s1297.py

from research import *
s=begin(1297,'Register the cap and count-rounding operations','How do theirforwardrules andinformationloss differ?',{},['C1296','C1202–C1212','C1277–C1278'])
ops=[{'id':'cap_resolved_life','input':'labelledbaselineL andresolvedcapacityc','action':'y=min(L,c)','output':'selectedlifecountwithsourcecounttag','preserved':'orderundercoordinatewiseincrease; unchangedinputbelowcap','lost':'excessL−c abovecap','retained_recovery':'branch-appropriateexcess/residualregister','evidence':['C1202','C1204','C1206']},{'id':'round_resolved_count','input':'specifiednonnegativeintegerrowcount','action':'Q(x)=5floor((x+2)/5)','output':'roundedrowcountplusoptionalrho=x−Q(x)','preserved':'order;translationsby5Z','lost':'within-cellresidualwhenomitted','retained_recovery':'Q(x)+rho=x;aggregatepathresidualisun-normalizedsum','evidence':['C1190','C1213','C1277','C1278']}]
a=artifact('model/operations_cap_and_round.json',json.dumps({'operations':ops,'composition':'Q(min(L,c))=min(Q(L),Q(c)) forconsistentlyresolvedcounts; separatelyroundeddatecapacitiesarenotthesameinput.','classification':'Monotone many-to-onemaps; notinvertibleaffinesymmetries.'},indent=2)+'\n')
finish(s,{'cap_round_operations':a},'Theinventorydistinguishes clippingawayexcess from forgettingaroundingresidual. Theirforwardcompatibility requiresconsistentlyresolvedcountsonbothroutes.','RegisterlosslessRounded-residualtranslation withoutmistakingitforinformationcompression.',{'two_ops':len(ops)==2,'distinct_losses':ops[0]['lost']!=ops[1]['lost']})