from math import prod
import hashlib
def run(load,read,check):
 summaries=[];checks=auth=0
 for n in range(445,469):
  cert=load(f'C{n}_CERTIFICATE.json');result=load(f'C{n}_RESULTS.json')
  for key,suffix in [('data_sha256','DATA'),('results_sha256','RESULTS'),('next_step_decision_sha256','NEXT_STEP')]:check(f'certificate_C{n}_{suffix}',hashlib.sha256(read(f'C{n}_{suffix}.json').encode()).hexdigest()==cert[key])
  check(f'passed_C{n}',result['status']=='passed')
  summaries.append({'step':f'C{n}','title':cert['title'],'main_result':cert['main_result']});checks+=result['assertions_passed'];auth+=result['source_checks_passed']
 r=load('C286_DATA.json')['target_register'];vertices=[2731,3765,2735,2733];anchors=[3248,3250,2758,2756]
 def count(xs,native):return prod(sum(z['center']==x and not(native and z['tradition']=='LXX' and z['Cainan']==0) for z in r) for x in xs)
 clarification={'C465_vertex_only_count':[count(vertices,False),count(vertices,True)],'complete_anchored_mixed_cycle_count':[count(vertices+anchors,False),count(vertices+anchors,True)],'meaning':'C46512-to12 counts its four listed cycle vertices only. Including the four required operator anchors gives48-to12. No coordinate, arrow, cycle or interval conclusion changes.'}
 check('mixed_cycle_count_clarification',clarification['C465_vertex_only_count']==[12,12] and clarification['complete_anchored_mixed_cycle_count']==[48,12])
 audit=load('PRE_C469_SEALED_AUDIT.json');check('prior72_publications',audit['published_files']==72 and audit['status']=='passed')
 check('all_scoped_reports',len(summaries)==24)
 return {'step':'C469','completed_steps':list(range(445,470)),'predecessor_summaries':summaries,'predecessor_main_checks':checks,'predecessor_authentication_checks':auth,'predecessor_sealed_audit':audit['totals'],'alternate_method':load('C468_DATA.json')['verified_totals'],'label_count_clarification':clarification,'synthesis':{'source_supported_interval_ladder':{'pairs':[[2148,3206],[2020,3170],[1956,3206]],'spans':[1058,1150,1250],'pivots':[3620,2756]},'related_shorter_ladder':{'pairs':[[1895,2953],[1745,2895]],'spans':[1058,1150],'pivot':3620},'input_row_translation':253,'output_row_translation':275,'mixed_operator_reachability_K_hits':0,'fixed_Mirror_complete_pair_images':5,'fixed_Mirror_inherited_17K_assignments':2,'C287_archived_complete_17K_rows':4,'essential_companion_pivot':3620,'LXX_OFF_coordinate_dependency':False},'standing_scope':'Mirror/529; regular Gears Noah/Shem/Flood only; no new source, phase, global axis or canonical graph edit.','canonical_or_graph_edits':False,'new_independent_agent_review':False,'C470_executed':False,'next_proposed_question':'Census all existing1150-year source pairs, test common E transport to1250 at the same eight fixed pivots, and record which have a complete sourced2K predecessor. Do not add pivots, phases or dates.'}