Coordination Conjectures

Open problems in coordination typology stated as sorry-marked theorems. These are genuinely open questions where no existing theory derives the prediction from first principles.

Unlike proved theorems in Typology.lean, these mark the frontier of what M&S decomposition + processing theory should explain.

theorem Phenomena.Coordination.Conjectures.predict_acquisition_asymmetry (sys : Typology.ConjunctionSystem) (h_all : Typology.hasAllThreeStrategies sys = true) (h_bound : sys.muBoundness = some Typology.Boundness.bound) : ∃ (costMetric : Studies.BillEtAl2025.ConjunctionStrategy → Typology.ConjunctionSystem → ℕ), costMetric Studies.BillEtAl2025.ConjunctionStrategy.jMu sys > costMetric Studies.BillEtAl2025.ConjunctionStrategy.jOnly sys

Open problem: predict the @cite{bill-etal-2025} acquisition asymmetry.

No existing account predicts the full cross-linguistic pattern:

• @cite{mitrovic-sauerland-2016} + Transparency Principle → predicts J-MU easiest. Wrong for Georgian.
• @cite{szabolcsi-2015} → alternative quantifier-particle analysis. Doesn't predict it.
• @cite{haslinger-etal-2019} → plural/distributive analysis. Doesn't predict it.

A complete theory should derive: when MU is morphologically bound, J-MU incurs extra acquisition cost (segmentation difficulty outweighs transparency benefit). When MU is free, no such cost arises, yielding the Hungarian null.

This requires a processing/acquisition model where morphological complexity (boundness) and syntactic transparency (overt form-meaning mapping) are competing factors. The sorry marks this as the central open gap in the coordination typology — the M&S categories describe the space but don't yet predict which regions are hard to acquire.

[sorry: requires a cost metric that weights segmentation difficulty against transparency benefit; no existing theory provides this]