from pathlib import Path
import hashlib
ROOT=Path(__file__).resolve().parent.parent
def run(load,check):
 summaries=[];main=auth=0
 for n in range(424,433):
  c,d,r,nxt=[load(f'C{n}_{x}.json') for x in ['CERTIFICATE','DATA','RESULTS','NEXT_STEP']]
  check(f'C{n} completion',c['step']==d['step']==r['step']==f'C{n}' and c['status']=='completed' and r['status']=='passed')
  for key,name in [('data_sha256',f'C{n}_DATA.json'),('results_sha256',f'C{n}_RESULTS.json'),('next_step_decision_sha256',f'C{n}_NEXT_STEP.json')]:check(f'C{n} '+key,hashlib.sha256((ROOT/'sources'/name).read_bytes()).hexdigest()==c[key])
  prev='C423_CERTIFICATE.json' if n==424 else f'C{n-1}_CERTIFICATE.json';check(f'C{n} predecessor',c['previous_certificate_sha256']==hashlib.sha256((ROOT/'sources'/prev).read_bytes()).hexdigest())
  check(f'C{n} next decision',nxt['next_proposed_step']==f'C{n+1}' and not nxt['executed'] and bool(nxt['reason_selected_after_current_result']))
  main+=r['assertions_passed'];auth+=r['source_checks_passed'];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']})
 expected={424:{'labelled_seed_pairs':16,'coordinate_seed_pairs':8,'same_context_station_pair_trials':768,'additional_2K_station_pairs':0},425:{'Flood_start_records':72,'Noah_death_records':96,'unfiltered_labelled_trials':6912,'two_K_labelled_hits':16,'distinct_source_term_patterns':1},426:{'reconstructed_regular_records':528,'labelled_2K_pairs':46,'coordinate_2K_pairs':26,'context_templates':4,'sum_of_template_coordinate_counts':27,'coordinate_pairs_in_multiple_templates':1},427:{'MT_Noah_death_records':24,'MT_Flood_close_records':24,'record_pair_trials':576,'coordinate_coincidences':2,'coincidences_with_existing_2K_upper':1},428:{'regular_2K_coordinate_pairs':26,'cumulative_2K_Shem_Flood_pairs':6,'join_trials':156,'two_17K_coordinate_joins':4,'labelled_regular_join_realizations':6,'new_geometry_outside_C287':0},429:{'source_2K_coordinate_pairs':26,'operator_trials':104,'sourced_E_outputs':13,'sourced_E2_outputs':13,'sourced_P_outputs':0,'sourced_J_outputs':0,'complete_two_E_ladders':4,'E2_endpoint_only_cases':9},430:{'Flood_held_coordinate_arrows':9,'record_labelled_E_arrows':20,'T2_labelled_arrows':16,'T3_labelled_arrows':4,'formal_coordinate_family_cases':12,'admitted_Noah_death_input_cases':8,'Gear3_Noah_death_inputs':0,'Gear3_any_source_inputs':1},431:{'target_E2_maps':13,'first_pivot_trials':4849,'sourced_pivot_pair_solutions':39,'distinct_pivot_pair_solutions':26,'maps_with_sourced_path':5,'endpoint_only_maps_repaired':1,'complete_coordinate_paths':5},432:{'source_excerpt_cards':9,'direct_source_records_reconstructed':18,'first_pivot_source_labels':1,'second_pivot_source_labels':2,'complete_record_labelled_paths':2,'separate_Noah_biographies':3,'plus2_intermediate_sources':0,'fixed_pivot_component_assignments':8,'preserved_fixed_pivot_assignments':0,'joint_shifted_comparisons':2,'new_protocol_prescriptions_established':0}}
 for n,x in expected.items():check(f'C{n} result inventory',load(f'C{n}_DATA.json')['counts']==x)
 audit=load('PRE_C433_SEALED_AUDIT.json');check('nine sealed packets and27 publications',audit['status']=='passed' and audit['totals']['packets']==9 and audit['totals']['main_output_comparisons']==18 and audit['totals']['successful_publications']==27)
 sec=load('ROOT_SECOND_METHOD_RESULTS.json');check('separate root implementation',sec['status']=='passed' and sec['check_count']==719 and sec['source_records_generated']==528 and sec['labelled_2K_pairs']==46 and sec['context_templates']==4 and sec['fixed_17K_rectangles']==4 and sec['complete_coordinate_paths']==5 and sec['new_distinct_pivot_paths']==[[3206,3620,2756,2020]] and not sec['C434_executed'] and not sec['new_independent_agent_review'])
 check('C423 data binding',hashlib.sha256((ROOT/'sources/C423_DATA.json').read_bytes()).hexdigest()==load('C423_CERTIFICATE.json')['data_sha256'])
 for name,want in [('File_18.md','68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5'),('File_09.md','45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e'),('C265_CERTIFICATE.json','112bdcdd23e7580512f6b6a1c4222f746e6552f71b92755932397dbd25dce2de')]:check('retained hash '+name,hashlib.sha256((ROOT/'sources'/name).read_bytes()).hexdigest()==want)
 for name in ['File_02.md','File_46.md','File_11.md','C365_DATA.json']:check('baseline source binding '+name,hashlib.sha256((ROOT/'sources'/name).read_bytes()).hexdigest()==load('C423_SOURCE_MANIFEST.json')[name]['sha256'])
 check('C265 checkpoint accessible','C265' in (ROOT/'sources/C265_CHECKPOINT.md').read_text());check('current ten-step authorization',load('AUTHORIZATION.json')['authorized_steps']==[f'C{n}' for n in range(424,434)] and not load('AUTHORIZATION.json')['C434_authorized'])
