s1157.py

from research import *
from algebra import Matrix
s=begin(1157,'Measure amplitude information retained by whole totals','Which source parameters disappear when the ordered fields are summed?',{},['C1156','C1154'])
d=json.loads((ROOT/'model/postflood_amplitude_dictionary.json').read_text())
def total(mask):return [sum(F(row[j]) for row in mask) for j in range(3)]
reg,sp,lx=map(total,[d['R_mask'],d['SP_A_mask'],d['LXX_A_mask']]);M=Matrix([sp,lx])
a=artifact('model/postflood_total_measurements.json',json.dumps(clean({'regular_total_row':reg,'SP_life_total_row':sp,'LXX_life_total_row':lx,'life_total_rank':M.rank(),'life_total_kernel':[list(x) for x in M.nullspace()],'values':[sum(x*y for x,y in zip(row,[100,60,27])) for row in [reg,sp,lx]]}),indent=2)+'\n')
finish(s,{'total_measurements':a,'measurement_rows':[reg,sp,lx],'life_total_rank':M.rank()},'The totals are6.5u,−2t and4u+2a. The two lifespan totals have rank2 and cannot separateu froma; LXX’s total also cancels its two opposite t contributions. Ordered rows preserve information absent from their sum.','Ask whether combining regular and cumulative outer totals recovers the amplitudes under fixed source supports.',{'source_totals':list(M*Matrix([100,60,27]))==[-120,454],'rank2':M.rank()==2,'LXX_t_cancels':lx[1]==0})