"""Independent exact arithmetic audit of the attached September 28 spine study.

This accepts the six declared source coordinate pairs and checks their consequences.
It is not a re-derivation of the underlying source-table lifespan totals.
No source or completed C1431 research artifact is changed.
"""
from fractions import Fraction as Q
from hashlib import sha256
from pathlib import Path
import json

ROOT = Path(__file__).resolve().parent
SOURCE = ROOT.parent / '490d_LXX_Reversed_Spines_and_Accepted_SP_Solution_20260928.md'

def reverse_placeholders(n):
    if not isinstance(n, int) or n <= 0:
        raise ValueError('A positive integer duration is required')
    scale = 1
    while n % 10 == 0:
        n //= 10
        scale *= 10
    return int(str(n)[::-1]) * scale

checks = []
def eq(group, label, actual, expected):
    checks.append(dict(group=group, label=label, actual=actual, expected=expected, passed=actual == expected))
    assert actual == expected, (label, actual, expected)

declared = {
    'MT_regular': (4106, 2456, [1406,6416,12026], [6,4106,9116,14726]),
    'MT_cumulative': (14006,4836,[1406,4836,12026],[6,4106,7536,14726]),
    'LXX_regular': (5486,3236,[1406,5216,10436],[6,4106,7916,13136]),
    'LXX_cumulative': (14896,5746,[1406,5746,10936],[6,4106,8446,13636]),
    'SP_regular_accepted_Fall': (4406,3106,[1406,8506,11606],[6,4106,11206,14306]),
    'SP_cumulative_accepted_Fall': (13396,4716,[1406,2736,11416],[6,4106,5436,14116]),
}
computed = {}
for name, (c,f,expected2,expected3) in declared.items():
    legs = [f-1406,c-f]
    reversed_legs = [reverse_placeholders(s) for s in legs]
    path2 = [1406]
    for duration in reversed_legs:
        path2.append(path2[-1]+duration)
    path3 = [6,6+reverse_placeholders(1400)]
    for duration in reversed_legs:
        path3.append(path3[-1]+duration)
    eq('six_spines',name+' two-stage path',path2,expected2)
    eq('six_spines',name+' three-stage path',path3,expected3)
    eq('stage_translation',name+' common shift',path3[-1]-path2[-1],2700)
    computed[name] = dict(source_head=c,flood=f,original_legs=legs,reversed_legs=reversed_legs,
        path2=path2,path3=path3,two_stage_gain=path2[-1]-c)

for label,prefix,gap in [('MT','MT',0),('LXX','LXX',500),('SP','SP',-190)]:
    r = computed[prefix+'_regular'+('_accepted_Fall' if prefix=='SP' else '')]
    c = computed[prefix+'_cumulative'+('_accepted_Fall' if prefix=='SP' else '')]
    for field in ['path2','path3']:
        eq('regular_cumulative_difference',label+' '+field,c[field][-1]-r[field][-1],gap)
    eq('gain_balance',label+' gap decomposition',
       c['source_head']-r['source_head']+c['two_stage_gain']-r['two_stage_gain'],gap)

for label,actual,expected in [
    ('LXX inter-leg cancellation',(4340-3810)+(5190-5220),500),
    ('MT cumulative fixed leg',reverse_placeholders(3430),3430),
    ('LXX cumulative fixed leg',reverse_placeholders(4340),4340),
    ('SP cumulative fixed leg',reverse_placeholders(8680),8680),
    ('SP fixed leg twice LXX',8680,2*4340),
    ('SP regular Fall adjustment',4411-5,4406),
    ('SP cumulative Fall adjustment',13401-5,13396),
    ('SP regular source segment',4406-3106,1300),
    ('SP cumulative source segment',13396-4716,8680),
]: eq('source_and_fixed_segments',label,actual,expected)

for label,actual,expected in [
    ('Flood translation',5746-4836,910),('Shem translation',6346-5436,910),
    ('Target translation',1446-536,910),('MT Shem restoration',5436-536,4900),
    ('LXX Shem Exodus',6346-1446,4900),('MT Flood restoration',4836-536,4300),
    ('LXX Flood Exodus',5746-1446,4300),('9030 two-stage',10436-1406,9030),
    ('9030 shifted',13136-4106,9030),('9030 factor',9030,21*430),
    ('12600 LXX',13136-536,12600),('12600 MT',14006-1406,12600),
    ('870 heads',14006-13136,870),('870 targets',1406-536,870),
]: eq('LXX_MT_translations',label,actual,expected)

for label,actual,expected in [
    ('cumulative span',13636-1446,12190),('regular span',13136-1406,11730),
    ('cumulative endpoint',13636-Q(25,23)*(13636-1446),386),
    ('regular endpoint',13136-Q(25,23)*(13136-1406),386),
    ('difference expansion',Q(25,23)*(500-40),500),
]: eq('LXX_common_expanded_endpoint',label,actual,expected)

