import hashlib,json

def run(load,read,check):
    summaries=[];main=auth=0
    for n in range(435,444):
        c=load(f'C{n}_CERTIFICATE.json');r=load(f'C{n}_RESULTS.json');d=load(f'C{n}_DATA.json');decision=load(f'C{n}_NEXT_STEP.json')
        for key,name in [('data',f'C{n}_DATA.json'),('results',f'C{n}_RESULTS.json'),('next_step_decision',f'C{n}_NEXT_STEP.json')]:
            check(f'C{n} sealed '+key,hashlib.sha256(read(name).encode()).hexdigest()==c[key+'_sha256'])
        prev='C434_CERTIFICATE.json' if n==435 else f'C{n-1}_CERTIFICATE.json'
        check(f'C{n} predecessor link',c['previous_certificate_sha256']==hashlib.sha256(read(prev).encode()).hexdigest())
        check(f'C{n} completed with sequential reassessment',c['status']=='completed' and r['status']=='passed' and decision['next_proposed_step']==f'C{n+1}' and decision['authorization_remaining']==444-n)
        summaries.append({'step':f'C{n}','title':c['title'],'main_result':c['main_result'],'calculation_checks':r['assertions_passed'],'authentication_checks':r['source_checks_passed'],'next_question':decision['question']})
        main+=r['assertions_passed'];auth+=r['source_checks_passed']
    check('nine steps and27 saved files authenticated',len(summaries)==9 and load('PRE_C444_SEALED_AUDIT.json')['totals']['published_files']==27)
    sec=load('SECOND_METHOD_RESULTS.json')
    check('alternate source reconstruction and164 checks pass',sec['status']=='passed' and sec['check_count']==164 and sec['source_records_generated']==528 and sec['regular_coordinates']==373)
    check('C435 complete paths agree with alternate method',sec['forward_complete_paths']==[[3206,2148,2020,1956],[3206,3206,3170,3206]])
    check('C436 label identity audit retained',load('C436_DATA.json')['counts']=={'label_assignments':16,'same_record_returns':8,'alias_switches':8,'all_SP_paths':1,'unchanged_context_paths':0})
    check('C437 finite profile boundary retained',load('C437_DATA.json')['counts']=={'profiles':6,'sourced_centers':4,'complete_five_point_profiles':1})
    check('C438 full reflection inventory retained',sec['reflection_coordinate_orbits']==106 and sec['reflection_labelled_pairs']==258)
    check('C439 complete complement class retained',load('C439_DATA.json')['counts']['labelled_pairs']==128)
    check('C440 typed versus coordinate500 map retained',sec['typed_inverse_500']==40 and sec['additional_aliases']==8 and load('C440_DATA.json')['counts']['coordinate_target_pairs']==16)
    check('C441 reduced grammar has six classes and six coordinate overlaps',load('C441_DATA.json')['counts']['classes']==6 and load('C441_DATA.json')['counts']['double_memberships']==6)
    check('C442 reversed E source boundary retained',sec['reverse_complete_paths']==[[3188,3170,3206,3170]])
    check('C443 fixed Mirror boundary retained',sec['Mirror_sourced_slots']==37 and sec['Mirror_complete_orbits']==5 and load('C443_DATA.json')['counts']['core_source_hits']==0)
    check('C265 certificate remains authenticated',hashlib.sha256(read('C265_CERTIFICATE.json').encode()).hexdigest()=='112bdcdd23e7580512f6b6a1c4222f746e6552f71b92755932397dbd25dce2de')
    check('authorization ends atC444',load('BATCH_AUTHORIZATION.json')['steps']==list(range(435,445)) and not sec['C445_executed'])
    return {'step':'C444','completed_steps':list(range(435,445)),'predecessor_summaries':summaries,'predecessor_main_checks':main,'predecessor_authentication_checks':auth,
            'predecessor_sealed_audit':load('PRE_C444_SEALED_AUDIT.json'),'alternate_method':sec,
            'synthesis':{'new_loop':'3206→3170→3206 withp3620/q2756; opposite signed18×23→18×25 gaps.',
                         'source_midpoint':'3188 MT NoahG2/C1/T0/F1; outer radius432, inner radius18;24:1.',
                         'source_reflections':'Four sourced centers and six source classes account for106 coordinate orbits/258 labelled pairs.',
                         'E_boundary':'Only the zero-net loop survives source reflection; reflected2K path4228/4356/4420 is absent.',
                         'Mirror_boundary':'One four-year partial image survives; the core profile has no image in the retained48-record LXX cumulative menu.'},
            'regular_sources_unchanged':True,'canonical_or_graph_edits':False,'new_independent_agent_review':False,'C445_executed':False,
            'next_proposed_question':'Census all ordered compositions of the four fixed local reflections over373 source inputs, requiring sourced intermediate and output records, and reduce the resulting partial maps to source-qualified translations.5968 trials; no new centers or coordinates.'}