s1059.py

from research import *
s=begin(1059,'All proper E prefixes remain fractional','Does an integral outer completion imply integral internal coordinates?',{},['C1058','File52c §3.4'])
p=json.loads((ROOT/'model/completed_path_inputs.json').read_text());rows=[]
for name,original in p['original_paths'].items():
 parts=[inv(x) for x in original];prefixes=[sum(parts[:i]) for i in range(1,len(parts)+1)];images=[E*x for x in prefixes];rows.append({'path':name,'one_pass_parts':parts,'prefixes':prefixes,'residues23':[x%23 for x in prefixes],'E_prefixes':images,'coordinate_images':[6+x for x in images]})
a=artifact('model/completed_path_prefix_field.json',json.dumps(clean(rows),indent=2)+'\n')
finish(s,{'prefix_field':a,'residues_by_path':[r['residues23'] for r in rows]},'All four paths complete14720→16000, but every proper E prefix remains fractional with denominator23. Integral outer completion is weaker than integral preservation of all source boundaries.','Identify the finest numerical coarsening compatible with integral E block lengths.',{'whole_duration':all(r['prefixes'][-1]==14720 for r in rows),'only_final_integral':all(all(x.denominator==23 for x in r['E_prefixes'][:-1]) and r['E_prefixes'][-1]==16000 for r in rows)})