s777.py

from research import *
s=begin(777,'Derive the whole interval-response law','Which switches can affect a given interval?',{},['C772–776'])
f=json.loads((ROOT/'model/finite_birth_configurations.json').read_text());checked=0;ok=True;examples={}
for t,states in f.items():
    base=states['000'];names=[n for n in base];hi=names.index('Arphaxad');ti=names.index('Terah')
    masks={n:(1,int(i<=ti),int(i<=hi)) for i,n in enumerate(names)}
    for key,d in states.items():
        bits=[int(z) for z in key]
        for i,n in enumerate(names):
            for m in names[i+1:]:
                prediction=sum(w*b*(masks[n][k]-masks[m][k]) for k,(w,b) in enumerate(zip([215,60,130],bits)))
                ok &= (d[n]-d[m])-(base[n]-base[m])==prediction;checked+=1
for n,m in [('Adam','Arphaxad'),('Arphaxad','Shelah'),('Terah','Abraham')]:
    examples[n+'→'+m]={key:d[n]-d[m] for key,d in f['MT'].items()}
finish(s,{'formula':'delta span =215 ds(S_i−S_j)+60 dt(T_i−T_j)+130 dc(H_i−H_j)','examples':examples,'dependent_comparisons':checked},'Intervals inside one support block are invariant; intervals crossing a hinge detect exactly that hinge. The entire finite family follows one incidence rule.','Test matched configurations on the newly aligned SP/LXX birth suffix.',{'whole_family':ok})