TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/e_series_role_review/check_roles.py
Original file SHA-256: 47cd63f5a4668dfb0ce5d4d4e665106c2d24371c9fd32ea97593e9f04e9daa96
Inclusive original lines: 1-93
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | """Three decisive exact role tests in the already given native root/source chart.
000002 | 
000003 | No new source, metric, coupling or state is chosen. Reuse the existing
000004 | original eightfold-source root builder; never run its writing main().
000005 | """
000006 | from pathlib import Path
000007 | from fractions import Fraction as F
000008 | from itertools import combinations
000009 | import importlib.util
000010 | import json
000011 | import sympy as sp
000012 | 
000013 | ROOT=Path(__file__).resolve().parents[4]
000014 | path=ROOT/'experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/dynamic_reconstruction_20261027/check_a7_e7_clock.py'
000015 | spec=importlib.util.spec_from_file_location('existing_a7_e7_source',path)
000016 | old=importlib.util.module_from_spec(spec)
000017 | spec.loader.exec_module(old)
000018 | 
000019 | 
000020 | def need(ok, message):
000021 |     if not ok:
000022 |         raise RuntimeError(message)
000023 | 
000024 | 
000025 | def run():
000026 |     roots=frozenset(tuple(int(2*x) for x in r) for r in old.e8_roots())
000027 |     dot=lambda a,b:sum(x*y for x,y in zip(a,b))
000028 |     axes=((1,1,1),(1,-1,-1),(-1,1,-1),(-1,-1,1))
000029 |     corners=[frozenset(r for r in roots if
000030 |                       r[5]*a[0]==r[6]*a[1]==r[7]*a[2]) for a in axes]
000031 |     need(all(len(c)==72 for c in corners),'four E6 corners')
000032 |     normals=[]
000033 |     for r in sorted(roots):
000034 |         if any(r[:5]) or sum(x!=0 for x in r)!=2:
000035 |             continue
000036 |         if next(x for x in r if x)!=2:
000037 |             continue
000038 |         normals.append(r)
000039 |     need(len(normals)==6,'six unoriented D3 root normals')
000040 |     edges=[]
000041 |     for i,j in combinations(range(4),2):
000042 |         need(len(corners[i]&corners[j])==40,'common D5')
000043 |         matches=[n for n in normals if all(dot(n,r)==0 for r in corners[i]|corners[j])]
000044 |         need(len(matches)==1,'unique E7 edge')
000045 |         target={r for r in roots if dot(matches[0],r)==0}
000046 |         closed=set(corners[i]|corners[j]);front=set(closed)
000047 |         while front:
000048 |             add={tuple(x+y for x,y in zip(a,b)) for a in front for b in closed}
000049 |             front=(add&roots)-closed;closed.update(front)
000050 |         need(closed==target and len(closed)==126,'two E6 generate precisely E7')
000051 |         edges.append({'vertices':[i,j],'normal':list(matches[0]),
000052 |                       'intersection_roots':40,'union_roots':104,'closure_roots':126})
000053 |     need(len({tuple(x['normal']) for x in edges})==6,'whole tetrahedron edge dictionary')
000054 | 
000055 |     # A root-current cut is an inclusion of a subalgebra, not a quotient map.
000056 |     # Removed root alpha has a nonzero retained Cartan projection, so
000057 |     # P[e_alpha,e_-alpha] != [Pe_alpha,Pe_-alpha]=0, with either bracket sign.
000058 |     alpha6=[F(1),0,0,0,0,F(1),0,0]
000059 |     p6=alpha6[:5]+[F(1,3)]*3
000060 |     alpha7=[F(1),F(1),0,0,0,0,0,0]
000061 |     p7=[F(x)-F(1,4) for x in alpha7]
000062 |     need(sum(x*x for x in p6)==F(4,3),'nonzero E6 projected coroot')
000063 |     need(sum(x*x for x in p7)==F(3,2),'nonzero E7 projected coroot')
000064 | 
000065 |     rho2=(7,5,3,1,-1,-3,-5,-7)
000066 |     neutral={r for r in roots if sum(r)==0}
000067 |     need(len(neutral)==126,'actual Q neutral E7')
000068 |     commuting={r for r in neutral if dot(rho2,r)==0}
000069 |     need(len(commuting)==8 and sp.Matrix(list(commuting)).rank()==4,'four A1 zero-mode roots')
000070 |     need(all(dot(a,b) in (0,8,-8) for a in commuting for b in commuting),'orthogonal A1 factors')
000071 |     counter=(2,-2,0,0,0,0,0,0)
000072 |     need(counter in neutral and -F(dot(rho2,counter),4)==-1,'neutral is not source-time invariant')
000073 |     for a in (F(1,4),F(3,4)):
000074 |         all_commuting={r for r in roots if
000075 |                        -F(dot(rho2,r),4)+(2*a-1)*F(sum(r),4)==0}
000076 |         need(all_commuting==commuting,'same horizontal source-time centralizer in both quarters')
000077 |     result={'scope':'given native E8 lattice and original eightfold source H8 only',
000078 |             'tetrahedron':{'E6_vertices':4,'E7_edges':edges},
000079 |             'root_cut_projection':{'E6_nonzero_projected_coroot_norm2':str(sum(x*x for x in p6)),
000080 |                                    'E7_nonzero_projected_coroot_norm2':str(sum(x*x for x in p7)),
000081 |                                    'is_Lie_homomorphism':False},
000082 |             'actual_H8':{'Q_neutral_E7_roots':126,
000083 |                          'ordinary_horizontal_commuting_roots':8,
000084 |                          'horizontal_root_type':'4A1',
000085 |                          'neutral_counterexample':'[H8,J_(e0-e1,0)]=-J_(e0-e1,0)',
000086 |                          'all_affine_commuting_modes_classified':False},
000087 |             'physical_E8_E7_E6_gauge_or_breaking_rule_derived':False}
000088 |     Path(__file__).with_name('role-check-results.json').write_text(json.dumps(result,indent=2)+'\n')
000089 |     print(json.dumps(result,indent=2))
000090 | 
000091 | 
000092 | if __name__=='__main__':
000093 |     run()