Statistical Evidence for Proto-Indo-European as a Field Invariant: The Pratihara Model and the Failure of Tree Chronologies
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2026
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| author | Bharadwaj, Hemu |
| author_facet | Bharadwaj, Hemu |
| contents | <p>Traditional phylogenetic models of language evolution assume Proto-Indo-European (PIE) as<br>a temporally prior spoken proto-language, enabling tree-based divergence dating. This paper<br>presents statistical evidence from cross-family validation that PIE is instead a field invariant—<br>a constraint set abstracted from a long-duration linguistic field—and that tree chronologies<br>systematically fail in anchor-rich families.<br>Using the Pratihara Model (Layered-Mesh with Anchors), we demonstrate through fourpoint<br>violations, anchor ablation variance, reticulation metrics, and split stability tests that<br>Indo-European, Semitic, and Sinitic exhibit field behavior (high reticulation, split instability,<br>invariant persistence), while Niger-Congo, Dravidian, and Papuan exhibit tree behavior (low<br>reticulation, stable splits, reliable clocks). This classification rule is empirical, not interpretive:<br>anchor-rich families behave as fields; weak-anchor families as trees.<br>Statistical consequences are unavoidable: (1) PIE cannot be treated as a temporally prior<br>spoken language—it is a field invariant with no intrinsic clock; (2) Tree chronologies over-date<br>anchor-rich families by misinterpreting lateral transmission and register mixtures as deep divergence;<br>(3) Sanskrit stabilization must predate major diversification (≳5000 BCE) on structural<br>grounds alone, independent of archaeology or astronomy; (4) Indo-Iranian “splits” are tree-forcing<br>artifacts that collapse under anchor ablation.<br>These results force a methodological correction: tree-based dating is valid only for weakanchor<br>families. For anchor-rich families, chronology becomes partial-order</p> <p>(field emergence →anchor stabilization → vernacular drift → register alignments → late branching),</p> <p>not absolute<br>tree-calibrated dates.</p> |
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| id | zenodo_https___doi_org_10_5281_zenodo_18242231 |
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| publishDate | 2026 |
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| spellingShingle | Statistical Evidence for Proto-Indo-European as a Field Invariant: The Pratihara Model and the Failure of Tree Chronologies Bharadwaj, Hemu Proto-Indo-European, Pratihara Model, field invariant, tree model failure, network phylogenetics, four-point violations, anchor ablation, cross-family validation, linguistic field theory <p>Traditional phylogenetic models of language evolution assume Proto-Indo-European (PIE) as<br>a temporally prior spoken proto-language, enabling tree-based divergence dating. This paper<br>presents statistical evidence from cross-family validation that PIE is instead a field invariant—<br>a constraint set abstracted from a long-duration linguistic field—and that tree chronologies<br>systematically fail in anchor-rich families.<br>Using the Pratihara Model (Layered-Mesh with Anchors), we demonstrate through fourpoint<br>violations, anchor ablation variance, reticulation metrics, and split stability tests that<br>Indo-European, Semitic, and Sinitic exhibit field behavior (high reticulation, split instability,<br>invariant persistence), while Niger-Congo, Dravidian, and Papuan exhibit tree behavior (low<br>reticulation, stable splits, reliable clocks). This classification rule is empirical, not interpretive:<br>anchor-rich families behave as fields; weak-anchor families as trees.<br>Statistical consequences are unavoidable: (1) PIE cannot be treated as a temporally prior<br>spoken language—it is a field invariant with no intrinsic clock; (2) Tree chronologies over-date<br>anchor-rich families by misinterpreting lateral transmission and register mixtures as deep divergence;<br>(3) Sanskrit stabilization must predate major diversification (≳5000 BCE) on structural<br>grounds alone, independent of archaeology or astronomy; (4) Indo-Iranian “splits” are tree-forcing<br>artifacts that collapse under anchor ablation.<br>These results force a methodological correction: tree-based dating is valid only for weakanchor<br>families. For anchor-rich families, chronology becomes partial-order</p> <p>(field emergence →anchor stabilization → vernacular drift → register alignments → late branching),</p> <p>not absolute<br>tree-calibrated dates.</p> |
| title | Statistical Evidence for Proto-Indo-European as a Field Invariant: The Pratihara Model and the Failure of Tree Chronologies |
| topic | Proto-Indo-European, Pratihara Model, field invariant, tree model failure, network phylogenetics, four-point violations, anchor ablation, cross-family validation, linguistic field theory |
| url | https://doi.org/10.5281/zenodo.18242231 |