s1226.py

from research import *
s=begin(1226,'Close the source-to-Key rectangle','Do the two source-generated radii produce the same40-year gain?',{},['C1224','C1225','Strategy §4.3'])
r=json.loads((ROOT/'model/SP_rectangle_regular_provenance.json').read_text())['Exodus_radius'];c=json.loads((ROOT/'model/SP_rectangle_cumulative_provenance.json').read_text())['Exodus_radius'];pr=P*r;jc=J*c
a=artifact('model/SP_rectangle_source_to_keys.json',json.dumps(clean({'inputs':[r,c],'keys':['70/69','300/299'],'outputs':[pr,jc],'gains':[pr-r,jc-c],'same_held_heads':[4206,13406],'target_nodes':[4206-pr,13406-jc],'gap_before':c-r,'gap_after':jc-pr,'gap_priestly_expansion':E*(c-r),'status':'new source-mechanism provenance for an already established rectangle, not a new numerical alignment'}),indent=2)+'\n')
finish(s,{'rectangle':a,'gains':[pr-r,jc-c],'gap':c-r},'The reconstructed inputs give the established40/40 gains to Conquest1406, preserving9200, whose25/23 expansion is10000. The advance is the genealogy-to-cap-to-Key explanation, not another independent occurrence of those numbers.','Determine which supplied placements are essential to the equal-gain equality.',{'gains40':pr-r==jc-c==40,'same_target':4206-pr==13406-jc==1406,'gap9200':jc-pr==c-r==9200,'expanded10000':E*(c-r)==10000})