PhronesisWe apply the Displacement Framework to dyscalculia (Specific Learning Disorder with impairment in mathematics, DSM-5), formalizing it as a neurological deficit of the numerical cognition ground state S°_numeric rather than as a wrong attractor. The numerical ground state is defined across five dimensions: functional approximate number system (ANS), calibrated number-line representation, accessible arithmetic fact retrieval, fluid symbol-to-magnitude mapping, and learnable procedural arithmetic.
The core neurological finding — reduced Weber fraction acuity and atypical intraparietal sulcus activation — represents a genuine deficit in the ANS foundation that normally grounds symbolic mathematics in magnitude understanding. Without this foundation, arithmetic becomes brittle rote memorization that fails under working memory load. A critical secondary wrong attractor, math anxiety W_manx, reliably develops from dyscalculia and operates as an independent maintaining mechanism: consuming working memory resources through intrusive worry, generating avoidance of mathematical contexts, and priming threat responses to numerical tasks.
The DF dual-track treatment necessity is formalized: treating math anxiety alone leaves the structural deficit in place; treating dyscalculia without addressing math anxiety leaves the avoidance loop intact. Structural underdiagnosis is analyzed as generating iatrogenic Φ — the 'math isn't for everyone' cultural normalization and timed-testing practices are identified as Φ-maximizing educational interventions.
Nine formal propositions are derived. ANS-targeted training and the concrete-to-representational-to-abstract (CRA) sequence are formalized as return path interventions.