Statistical Evidence for Proto-Indo-European as a Field Invariant: The Pratihara Model and the Failure of Tree Chronologies

Traditional phylogenetic models of language evolution assume Proto-Indo-European (PIE) asa temporally prior spoken proto-language, enabling tree-based divergence dating. This paperpresents 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 chronologiessystematically fail in anchor-rich families.Using the Pratihara Model (Layered-Mesh with Anchors), we demonstrate through fourpointviolations, anchor ablation variance, reticulation metrics, and split stability tests thatIndo-European, Semitic, and Sinitic exhibit field behavior (high reticulation, split instability,invariant persistence), while Niger-Congo, Dravidian, and Papuan exhibit tree behavior (lowreticulation, stable splits, reliable clocks). This classification rule is empirical, not interpretive:anchor-rich families behave as fields; weak-anchor families as trees.Statistical consequences are unavoidable: (1) PIE cannot be treated as a temporally priorspoken language—it is a field invariant with no intrinsic clock; (2) Tree chronologies over-dateanchor-rich families by misinterpreting lateral transmission and register mixtures as deep divergence;(3) Sanskrit stabilization must predate major diversification (≳5000 BCE) on structuralgrounds alone, independent of archaeology or astronomy; (4) Indo-Iranian “splits” are tree-forcingartifacts that collapse under anchor ablation.These results force a methodological correction: tree-based dating is valid only for weakanchorfamilies. For anchor-rich families, chronology becomes partial-order (field emergence →anchor stabilization → vernacular drift → register alignments → late branching), not absolutetree-calibrated dates.