TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/automatic_identification/check_clock_four_cycle_class.py
Original file SHA-256: 0c74e5e98dd56a0eafcd7876ff799406ba35ff8259f576e52b2d386ca77cd5b8
Inclusive original lines: 1-98
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | [OMITTED: non-scientific conversation or execution metadata]
000002 | 
000003 | The unchanged native helper performs its own old root/flag checks on import.
000004 | Those checks are reused, not a new scientific result of this application.
000005 | """
000006 | from pathlib import Path
000007 | from collections import Counter
000008 | from itertools import product
000009 | import importlib.util
000010 | import json
000011 | 
000012 | ROOT=Path(__file__).resolve().parents[4]
000013 | path=ROOT/'experiments/theory-contracts/e-series-joint-source-20261023/compiler_closure.py'
000014 | spec=importlib.util.spec_from_file_location('existing_native_compiler',path)
000015 | old=importlib.util.module_from_spec(spec)
000016 | spec.loader.exec_module(old)
000017 | 
000018 | 
000019 | def require(ok,message):
000020 |     if not ok:
000021 |         raise RuntimeError(message)
000022 | 
000023 | 
000024 | def run():
000025 |     rows=[]
000026 |     for a in (1,3,5,7):
000027 |         for b in range(4):
000028 |             # Four times the actual torus parameter. Family eigenphases are
000029 |             # (1,3,-3,-1)/8 on the four tetrahedral Spin6 weights.
000030 |             av=(a,a,a,b,b,2,-1,0)
000031 |             require(sum(av)%2==0, '4v belongs to actual E8 lattice')
000032 |             c=[8,0,0,0]
000033 |             for r in old.ROOTS:
000034 |                 d=sum(x*y for x,y in zip(av,r))
000035 |                 require(d%2==0,'quarter phase integrality')
000036 |                 c[(d//2)%4]+=1
000037 |             want=[64,64,56,64] if b%2==0 else [70,56,66,56]
000038 |             require(c==want,'full exact E8 weight-one character')
000039 |             rows.append({'a':a,'b':b,'char':c,
000040 |                          'matches_native_J':c==[60,64,60,64]})
000041 |     require(not any(x['matches_native_J'] for x in rows),
000042 |             'none in the native full field conjugacy class')
000043 |     out={'scope':'Given fixed Spin10/SU4 embedding, SM-commuting Spin10 torus with fourth power minus-one and one SU4 four-cycle lift. Complete covering representatives; no preferred field conjugator or physical Yukawa dictionary.',
000044 |          'family_four_cycle_torus_four_v':[2,-1,0],
000045 |          'candidates':rows,'native_matches':0,
000046 |          'root_arithmetic':'exact doubled native E8 roots',
000047 |          'complete_class_argument':'CLOCK-CLASS-PROOF.txt'}
000048 |     Path(__file__).with_name('clock-four-cycle-class-test.json').write_text(
000049 |         json.dumps(out,indent=2)+'\n')
000050 |     histogram=Counter()
000051 |     matches=[]
000052 |     d5=[tuple(x//2 for x in r[:5]) for r in old.INTEGER_ROOTS
000053 |         if all(x==0 for x in r[5:])]
000054 |     for n0 in product(range(4),repeat=5):
000055 |         if sum(n0)%2==0:
000056 |             continue
000057 |         for central in (0,1):
000058 |             n=list(n0)
000059 |             n[0]+=4*central
000060 |             av=tuple(n)+(2,-1,0)
000061 |             c=[8,0,0,0]
000062 |             for r in old.ROOTS:
000063 |                 d=sum(x*y for x,y in zip(av,r))
000064 |                 require(d%2==0,'general lift phase integral')
000065 |                 c[(d//2)%4]+=1
000066 |             histogram[tuple(c)]+=1
000067 |             if c==[60,64,60,64]:
000068 |                 require(sum(x%2 for x in n)==3 and
000069 |                         sorted(x%4 for x in n if x%2==0)==[0,2],
000070 |                         'native class matching condition')
000071 |                 fixed=[r for r in d5 if sum(x*y for x,y in zip(n,r))%4==0]
000072 |                 require(len(fixed)==6,'Spin10 centralizer has six roots')
000073 |                 # All fixed roots use exactly the three odd planes, and have
000074 |                 # the A2 sum/difference pattern. Together with Cartan rank5
000075 |                 # they give A2 plus three abelian directions.
000076 |                 require(all(all(r[j]==0 for j in range(5) if n[j]%2==0)
000077 |                             for r in fixed),'fixed roots confined to three planes')
000078 |                 matches.append(n)
000079 |     require(sum(histogram.values())==1024 and len(matches)==320,
000080 |             'whole general Spin10 lift class')
000081 |     general={'scope':'All Spin10 torus lifts with g5^4=-1 and fixed SU4 four-cycle conjugacy class, before fixed SM commutation. Complete covering representatives modulo4D5; original root helper.',
000082 |              'representatives':1024,
000083 |              'character_histogram':{str(k):v for k,v in sorted(histogram.items())},
000084 |              'native_character_matches':320,
000085 |              'matching_condition':'Exactly3 odd Spin vector planes and2 even planes with residues0,2',
000086 |              'matching_Spin10_centralizer_root_count':6,
000087 |              'Spin10_fixed_semisimple_algebra_for_matches':'A2 only, plus3 abelian directions',
000088 |              'not_a_new_original_source_selection':True}
000089 |     Path(__file__).with_name('clock-general-spin10-class.json').write_text(
000090 |         json.dumps(general,indent=2)+'\n')
000091 |     print(json.dumps({'covering_representatives':len(rows),
000092 |                       'characters':sorted(set(tuple(x['char']) for x in rows)),
000093 |                       'native_matches':0,'general_representatives':1024,
000094 |                       'general_native_matches':320}))
000095 | 
000096 | 
000097 | if __name__=='__main__':
000098 |     run()