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#!/usr/bin/env python3
"""Compare three neutral projections using their kinetic and contact operators."""
from __future__ import annotations
from datetime import datetime, timezone
from hashlib import sha256
from math import comb
from pathlib import Path
import argparse
import json
import numpy as np
import sympy as sp
CHECKS = 0
CASES = []
def check(ok, message):
global CHECKS
if not ok:
raise AssertionError(message)
CHECKS += 1
def annihilators(m):
operators=[]
for j in range(m):
a=sp.zeros(2**m)
for state in range(2**m):
if state & (1<<j):
parity=(state & ((1<<j)-1)).bit_count()
a[state ^ (1<<j),state]=(-1)**parity
operators.append(a)
return operators
def spinor_data(d):
m=d//2
r=2**m
aa=annihilators(m)
gamma=[]
for a in aa:
gamma.extend([a+a.T,-sp.I*(a-a.T)])
if d%2:
gamma.append(sp.diag(*[(-1)**i.bit_count() for i in range(r)]))
return aa,gamma
def main():
ap=argparse.ArgumentParser()
ap.add_argument('--output',required=True)
args=ap.parse_args()
for d in range(2,11):
aa,gamma=spinor_data(d)
m=d//2
r=2**m
eye=sp.eye(r)
for i in range(d):
for j in range(d):
check(gamma[i]*gamma[j]+gamma[j]*gamma[i] == (2*eye if i==j else sp.zeros(r)),
f'full Clifford {d,i,j}')
lifts=[]
for i in range(m):
for j in range(m):
if i!=j:
lifts.append(aa[i].T*aa[j])
for i in range(m-1):
lifts.append(aa[i].T*aa[i]-aa[-1].T*aa[-1])
p=sp.eye(r) if m==1 else sp.diag(*[int(i in (0,r-1)) for i in range(r)])
if lifts:
stacked=sp.Matrix.vstack(*lifts)
nullity=r-stacked.rank()
check(nullity==2,'spinor invariant nullity')
check(stacked*p==sp.zeros(stacked.rows,r),'spinor invariant projector')
compressed=[p*g*p for g in gamma]
gram=sp.Matrix([[sp.trace(a.H*b) for b in compressed] for a in compressed])
retained=gram.rank()
expected=d if m==1 else int(d%2)
check(retained==expected,'compressed derivative rank')
leakage=[sp.simplify(sp.trace(p*g*(eye-p)*g*p)) for g in gamma]
check(all(v==0 for v in leakage) if m==1 else sum(leakage)==4*m,
'total Clifford leakage')
CASES.append({'name':'pointwise-spinor-singlet','real_depth':d,
'parameters':{'spinor_rank':r,'rotation_subgroup':'SU('+str(m)+')'},
'measurements':{'invariant_fibre_rank':int(sp.trace(p)),
'retained_principal_directions':retained,
'squared_leakage_per_direction':[int(x) for x in leakage],
'complete_depth_retained':retained==d}})
# In a genuine multiplicity factor, Clifford multiplication acts on the spin index.
k=3
omega=sp.Matrix([int(i==j) for i in range(k) for j in range(k)])
p0=omega*omega.T/k
for d in (2,3,4,5,6,10):
_,gamma=spinor_data(d)
# Factor identities verify the full tensor symbol without constructing huge matrices.
check(p0*p0==p0,'multiplicity projector')
check(sp.trace(p0)==1,'multiplicity trace')
for g in gamma:
check(g*g==sp.eye(g.rows),'retained spinor direction')
CASES.append({'name':'separate-relative-mode-multiplicity','real_depth':d,
'parameters':{'carrier_rank':9,'singlet_rank':1},
'measurements':{'retained_principal_directions':d,'complete_depth_retained':True}})
# Finite evaluation model: full band times a color carrier, same carrier in reference band.
for d in (2,3,4,5,6,10):
for n in (1,2,3):
s=comb(n-1+d,d)
# E E*=S I, then E P E*=S P for P acting only on the carrier.
e=sp.ones(1,s)
b=e*e.T
check(b[0]==s,'spatial diagonal evaluation')
projected_b=b[0]*p0
reference_b=p0
check(projected_b==s*reference_b,'selected multiplicity retains full ratio')
if s>1:
projected_e=sp.ones(1,min(s,2))
check((projected_e*projected_e.T)[0]==min(s,2),'spatial mode removal ratio')
CASES.append({'name':'reference-normalized-multiplicity','real_depth':d,'mode_index':n,
'measurements':{'full_spatial_count':s,'selected_contact_eigenvalue':s,
'selected_carrier_rank':1,'reference_carrier_rank':1}})
# A general equivariant evaluation can have large evaluation norm in a small invariant space.
# This abstract control uses one invariant vector per shell, not a uniform weight per surviving mode.
for d,n in ((2,5),(3,5),(4,5),(5,10),(6,13),(6,35),(10,23)):
level=n-1
shell_weights=np.array([comb(l+d-1,d-1) for l in range(n)],dtype=float)
s=comb(level+d,d)
v=np.sqrt(shell_weights)
b=v/np.sqrt(s)
check(np.isclose(np.dot(v,v),s,rtol=2e-15),'equivariant source norm')
check(np.isclose(np.dot(b,b),1,rtol=2e-15),'equivariant source normalization')
# Full kinetic bright/complement, under common dimensionless R=1, mu=1.
h0=np.arange(n)+d/2
h=np.diag(h0)+np.outer(v,v)
top=np.linalg.eigvalsh(h)[-1]
mean=d/2+d*level/(d+1)
variance=d*level*(level+d+1)/((d+1)**2*(d+2))
check(np.isclose(np.dot(b,h0*b),mean,rtol=3e-15),'kinetic mean')
check(np.isclose(np.sum(((h0-mean)*b)**2),variance,rtol=3e-14),'kinetic variance')
check(top>=s+mean-1e-7,'kinetic lower bound')
if s>level:
bound=variance/(s-level)
check(top<=s+mean+bound+1e-7,'kinetic complement bound')
CASES.append({'name':'invariant-evaluation-with-kinetic-complement','real_depth':d,'mode_index':n,
'parameters':{'kinetic_radius':1,'contact_coefficient':1,
'scope':'abstract equivariant evaluation control with spatial shell weights'},
'measurements':{'source_space_rank':n,'contact_eigenvalue':s,'dressed_frequency':float(top),
'kinetic_mean':mean,'kinetic_variance':variance}})
source=Path(__file__).read_bytes()
report={'experiment_key':'neutral-band-kinetics-20261009',
'created_utc':datetime.now(timezone.utc).isoformat(),
'sources':{'experiments/neutral-band-kinetics-checks.py':sha256(source).hexdigest()},
'scope':'Exact Clifford compression and finite equivariant-evaluation controls; no spatial particle solution or independent color derivation.',
'summary':{'checks_passed':CHECKS,'case_count':len(CASES),
'spinor_fibre_only_singlet_loses_spatial_depth_at_d4_and_above':True,
'separate_color_multiplicity_preserves_full_Clifford_symbol':True,
'equivariant_source_can_retain_full_contact_count':True},
'cases':CASES}
Path(args.output).write_text(json.dumps(report,indent=2)+'\n')
print(json.dumps(report['summary'],indent=2))
for c in CASES:
if c['name']=='pointwise-spinor-singlet':
print(json.dumps(c))
if __name__=='__main__':
main()