from research import *
s=begin(1305,'Register the cap-round compatibility square','Which agreementofroutes isvalid for allresolvedcounts?',{},['C1304','C1209–C1212'])
r={'id':'cap_round_monotonicity','class':'identity','statement':'Q(min(L,c))=min(Q(L),Q(c))','inputs':'SameintegerL,c andsameorder-preservingQ onresolvedcountmeasures','proof':'WhicheverofL,c issmallerhasthenolargerQvalue;bothroutesselectthatvalue.','application':'NineSPpreNoah lifecounts,withinclusivecapacityresolvedbeforeQ','information':'Equalityofroutesdoesnotrestoreexcesslifeorroundingresidual.','limits':['Usingexactc ononlyonerouteisadifferentcomparison','RoundingBCbirth/Floodlabelsfirstdoesnotcomputethesameresolvedcapacity','OrdinarybiographicalL=b+r isnotinferredforinclusiveSPcounts'],'evidence':['C1202–C1212','model/cap_round_commutation_scope.json','model/cap_round_visibility_witnesses.json']}
a=artifact('model/relation_cap_round.json',json.dumps(r,indent=2)+'\n')
finish(s,{'cap_round_relation':a},'Thecap-round square is atrueoperationidentity withconsistentcount inputs. Itsagreementexplainsforwardcompatibility while thelostinformationandcountdomainremain explicit.','Registertheresidualtranslationcomposition anditsaggregatepathversion.',{'three_limits':len(r['limits'])==3,'identity_class':r['class']=='identity'})