s556.py

from research import *
s=begin(556,'Generate all collateral Joseph intervals','Do two fixed-offset constructions account for every source Joseph rail?',{'Levi':1933,'Kohath':1796,'Joseph_life':110},['File61 §§11.2–11.3A; File62 §5.2'])
t=json.loads((ROOT/'prep/file61_62_tables.json').read_text())['joseph_intervals'];out=[]
for r in t:
 p=F(7,2) if r['phase_state']=='Aaron_Tishri_exact' else F(0);d=r['clutch'];L=1933+p-d;K=1796+p-d
 v=(L,L-110) if r['portion']=='forward' else (K+110,K)
 assert v==(F(r['start']),F(r['end']));out.append(v)
finish(s,{'intervals':out,'matches':12},'Two collateral constructors, (L,L−110) and (K+110,K), generate all12 exact-phase Joseph intervals. Joseph remains a collateral interval, not an added trunk generation.','Derive the invariant geometry shared by these interval pairs.',{'count':len(out)==12,'lifespans':all(a-b==110 for a,b in out)})