TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_exact_cutoff_higgs_measure.py
Original file SHA-256: a214ba46a5eb61d70463995c14b634d037ec24ec626152f385ae408567e1d071
Inclusive original lines: 1-57
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 | """R055: fixed-rank bounded cutoff/flat Higgs volume discriminator.
000002 | Analytic proof decides the class. Native96 checks are constructor controls.
000003 | No physical Higgs measure, regulator or Yukawa is selected.
000004 | """
000005 | from pathlib import Path
000006 | import sys,json
000007 | import numpy as np
000008 | import sympy as s
000009 | ROOT=Path(__file__).resolve().parents[4]
000010 | sys.path.insert(0,str(ROOT/'verification'))
000011 | import v252_full_finite_triple as v
000012 | checks={};details={}
000013 | def need(name,ok):
000014 |     checks[name]=bool(ok)
000015 |     if not ok:raise AssertionError(name)
000016 | rng=np.random.default_rng(252)
000017 | Ys=[rng.normal(size=(3,3))+1j*rng.normal(size=(3,3)) for _ in range(4)]
000018 | mr=rng.normal(size=(3,3));MR=mr+mr.T
000019 | z3=np.zeros((3,3),complex);z2=np.zeros((2,2),complex)
000020 | DY=v.full_D(*Ys,z3);DM=v.full_D(z3,z3,z3,z3,MR)
000021 | P=v.rep(1,z2,z3);K=v.Kswap();gamma=v.grading();p=.25
000022 | def phi(H):
000023 |     h1,h2=H;q=np.array([[np.conj(h2),h1],[-np.conj(h1),h2]])
000024 |     a=v.rep(0,q,z3);B=a@(DY@P-P@DY);B=B+B.conj().T
000025 |     return B+K@B.conj()@K+DM
000026 | grid=[0.,1.,2.,4.,16.,64.];rows=[]
000027 | for i,radius in enumerate(grid):
000028 |     ph=phi((0j,complex(radius)));h=p*gamma-1j*gamma@ph
000029 |     need(f'native96_Hermitian_{i}',np.max(abs(h-h.conj().T))<1e-11)
000030 |     ev=np.linalg.eigvalsh(h)
000031 |     he=float(np.exp(-ev**2).sum());po=float(np.exp(-abs(ev)).sum())
000032 |     need(f'whole96_heat_trace_bounded_{i}',0<=he<=96+1e-12)
000033 |     need(f'whole96_even_Poisson_trace_bounded_{i}',0<=po<=96+1e-12)
000034 |     rows.append(dict(radius=radius,heat=he,even_Poisson=po))
000035 | details['native96_controls']=rows
000036 | need('nontrivial_native96_radial_response',rows[-1]['heat']<rows[0]['heat'])
000037 | # Exact four-real-dimensional radial volume, regulator and tail statements.
000038 | x,e,R=s.symbols('x epsilon R',positive=True)
000039 | Z=s.simplify(2*s.pi**2*s.integrate(x**3*s.exp(-e*x*x),(x,0,s.oo)))
000040 | need('exact_regulated_flat_C2_partition',Z==s.pi**2/e**2)
000041 | mass=s.simplify(2*s.pi**2*s.integrate(x**3*s.exp(-e*x*x),(x,0,R))/Z)
000042 | need('exact_regulated_flat_ball_mass',s.simplify(mass-(1-s.exp(-e*R**2)*(1+e*R**2)))==0)
000043 | need('bounded_ball_mass_lost_at_zero_regulator',s.limit(mass,e,0,dir='+')==0)
000044 | need('ball_mass_leading_coefficient',s.limit(mass/e**2,e,0,dir='+')==R**4/2)
000045 | need('flat_partition_diverges',s.limit(Z,e,0,dir='+')==s.oo)
000046 | need('radial_H2_moment_diverges',s.simplify(-s.diff(s.log(Z),e))==2/e)
000047 | # General nonzero polynomial cone term grows, with any top degree >=0.
000048 | d=s.symbols('d',integer=True,nonnegative=True)
000049 | need('cone_radial_primitive_derivative',s.simplify(s.diff(x**(d+4)/(d+4),x)-x**(d+3))==0)
000050 | need('cone_radial_integral_diverges',s.limit(x**(d+4)/(d+4),x,s.oo)==s.oo)
000051 | need('quartic_truncation_not_exact_large_amplitude',s.limit(s.exp(-x),x,s.oo)==0 and s.limit(1-x+x*x/2,x,s.oo)==s.oo)
000052 | [OMITTED: non-scientific conversation or execution metadata]
000053 | need('odd_moment_can_vanish_despite_escape',s.integrate(x*s.exp(-e*x*x),(x,-s.oo,s.oo))==0)
000054 | need('constant_normalized_observable_converges',s.simplify(Z/Z)==1)
000055 | out=dict(all_passed=all(checks.values()),checks=checks,details=details,scope='Fixed-rank bounded cutoff and ordinary noncompact C2 volume only; no actual physical measure selection, no continuum/no-go claim, no new Lean')
000056 | Path(__file__).with_name('EXACT-CUTOFF-HIGGS-MEASURE.json').write_text(json.dumps(out,indent=2)+'\n')
000057 | print(json.dumps(dict(all_passed=out['all_passed'],controls=len(checks),native96=rows)))