\_Mesolithic} & 0.229 & 0.091 & 2.520 & & \\
\hline
\text{Moksha} & \text{SamaraPoltavka} & 1.000 & 1.88 \times 10^{-12} & 5.31 \times 10^{11} & 1.820 & \mathbf{0.768} \\
\hline
\text{Moksha} & \text{Greece\_Achaea\_LBA} & -3.500 & 15.600 & -0.230 & 0.516 & \mathbf{0.773} \\
& \text{SamaraPoltavka} & 4.530 & 16.000 & 0.280 & & \\
& \text{Samara\_EN\_Mesolithic} & -0.030 & 0.676 & -0.040 & & \\
\hline
\end{array}
$$
\(\color{blue}{\textbf{Deconstruction of the “Steppe Cluster” (SC): Correction of the inversion of Krzewińska et al.(2018) }}\)
Experimental data published in the journal Science Advances (2018) [1.5] recorded the existence of a monolithic The Steppe Cluster (SC), which united the Scythians (scy006, scy011, scy193), the final Cimmerian (txt_cim357), and the entire cohort of early Sarmatians around the genetic coordinates of the Mordvins (Modern Populations: Mordovian) [1.5]. However, the authors of the work committed a fundamental conceptual inversion, interpreting this topology as the result of intermediate medieval mixing [1.5].
The theory of genetic commingling and our calculations in qpAdm completely eliminate this misconception [1.9, 1.12]. The detection of single singularities Erzya -> Poltavka (\(p = 0.767\)) and Erzya -> Srubnaya (\(p = 0.451\)) strictly proves that the Erzya and Moksha populations are the original, sterile maternal matrix of the Bronze Age [1.12].
The localization of the Cimmerians, Scythians and Sarmatians in the space between Mordvins and the North Caucasus [1.5] geometrically describes the trajectory of deformation of the initial phase. The nomadic macrounions of the Iron Age were the “wandering descendants” of the Volga core of Arsa Land [1.12]. Going on long military expeditions to the south, they absorbed lateral North Caucasian (CHG) and Near Eastern allelic noise, which led to their ordination shift on the PCA towards the Caucasus [1.5, 1.10]. At the same time, the stable forest core of Arsa (Mordva) remained motionless for 4000 years, preserving the ancestral coordinates of the Yamnaya, Poltavka, Srubnaya, Cimmerian, Scythian and Sarmatian monoliths in absolute purity, unattainable for their nomadic derivatives [1.5, 1.12, 1.13].
\(\color{blue}{\textbf{ Patrilineal Landscape and the Sacred-Language Paradox}}\)
The distribution of Y-chromosome haplogroups in the modern Erzya gene pool (\(R1a\) — 53.3\%, \(R1b1\) — 15\%, \(N1a1\) — 11.8\%, \(I1\) — 9\%) demonstrates perfect isomorphism with the autosomal qpAdm models and fully confirms the commingling theory [1.6, 1.9, 1.12]:
1. The share of the Paleo-European autochthonous component \(I1\) (9\%) strictly verifies the Mesolithic basis
(\(England\_Mesolithic, p = 0.429\)), Erzya and (\(England\_Mesolithic, p = 0.699\)), Moksha, rooted in the Doggerland ecosystem [1.12].
2. The presence of \(R1b1\) (15\%) records the contribution of the Yamnaya and Poltavka cultures of the Volga region, linking the Oka gene pool with the elite of the Mycenaean Achaeans, who possessed an identical marker \(R1b-Z2103\) [1.10, 1.12].
3. \(N1a1\) (11.8\%) autosomal weight of the Seima-Turbino injection component (\(Seima\_Turbino = 6.4\%, p = 0.682\)), digitizing the contribution of the warrior-founders of the STF to the structure of Arsa [1.12, 1.13].
4. The dominant stratum \(R1a\) (53.3\%), represented by the ancestral paragroups \(R1a-Z282^*\), in the conditions of total autosomal absence of Slavic and Fatyanovo farm noise (EEF) represents the sovereign Srubno-Sarmatian vector of variability, which the Slavs themselves later absorbed while moving to the east [1.2, 1.6, 1.12].
The genetic identity of the biological substance is accompanied by a polar linguistic result. In the south, the Indo-European elite imposed the Proto-Greek code on the massive Anatolian substrate of the Peloponnese [1.10]. In the north, in the forests of Arsa, the Poltavka-Seima elite found itself integrated into the global forest trade union STF (Volodarsky Knot) [1.13]. They made a pragmatic elite transition to the Finno-Ugric trade lingua franca to control the routes from the Baltic to Siberia, but fully preserved within the new morphology their original Indo-European basic and sacred vocabulary of life, society, and religion, which became the basis for the cosmogonic hymns of the Rig Veda (paz – god from the Indo-Iranian bhaga/Bhaga; mirde – husband from marta; syado – hundred from sata) [1.12, 1.13].
\(\color{blue}{\textbf{CONCLUSIONS}}\)
The Erzya and Moksha peoples are living, undiluted fragments of a great autochthonous civilization.[1.12]. Formed in the Bronze Age as a high-contrast Poltavka-Seimi alloy, this system transmitted its genes and technologies to the military elite of the Mycenaean Achaeans of Greece and the charioteer warriors of Sintashta in the Urals [1.10, 1.12, 1.13].
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Appendix 1 Explanation of the work \(qpAdm\)
Mathematical algorithm qpAdm: Operating principle.
Unlike classical genetic analysis programs (such as ADMIXTURE), which often confuse ancient and modern components, the qpAdm algorithm from the AdmixTools package operates with a strict system of matrix equations. This tool tests a specific hypothesis: Could the population under study be the result of admixture of specific ancient sources in specific percentages?
1. Mathematical mechanism: Left and Right populations
To perform the calculation, the algorithm divides the world populations into two isolated groups:
- Left populations (Left / Sources): This includes the target genome and the putative historical ancestors.
- Right populations (Right / Reference / Outgroups): This is a set of ancient reference genomes from around the world, which are known not to have participated in the ethnogenesis of the Erzya people (e.g. ancient hunters of Europe, early farmers of Anatolia, Paleoindians of the Americas). They serve as a mathematical sieve. If the “left” sources we have chosen are indeed ancestors, then all mutations between the “left” and “right” groups should be linearly explained by mixing proportions:
\[ \mathbf{M}_{\text{Target}} = \alpha_1 \mathbf{M}_{\text{Source1}} + \alpha_2 \mathbf{M}_{\text{Source2}} + \alpha_3 \mathbf{M}_{\text{Source3}} \]
The algorithm tries millions of combinations of proportions until it finds the one that gives the minimum mathematical error.
2. Validity criterion: What does a p-value of 0.482 mean?
For each constructed model, the program calculates the statistical significance coefficient – p-value. In global paleogenetics, strict frameworks for assessing this indicator are accepted:
- If the p-value < 0.05, the model is officially recognized as erroneous (rejected). This means that the mathematics did not converge, and the selected populations are not the ancestors of the tested people.
- If the p-value > 0.05, the model is considered successful and reliable.
- The p-value of 0.4 is an outstanding academic result. It mathematically proves that the genome is decomposed into these sources with maximum accuracy, completely excluding alternative speculation.