s1186.py

from research import *
from algebra import Matrix
s=begin(1186,'Test head identification after shared-amplitude compression','Do two chronology heads identify the four-amplitude form?',{},['C1183','C1185'])
d=json.loads((ROOT/'model/whole_genealogy_four_model.json').read_text());rows=d['matrix'];H=Matrix([[sum(F(rows[i][j]) for i in range(k,38,2)) for j in range(4)] for k in [0,1]]);out=list(H*Matrix(d['values']));ns=[list(v) for v in H.nullspace()]
a=artifact('model/whole_genealogy_four_head_information.json',json.dumps(clean({'matrix':H.tolist(),'values':out,'rank':H.rank(),'kernel_basis':ns,'explanation':'t cancels from the cumulative sum; lambda trades against twice a'}),indent=2)+'\n')
finish(s,{'head_information':a,'kernel':ns},'Even the four-amplitude form leaves two directions hidden from the heads: the sixty-year allocation and the trade between Lamech’s correction and the paired early increments. Complete fields are needed to locate them.','Restore native Cainan and distinguish insertion information from coefficient compression.',{'heads':out==[1250,430],'rank2':H.rank()==2,'kernel2':len(ns)==2,'t_unseen':all(row[3]==0 for row in H.tolist())})