s1306.py

from research import *
s=begin(1306,'Register coherent translation through Rounded residuals','How does exactsourcechange remaincompatiblewiththeRoundedrepresentation?',{},['C1305','C1218–C1221','C1278'])
r={'id':'rounded_residual_coherence','class':'identity','statement':'encode(x+d)=T_d(encode(x));T_eT_d=T_(d+e),whereencode(x)=(Q(x),x−Q(x))','proof':'Bothsidesreconstructtheuniqueexactvaluex+doreventuallyx+d+e,andnearestfiveencodingisunique.','aggregate_statement':'Fororderedrowdataw=y+rho, Uw=Uy+Urho;Urhoisnotrenormalized.','applications':['105ordinaryintertraditionmeasurements','complete25-nodeMosesexactfield'],'limits':['Droppingrhoallowsall-inputtranslationonlyford in5Z','ChronologicaladmissionofintermediateTstatesremainsaseparatesourcecondition','BlockroundingQ(Bw)usuallydiffersfromB Q(w)'],'evidence':['model/all_ordinary_lifted_translations.json','model/rounded_translation_composition.json','model/Moses_complete_residual_recovery.json']}
a=artifact('model/relation_rounded_residuals.json',json.dumps(r,indent=2)+'\n')
finish(s,{'residual_relation':a},'TheRoundedplusresidual representation carries exactsourcechanges coherently, anditsaccumulatedresiduals recovercompletepaths. Itworks byretaininginformation, notby makingroundingadditive.','Register uniformKeycompatibility withsums andthelimitforcomponent-specificKeys.',{'two_applications':len(r['applications'])==2,'proof_bound':all((ROOT/p).exists() for p in r['evidence'])})