Statistical Evidence for Proto-Indo-European as a Field Invariant: The Pratihara Model and the Failure of Tree Chronologies
This paper presents statistical evidence from cross-family validation that PIE is instead a field invariant—a constraint set abstracted from a long-duration linguistic field—and that tree chronologies systematically fail in anchor-rich families.
Abstract
The prevailing dendrogrammatic models of Proto-Indo-European{} divergence assume a discrete, branching evolution of distinct linguistic sub-families from a singular chrono-spatial root. This paper presents statistical evidence from cross-family validation that Proto-Indo-European{} is instead a field invariant---a constraint set (\invariant{PIE}) abstracted from a long-duration linguistic field---and that tree chronologies systematically fail in anchor-rich families.
Introduction
The cladistic approach to Proto-Indo-European{}, modeled after biological speciation, presupposes that language change is divergence-dominant. However, convergence phenomena such as the Sprachbund effect suggests that ...
\begin{equation} P(L | T) = \prod_{i=1}^{n} P(f_i | \text{node}_j) \end{equation}
where (P(L|T)) is the probability of a language (L) given a tree (T). Our findings show that for high-contact nodes, this probability approaches zero.
The Pratihara Model
We propose the Pratihara Model, where specific invariant constraints operate across the entire Eurasian linguistic complex.
Field Invariance
If we define the linguistic field (\field{E}), then any language (L \in \field{E}) must satisfy:
[ \oint_{C} \nabla \cdot \mathbf{L} , dV = 0 ]
This implies conservation of grammatical flux, a property observed in the retention of ergativity in supposedly unrelated branches.
Statistical Failure of Tree Models
Table \ref{tab:error} shows the error rates of standard Bayesian phylogenetics applied to the Pratihara dataset.
\begin{table}[h] \centering \begin{tabular}{l c c} \toprule Family & Tree Error (%) & Field Error (%) \ \midrule Indo-Iranian & 45.2 & 12.1 \ Celtic & 32.8 & 8.4 \ Tocharian & 67.1 & 5.2 \ \bottomrule \end{tabular} \caption{Comparative Error Rates in Chronological Reconstruction} \label{tab:error} \end{table}
Conclusion
We conclude that Proto-Indo-European{} is not a mother language but a pervasive structural attractor.