for label,actual,expected in [
    ('MT 344',Q(12026-4114,23),344),('LXX 354',Q(13636-5494,23),354),
    ('LXX 364',Q(13636-5264,23),364),('anchor gap',13636-12026,23*70),
    ('source gap',5494-4114,1380),('first 230 increment',1610-1380,230),
    ('second 230 increment',5494-5264,230),('LXX to MT square',13636-4114,18*23**2),
    ('square priestly',Q(25,23)*9522,10350),('square prophetic',Q(70,69)*9522,9660),
    ('apparent LXX',14894+30,14924),('apparent partition left',14924-14004,920),
    ('apparent partition right',14004-13636,368),('apparent total expansion',Q(25,23)*1288,1400),
    ('apparent other boundary',14896+30-13636,1290),
]: eq('actual_node_and_apparent_comparisons',label,actual,expected)

for label,actual,expected in [
    ('SP two-stage displacement',11606-4406,7200),
    ('SP reversal gain',7100-1700+3100-1300,7200),
    ('MT original span reversal',reverse_placeholders(4106-1406),7200),
    ('corrected MT endpoint subtraction',11606-4106,7500),
    ('SP 9900',14306-4406,9900),('SP 9890',14306-4416,9890),
    ('MT 9900',14006-4106,9900),('MT 9890',14006-4116,9890),
    ('MT actual completion 9890',14004-4114,9890),('9890 factor',9890,23*430),
    ('head translation',14306-14006,300),('lower translation',4406-4106,300),
    ('upper translation',4416-4116,300),('9900 generation',7200+2700,9900),
    ('2736 Exodus',2736-1446,1290),('SP cumulative 7000',11416-4416,7000),
    ('SP cumulative 10000',14116-4116,10000),('7000 to10000 accounting',10000-7000,2700+300),
]: eq('SP_MT_bridges',label,actual,expected)

expanded_lxx = 1406+Q(70,69)*(13136-1406)
eq('LXX_SP_return','held-Conquest LXX expansion',expanded_lxx,13306)
for label,actual,expected in [
    ('LXX expansion gain',expanded_lxx-13136,170),
    ('SP upper to LXX Creation',14306-5486,180*49),
    ('expanded LXX to LXX Creation',expanded_lxx-5486,170*46),
    ('SP lower to LXX Creation',11606-5486,17*360),
    ('source1700 returns',expanded_lxx-11606,3106-1406),
    ('upper1000',14306-expanded_lxx,1000),
    ('8820 decomposition',14306-5486,1000+7820),
    ('8820 stage decomposition',14306-5486,2700+6120),
    ('1700 factor difference',7820-6120,17*(460-360)),
]: eq('LXX_SP_return',label,actual,expected)

for label,actual,expected in [
    ('BC toAD30',10436+30-1,10465),('legacy factor',10465,7*1495),
    ('Enochian factor',10465,35*299),('legacy expansion',Q(1496,1495)*10465,10472),
    ('legacy AD endpoint',Q(1496,1495)*10465-10436+1,37),
    ('Enochian expansion',Q(300,299)*10465,10500),
    ('Enochian AD endpoint',Q(300,299)*10465-10436+1,65),
    ('Conquest toAD65',1406+65-1,3*490),
]: eq('civil_cross_era',label,actual,expected)
for source,targets in [(4836,[-6,30,65]),(4829,[2,37,72])]:
    for years,target in zip([4830,4865,4900],targets):
        # Negative targets denote BC here solely for this expected-value check.
        actual = -(source-years) if years < source else years-source+1
        eq('civil_cross_era',str(source)+' duration'+str(years),actual,target)

def jsonable(obj):
    if isinstance(obj,Q): return obj.numerator if obj.denominator==1 else str(obj)
    if isinstance(obj,dict): return {k:jsonable(v) for k,v in obj.items()}
    if isinstance(obj,list): return [jsonable(v) for v in obj]
    return obj

result = dict(status='PASS',scope='Exact arithmetic using declared source coordinates; source-total reconstruction not rerun',
    source=str(SOURCE),source_sha256=sha256(SOURCE.read_bytes()).hexdigest(),
    checks=len(checks),groups=sorted(set(x['group'] for x in checks)),
    computed_spines=computed,results=checks,inverse_of_inverse_performed=False)
(ROOT/'spine_arithmetic_verification.json').write_text(json.dumps(jsonable(result),indent=2)+'\n')
print(json.dumps(dict(status=result['status'],checks=result['checks'],groups=len(result['groups']),source_sha256=result['source_sha256'])))