from research import *
s=begin(962,'Clipped support does not fix the cap','What interval of k preserves exactly the source clipped identities?',{},['C953','C954','C956'])
L=json.loads((ROOT/'model/sp_cap_inputs.json').read_text())['baseline_lives']; u=json.loads((ROOT/'model/sp_birth_regeneration.json').read_text())['suffixes']; a=[5,7,8]; thresholds=[l-v for l,v in zip(L,u)]; lo=max(thresholds[i] for i in range(9) if i not in a); hi=min(thresholds[i] for i in a)
finish(s,{'row_thresholds':thresholds,'support_interval':{'lower_inclusive':lo,'upper_exclusive':hi}},'Knowing only which three rows are strictly clipped allows584≤k<716. Exact source lives, not support alone, select601. This interval is a sensitivity result, not a statistical search.','Test what the aggregate lifespan sum can identify within that support interval.',{'bounds':(lo,hi)==(584,716),'source_inside':lo<=601<hi})