 summary='C424–C433 complete. The46 labelled regular2K pairs at26 coordinate pairs reduce to four context offsets:458,708,1057,1059, with separate role and local companion terms. The Flood-start/Noah-death class is1058=350+650+60−2 and has16 labels/eight coordinates; it adds no second2K station within its fixed contexts. The sole coordinate-template overlap3298/2240 comes from distinct MT Noah-death and Flood-close contexts;349=130+215+4 also produces2300, whose required2K upper3358 is absent. All156 fixed17K join trials recover only existing C287 i2–i5, all in the458 template; companion rectangles do not remove narrower primary operator qualifications. The104 fixed-upper E/E²/P/J tests have13 sourced E and13 sourced E² outputs, no P/J outputs and four complete fixed-pivot Noah ladders. Nine Flood-held E coordinate arrows have20 labelled realizations: two two-Gear input families meet at2240, while the three-Gear strip uses Noah death2238, Noah death/Flood close2240, and Flood close2242, with Shem-death outputs2146/2148/2150. No Gear4 is admitted. The all-pivot squared-E search gives39 sourced pivot-pair solutions and five sourced coordinate paths. One is new:2148→2020→1956, using pivots3620 then2756, exactly the held3206 squared-E map. Its64×23→64×25 and32×23→32×25 legs give128+64=192. Pivot3620 is SP companion Noah birth G1/C1/T0/F0;2756 is SP-primary or LXX-OFF Noah death G1/C0/T0/F1. The stations are different MT Shem-death states G2→G3→G1. Their own Noah biographies remain950; pivot separation864 crosses contexts. The fixed3206 intermediate2056 remains absent. The+2 target still lacks2022; eight other endpoint-only squared-E maps remain unrepaired. Nine current source cards reconstruct18 relevant records; fixed quarter components do not follow the two fixed pivots, although jointly shifted comparisons remain exact. No combined source prescription, new phase, global529/Mirror action or canonical edit is established.'
 restart='Latest completed C433. C434 is proposed and unexecuted, outside this completed authorization. Use the C433 compact restart kit as the active packet; read synthesis/checkpoint then the C424–C433 locator. Preserve C423 and older checkpoints as selective references, with their historical next-step paragraphs superseded. The important new positive result is the sourced varying-pivot factorization2148→2020→1956 about3620 then2756, equal to E² about3206. It replaces neither the missing fixed-pivot2056 nor the absent+2 intermediate2022. Its two source-labelled versions differ only in the second pivot SP-primary/LXX-OFF label. The pivots cross contexts and are not one864-year Noah biography. The four source-context templates and the sole2240 alias explain the complete2K census; all fixed17K joins remain old C287 i2–i5. The Flood-held E strip uses two overlapping two-Gear input families, not a Gear4 Noah or one unchanged three-Gear input role. The larger C431 pivot menu is distinct from earlier restricted return-graph searches; their negative results retain their stated scopes. Keep source points, roles, rails, variants, Gear bindings, generated coordinates and quarter ancestry distinct. Regular Gears Noah/Shem/Flood only; SP person companions local; Flood close independent; SP primary Noah death inclusive/harmonic; both500/100 and502/98 valid; LXX native CainanON and theoretical OFF distinct. K529, E25/23, P70/69; J300/299 is File02 gap conversion, not Residue Protocol or a global calendar operator. Global paired Mirror January AD1, local junction January AD2, no civil year zero. No new source point, phase, fitted axis, upstream/cumulative Gear, primer reopening or canonical graph edit. Corrected LXX8464 supplement stays awareness only:1564→1700,2484→2700,920→1000; AD3746/2300 superseded. C-series reports, original unprefixed reports and Engine reports remain distinct. The earlier incomplete September17 local ZIP differs from the subsequently verified intact original. Repeated coordinates, labels and verification implementations are not independent historical witnesses. Proposed C434 tests whether the existing Noah950, Noah–Shem500 and sojourn/Cainan/SP-companion context shift explain the new factorization through one source formula, then checks its finite Gear/Terah family without fitting pivots. That derivation and family census have not been executed in this batch.'
 return {'step':'C433','completed_steps':[f'C{n}' for n in range(424,434)],'predecessor_summaries':summaries,'predecessor_calculation_checks':main,'predecessor_authentication_checks':auth,'predecessor_sealed_audit_totals':audit['totals'],'root_second_method_checks':sec['check_count'],'reading_index_summary':summary,'restart_checkpoint':restart,'source_access':{'File_18_File_09':'current bytes match retained controlling hashes','File_02_File_46_File_11_C365':'current bytes match C423 frozen source manifest','C265':'actual checkpoint readable; certificate hash retained'},'new_independent_agent_review':False,'C434_executed':False,'canonical_or_graph_edits':False}