s640.py

from research import *
s=begin(640,'Solve the complete three-calendar congruence family','Do the fixed fourteen-year rail and thirteen-year flanks select the source count triple as the smallest positive solution?',{'conditions':['T=182m','T−14=168n','T−26=180p'],'counts':'positive integers'},['File70 §6 geometry; derived integer compatibility theorem'])
residues=[m for m in range(1,181) if (13*m-1)%12==0 and (m-13)%90==0]
solutions=[{'q':q,'T':2366+32760*q,'m':13+180*q,'n':14+195*q,'p':13+182*q} for q in range(3)]
finish(s,{'m_residue_mod180':residues,'general_T':'2366+32760q','general_counts':'m=13+180q; n=14+195q; p=13+182q','examples':solutions,'least_positive_solution':[2366,13,14,13]},'With the source offsets fixed, the full system has T=2366+32760q. Its least positive solution is exactly the source2366 and13/14/13 half-count triple. This is a conditional local minimality result, not a claim of a globally minimal chronology.','Relate the congruence period to the calendar lattice, then test the source no-Cainan companion.',{'fundamental_residue':residues==[13],'all_three_equations':all(r['T']==182*r['m'] and r['T']-14==168*r['n'] and r['T']-26==180*r['p'] for r in solutions),'least_positive':2366-32760<0})