s867.py

from research import *
s=begin(867,'Classify P and the complete shared-return fork','What singles out the finite Enoch fork without endpoint selection?',{'P':P,'domain':'r=0,...,76'},['C866','File43 display','File54 §6'])
rows=json.loads((ROOT/'model/NT_full_display.json').read_text()); lookup={r['r']:r for r in rows}
out=[]
for r in range(77):
 t=P*r
 if t.denominator==1:
  t=int(t);out.append({'r':r,'image_r':t,'source':lookup[r]['Luke'],'image':lookup[t]['Luke'],'source_BC':6+70*r,'image_BC':6+70*t})
es=json.loads((ROOT/'model/NT_E_returns.json').read_text())
joint=sorted({r['r'] for r in out}&{r['r'] for r in es})
a=artifact('model/NT_P_returns.json',json.dumps(out,indent=2)+'\n')
finish(s,{'returns':out,'joint_source_indices':joint,'artifact':a},'P returns exactly at multiples of69. On the complete r0–76 domain, Enoch at69 is the only nonzero source returning under both E and P, because lcm(23,69)=69. This is a dependent domain classification, not a probability result.','Transport the full indexed result to the admitted 36BC rail.',{'P_domain':[r['r'] for r in out]==[0,69],'joint':joint==[0,69],'Enoch_to_Jared':out[-1]['image']=='Jared'})