Downscaling the Spine-Cluster Architecture: K-12 Adaptation of Star-Topology Skills for a Zero-to-Competitive Python Pathway

The Spine-Cluster architecture for Star-Topology Skills instruction [1] specifies a two-axis decomposition of competitive-programming pedagogy: a seven-node linear spine of content-independent cognitive milestones (L1 . . . L7 ) and nine star clusters of algorithm families (S1 . . . S9 ), traversed under four deep-structure variation axes (input-size class, constraint-tightness, composition depth, problem-framing mode). The architecture targets Layer D — International Olympiad in Informatics-level trainees with C++ fluency and formaloperational cognition. We analyse whether the architecture can be downscaled to a K-12 audience spanning ages 8 through 18 while preserving its three load-bearing claims: contentindependent cognitive progression, deep-structure recognition through variation, and schema induction via multiple analogs. Drawing on ACT-R skill acquisition [2, 3], Chi-Feltovich-Glaser expert-novice categorisation [4], Gick-Holyoak schema induction [5], VanLehn's synthesis of cognitive skill acquisition [6], Sweller cognitive load theory [7, 8], Ericsson deliberate practice [9] bounded by [10], and post-Piagetian developmental psychology [11, 12, 13], we propose a minimum-deformation translation: a five-volume pathway Vol 0 (ages 8–11, unplugged) through Vol 4 (ages 15–18, contest-ready) with per-volume active milestone sets, a reduced five-cluster intermediate taxonomy (S1′ . . . S5′ ) for Vol 1–3 that expands to the full S1 . . . S9 at Vol 4, degenerateaxis bins for age-inaccessible variation dimensions (constrainttightness absent until Vol 3), and four per-boundary diagnostic instruments that certify milestone readiness without empirical cohort dependence. The adaptation preserves the architecture's transfer claim while respecting working-memory ceilings and domain-specific progression evidence. Five open questions — L5 bifurcation validity, intermediate taxonomy width, framingmode onset age, instrument psychometric validity, and textbookvs-tutor dispatch fidelity — remain for adult-elicitation probes under the program's no-cohort scope.