s901.py

from research import *
s=begin(901,'Unify endpoint interpolation and extrapolation','Can one span and one generated coordinate retain the entire source pair?',{},['C892','C831 weighted Creation bridge'])
proof={'coordinates':'D=C−R; W_lambda=lambda*C+(1−lambda)*R','recovery_R':'W_lambda−lambda*D','recovery_C':'W_lambda+(1−lambda)*D','determinant':1,'roles':{'lambda4/5':'weighted Creation comparison coordinate','lambda12':'twelvefold extrapolated macro head'},'limit':'shared representation does not equate source roles or coefficients'}
a=artifact('model/endpoint_coordinate_basis.json',json.dumps(proof,indent=2)+'\n')
finish(s,{'basis':a,'symbolic_coefficients':{'R_recovered':[0,1],'C_recovered':[1,0]}},'The pair (D,W_lambda) is an exact coordinate system for (C,R), for every fixed lambda. The old weighted bridge and new twelvefold head use the same endpoint algebra with different source-appointed coefficients and roles.','Recover every macro source pair and both inherited weighted Creation pairs from this basis.',{'determinant':1==1,'R_coefficients':12-12==0 and 1-12+12==1,'C_coefficients':12+1-12==1 and 1-12-1+12==0})