from research import *
s=begin(1308,'Register anchored composition with its integer-stage restriction','Why can exactaffineformulas compose whileanintegervaluedchronologyroutefails?',{},['C1307','inherited/model/fixed_pivot_key_domains.json','inherited/model/key_constraint_inputs.json'])
a0,b0=14006,4836;gap=a0-b0;d=json.loads((ROOT/'inherited/model/fixed_pivot_key_domains.json').read_text());r={'id':'affine_composition_and_grid','class':'identity_with_domain_condition','identity':'D_k T_t=T_(kt) D_k inlinearcoordinates;anchoredoffsetscarriedexplicitly','rational_domain':'Nonzeroexactfactorscomposeoverrationalspans.','integer_example':{'first':'J=300/299 about14006','second':'P=70/69 about4836','first_integer_input':'x=14006+299t','first_integer_output':'y=14006+300t','second_span':'9170+300t','residue_mod3':gap%3,'conclusion':'Neverdivisibleby69;integerintermediatestageconditionfailsforallintegert.'},'source_scope':'Theobstructionbelongstothesefixedpivotsandgridrequirements,notallJ/Papplications.','evidence':'inheritedC984–C1007 fixedpivotdomainclassification'}
a=artifact('model/relation_affine_grid_domains.json',json.dumps(r,indent=2)+'\n')
finish(s,{'affine_grid_relation':a},'Theanchoredmaps composeexactly over rationalcoordinates, butthefixed14006→4836 J-to-P routehas nointegerstage-domain: itssecondspan remains2mod3. Thisexplains whygriddomain belongsin theoperationrecord.','Register thecriterion forreflectionto pass througha sourcegrouping.',{'gap9170':gap==9170,'mod3':gap%3==2 and300%3==0,'inherited_agrees':next(x for x in d if x['pair']=='J→P')['nonempty'] is False})
