s877.py

from research import *
s=begin(877,'Derive the quarter-family divisibility law','What single condition explains each whole-family grid profile?',{'seed':F(161,4)},['C873,876'])
coeff={n:k*F(161,4) for n,k in [('E',E),('P',P),('J',J)]}
quarter_index={n:4*c for n,c in coeff.items()}
domain={n:c.denominator for n,c in quarter_index.items()}
rows=json.loads((ROOT/'model/quarter_carrier_images.json').read_text())
a=artifact('model/quarter_multiplier_law.json',json.dumps(clean({'coefficients':coeff,'quarter_index_coefficients':quarter_index,'divisors':domain}),indent=2)+'\n')
finish(s,{'coefficients':coeff,'quarter_index_divisors':domain,'artifact':a},'For source161m/4, E gives175m/4, P gives245m/6 and J gives525m/13. Quarter preservation is automatic for E, requires3|m for P and13|m for J. This explains the entire finite ladder.','Apply E to every head in File46 rather than only its outer width.',{'divisors':domain=={'E':1,'P':3,'J':13},'whole_family':all(r['quarter_grid'][n]==(r['m']%d==0) for r in rows for n,d in domain.items())})