The Steppe-Origin Transmission Model Revisited: A Simulation-Based Feasibility Analysis Not an Empty Set, but a Narrow One

A previous draft of this paper argued that the strong Steppe-origin transmission model (SOTM) --- the hypothesis that Steppe-related ancestry in later South Asian populations reflects a demographically viable pastoralist migration that transmitted Sanskritic/Vedic language and culture into India --- has an empty feasible set: no population trajectory can simultaneously satisfy source sparsity, transit dilution, target-population dilution, and language-preservation constraints. This revision reports the results of an extensive computational stress-test of that claim, using cohort-structured demographic simulation, Monte Carlo sweeps over archaeologically-grounded parameter ranges, and cross-checks against published ancient-DNA admixture-dating methodology (DATES/ALDER) and settlement-derived population estimates. The result is more precise than the original theorem: the feasible set is not empty, but it is narrow, and it survives only under a specific joint configuration that differs substantially from both the popular ``migration'' narrative and a literal reading of the original theorem. Smooth, continuous, generation-by-generation dilution --- the mechanism implicit in the original paper's own equations, and in most popular accounts --- is shown computationally to collapse to a negligible ancestry signal under every parameter regime tested, including regimes generous to the source population. A demographically coherent path exists only through (i) a two-stage process mediated by an intermediate population (the Bactria--Margiana Archaeological Complex, BMAC) rather than direct steppe-to-Indus contact, (ii) discrete, concentrated admixture events rather than continuous trickle, consistent with the actual structure of published ancient-DNA admixture-dating results, and (iii) contact with a small, localized regional population at the time of admixture rather than a civilizational-scale population. This narrow corner should not be read as a resolution of whether the historical event occurred: several parameters remain illustrative rather than independently sourced, and {sec:contradictions} catalogues specific, currently unreconciled tensions within the model itself. Most significantly, two independent corrections --- one from ancient-DNA-derived effective population size, one from the demographic implication of steppe-related ancestry appearing only in outlier individuals at BMAC rather than its core population --- converge, despite resting on unrelated evidence, on a feasibility estimate of roughly 1--2%, an order of magnitude below this paper's own less-constrained headline figure of 23.2%. We regard this convergence, not the higher figure, as the paper's clearest quantitative result. We regard the demonstration that a non-empty region exists, and the precise characterization of what it requires and how fragile that characterization is, as the paper's actual contribution --- not a claim that the region is realized in history. We further argue that the demographic-feasibility question and the language-transmission question are logically separable and require independent evidence; and that a common rescue mechanism for the language question --- appeal to later, well-documented institutions such as guru-\'si{s}ya lineage transmission --- is anachronistic when projected onto the proposed contact period, since it is attested only from a much later era of Indian history. We propose replacing origin-directional terminology (``Steppe-origin,'' ``sphere of influence'') with the symmetric archaeological concept of an interaction sphere. This paper's central contribution is, in the end, diagnostic rather than resolutive: it documents how contingent, parameter-sensitive, and currently under-determined the demographic feasibility question actually is, and argues that peer-reviewed sources in this literature frequently attach language- and culture-origin claims (regarding Sanskrit specifically, the Vedic ritual system, and Proto-Indo-European's correspondence to any one population) with more confidence than either the demographic mechanism or the linguistic evidence, examined on their own terms, can currently support. We close with concrete, falsifiable predictions rather than a settled conclusion.