verify babylonian algebra.py

from fractions import Fraction as F
from pathlib import Path
import json

def K(q,x,factor=F(70,69)):
    return F(q)+factor*(x-q)

def enc(x):
    if isinstance(x,F): return x.numerator if x.denominator==1 else str(x)
    if isinstance(x,dict): return {k:enc(v) for k,v in x.items()}
    if isinstance(x,(list,tuple)): return [enc(v) for v in x]
    return x

checks=[]
def ck(name,actual,expected):
    assert actual==expected,(name,actual,expected)
    checks.append({'name':name,'actual':enc(actual),'expected':enc(expected),'pass':True})

grid={'restoration':536,'Babylonian_opening':606,'MT_Minimum_Covenant':1866,
      'LXX_Actual_Year6_Cainan_OFF':5366,'MT_cumulative_Shem_SP_inverse_Flood3':5436,
      'LXX_regular_inverse_head3':13136,'SP_cumulative_inverse_head3':14116}
positions={k:F(v-536,70) for k,v in grid.items()}
ck('source appointed 70 grid',list(positions.values()),[0,1,19,69,70,180,194])
ck('restoration fixed Prophetic source node image',K(536,5366),5436)
ck('restoration fixed reciprocal source node image',K(536,5436,F(69,70)),5366)
ck('signed reciprocal displacement',K(536,5436,F(69,70))-5436,-70)
ck('Shem fixed Babylonian image',K(5436,606),536)
ck('Shem fixed reciprocal target',K(5436,536,F(69,70)),606)
ck('signed forward target displacement',K(5436,606)-606,-70)
ck('first 12600 partition',[13136-5436,5436-536],[7700,4900])
ck('alternate named 12600 partition',[13136-5366,5366-536],[7770,4830])
ck('first preserved total',7700+4900,12600)
ck('alternate preserved total',7770+4830,12600)
ck('Babylonian four node chain',[13136-5436,5436-606,606-536],[7700,4830,70])
ck('complete pair 70 translation',[5366+70,536+70],[5436,606])
ck('equal 69x70 spans',[5366-536,5436-606],[69*70,69*70])
ck('outer and inner crosses',[5436-536,5366-606],[70*70,68*70])
ck('Covenant reduced grid',19+F(25,23)*(180-19),194)
ck('Covenant actual grid',K(1866,13136,F(25,23)),14116)
ck('Covenant partitions',[13136-1866,14116-1866,1866-536],[70*161,70*175,70*19])
ck('shared two stage edge',10436-2736,7700)
ck('common stage pair translation',[10436+2700,2736+2700],[13136,5436])
ck('two stage restoration path',[10436-2736,2736-536,10436-536],[7700,2200,9900])
ck('three stage restoration path',[13136-5436,5436-536,13136-536],[7700,4900,12600])
ck('fixed restoration tail and total increments',[4900-2200,12600-9900],[2700,2700])
ck('Exodus Jerusalem restoration chain',[2736-1446,1446-586,586-536],[3*430,2*430,50])
ck('five 430 before Jerusalem',2736-586,5*430)
ck('Babylonian two subdivisions',[606-586,586-536,606-536],[20,50,70])
ck('SP inverse Flood Nativity tail',2736-6,2730)
ck('2730 displays',[39*70,F(15,2)*364,21*130],[2730,2730,2730])
ck('two stage Nativity total',10436-6,(110+39)*70)
ck('File29 MT Year6 plus60 Exodus counterpart',4176-1446,2730)
ck('endpoint translation to MT counterpart',[2736+1440,6+1440],[4176,1446])
ck('four prophetic years',1440,4*360)
ck('stage minus target shift',2700-(536-6),31*70)
ck('Nativity grid',[F(2736-6,70),F(10436-6,70),F(11416-6,70)],[39,149,163])
ck('Restoration grid',[F(5436-536,70),F(13136-536,70),F(14116-536,70)],[70,180,194])
ck('three parallel reduced shifts',[70-39,180-149,194-163],[31,31,31])
ck('fixed Babylonian target does not transfer',K(2736,606),F(13228,23))
assert K(2736,606)!=536

result={'status':'PASS','grouped_check_count':len(checks),
 'scope':'Named source comparisons and exact affine keys; fixed original inverse spines; no second decimal reversal. Counts are not independent discoveries.',
 'restoration70_grid':{k:{'BC':grid[k],'position70':enc(v)} for k,v in positions.items()},
 'signed_anchored_reciprocal':{'anchor_BC':536,'input_BC':5436,'factor':'69/70','signed_input_span':4900,'signed_output_span':4830,'output_BC':5366,'coordinate_change':-70},
 'source_reassessment':{'5366':'Initially a generated partition cut; independently identified in File29 as Actual LXX Year-6 / second-Cainan-removed comparison. Original native-Cainan inverse spine remains fixed.'},
 'checks':checks}
Path(__file__).with_name('babylonian_algebra.json').write_text(json.dumps(result,indent=2,ensure_ascii=False)+'\n')
print(json.dumps({'status':'PASS','grouped_check_count':len(checks)}))