from research import *
s=begin(758,'Classify cross-tradition interval preservation','When does rounding preserve a difference between traditions?',{},['C754–757'])
f=json.loads((ROOT/'model/all_rounding_fields.json').read_text());m=f['MT_native_OFF'];out={}
for t in ['LXX_native_ON','SP_native_OFF']:
    d={n:f[t][n]['D']-m[n]['D'] for n in m}
    out[t]={str(v):[n for n in m if d[n]==v] for v in sorted(set(d.values()))}
finish(s,{'comparison_classes':out,'criterion':'DeltaD_i=DeltaD_j iff the cross-tradition interval difference is unchanged by rounding'},'Equal comparison-residual plateaus identify complete preserved interval families. Cross-tradition compatibility follows from two local field values, without a new list of isolated matches.','Test whether admitted Cainan insertion preserves these residual fields.',{'LXX_classes':len(out['LXX_native_ON'])==3,'SP_classes':len(out['SP_native_OFF'])==3})