phase6.py

from pathlib import Path
import sys,json
sys.path.insert(0,str(Path(__file__).resolve().parents[1]))
from runner import *

run('Bind the shared cumulative lives','Which original source quantities justify theNoah extension in all three MSS?',
 lambda:{'Noah_lifespans':{'MT':950,'LXX':950,'SP':950},'Shem_lifespans':{'MT':600,'LXX':600,'SP':600},'rounding_residuals':[0,0],'domain':'serial cumulativelifespan boundaries'},
 'Noah950 andShem600 are common transmitted lifespan inputs, unchanged by five-year rounding; their cumulative adjacency follows the serial rule.',
 'Derive eachNoah boundary from its already frozenFlood seam.', ['File18.md §§2–4,6','File51a.md §16.2'])

run('Derive the cumulativeNoah nodes','What ordered source boundaries follow from the fixedFlood seams and950+600?',
 lambda:model('cumulative_source_nodes',{m:{'C':c,'F':f,'S':f+600,'N':f+1550,'A':1406} for m,c,f in [('MT',14006,4836),('LXX',14896,5746),('SP',13396,4716)]}),
 'Noah/Shem/Flood are6386/5436/4836 forMT,7296/6346/5746 forLXX, and6266/5316/4716 forSP.',
 'Rebuild the upperprefix from lifespan rows rather than infer it only from endpoints.')

def rows():
 names=['Adam','Seth','Enosh','Kenan','Mahalalel','Jared','Enoch','Methuselah','Lamech']
 common=[930,912,905,910,895,962,365,969]
 raw={'MT':common+[777],'LXX':common+[753],'SP':[930,912,905,910,895,847,365,720,653]}
 rounded={m:[5*((x+2)//5) for x in v] for m,v in raw.items()}
 return model('prefix_source_rows',{'names':names,'actual':raw,'rounded':rounded,'sums':{m:sum(v) for m,v in rounded.items()},'residuals':{m:[y-x for x,y in zip(raw[m],rounded[m])] for m in raw}})
run('Reconstruct the nine preNoah lifespans','Do the source-selected rows regenerate thethree cumulative prefixes?',rows,
 'The rounded sums are7620 forMT,7600 forLXX, and7135 forSP Creation. TheMT/LXX difference is solely the selectedLamech775/755 row.',
 'Apply the already acceptedSPFall adjustment to its sourceprefix.', ['File18.md selectedlifespan tables','File51a.md roundingrule'])

run('Place theSPFall in the prefix','Does theaccepted five-yearFall adjustment recover theprefix7130 andknown490 gap?',
 lambda:{'SP_Creation_prefix':model('prefix_source_rows')['sums']['SP'],'SP_Fall_prefix':model('prefix_source_rows')['sums']['SP']-5,'head_minus_Noah':13396-6266,'MT_SP_difference':7620-(7135-5),'row_loss':7620-7135},
 'SPFall gives7130=7135−5, preserving theknownMT–SP490=485+5 source difference aboveNoah.',
 'Freeze all seven nonempty named-cut selections before root execution.')

run('Specify the finite partition family','Which original segment selections will be compared without arbitrary new cuts?',
 lambda:model('partition_spec',{'order':['A','F','S','N','C'],'partitions':{'F':['F'],'S':['S'],'N':['N'],'FS':['F','S'],'FN':['F','N'],'SN':['S','N'],'FSN':['F','S','N']},'head_and_anchor':'alwaysretained','reversal':'eachoriginallegonce','empty_selection':'notpartofthisnamedspineextension'}),
 'The test contains exactly seven named-cut selections per manuscript, with source head andConquest held fixed.',
 'ExecuteMT first to retain its established secondarybranch controls.')

def execute(m):
 n=model('cumulative_source_nodes')[m];out={}
 for name,cuts in model('partition_spec')['partitions'].items():
  nodes=[n['A']]+[n[k] for k in cuts]+[n['C']]
  legs=[y-x for x,y in zip(nodes,nodes[1:])]
  out[name]={'source_nodes':nodes,'source_legs':legs,'inverse_legs':[inverse(x) for x in legs],'path1406':path(legs),'path6':path([1400]+legs,6),'total':sum(inverse(x) for x in legs)}
 model('partitions_'+m,out);return out

run('Execute the sevenMT partitions','WhichMT heads result from thefixed originalNoah/Shem/Flood cuts?',lambda:execute('MT'),
 'MTF/S remain12026;N/FS/FN agree at13016;SN reaches7706 andFSN8696. The inherited13016 branch is reproduced.',
 'Apply theidentical procedure to thedeclarednativeLXX.', ['File52c_latest.md §3.4'])

run('Execute the sevenLXX partitions','What does the same named-cut procedure produce fornativeLXX?',lambda:execute('LXX'),
 'LXXF gives10936;S/FS11926;N/FN17956;SN/FSN13636. The complete result retains all seven constructions.',
 'ExecuteacceptedSP with itsFallhead andunchangedlifespans.')

run('Execute the sevenSP partitions','Does theacceptedSP trunk preserve itshead across theNoah alternatives?',lambda:execute('SP'),
 'SPF/S/N/FS/FN allgive11416;SN/FSN give7096. The source-selectedFall does notneedanynew adjustment.',
 'Explain theall-three N=FN agreement through itslocalsegment law.')

run('CompareNoah-only withFlood+Noah','Do all three source lowerlegs satisfy the requiredreversal additivity?',
 lambda:model('lower_1550_law',{m:{'a':a,'merged_original':a+1550,'merged_inverse':inverse(a+1550),'split_inverse':inverse(a)+inverse(1550),'defect':inverse(a+1550)-inverse(a)-inverse(1550)} for m,a in [('MT',3430),('LXX',4340),('SP',3310)]}),
 'All three localdefects vanish:8940=3430+5510,9850=4340+5510,6840=1330+5510. ThereforeN andFN agree.',
 'Identify thedigit condition that explains these particularadditive cases.')

run('Explain thelower merge mechanism','Why does the1550 merge preserve these three reversed totals?',
 lambda:{'significant_core_additions':[[343,155,498],[434,155,589],[331,155,486]],'each_place_adds_without_carry':all(all(x+y<10 for x,y in zip(map(int,str(a)),map(int,'155'))) for a in [343,434,331]),'register':'three-digitcore,onetrailingzero throughout'},
 'Everyplace adds withoutcarry andthethree-digit/one-zero register stays fixed. Reversal distributes over these particular sums.',
 'Now split the shared1550 block itself into theoriginal600 and950 lives.')