OPERATOR AXIOMS
✓ A1 Linearity
✓ A2 ∥T∥op ≤ 50.0
✓ A3 Self-adjoint T*=T
✓ A4 Hilbert–Schmidt
✓ A5 Compact
✓ A6 PSD ⟨Tf,f⟩≥0
✓ A7 σ(T)⊂[0,∥T∥]
✓ A8 Block consistency

VALIDATION R1–R10
✓ R1 Self-adjointness
✓ R2 Rank-corr ρS=1.0000
✓ R3 Counting N(T)
✓ R4 GUE pair corr.
✓ R5 HS norm/compact
✓ R6 Trace/heat kernel
✓ R7 ξ-symmetry
✓ R8 Real spectrum
✓ R9 Domain/BC
✓ R10 Large-N converg.

Passed: 10 · Failed: 0
TAP-HSO RESONANCE SCALAR
R = 1.0000
Qₘᵢₙ > 0 · σ(T) ⊂ ℝ · 20/20 CERTIFIED
MASTER EQUATIONS
ĤΨₙ = γₙΨₙ
Hilbert–Pólya eigenvalue eq.
R = ⟨ψ,D*Dψ⟩ / ⟨ψ,Kψ⟩
TAP-HSO Resonance Scalar
kH(t) = (6/H²)sech⁴(t/H)
Bochner-repaired kernel
RH ⟺ Q∞H > 0
Analyst's Problem (T2)
QH=DH+OH, Banalytic<1
Gap G1 closed · XII.1∞

HPH LOCK (T₀=0)
F(0) = 2967.813
F′(0) = 0.0 ✓
F″(0) = −3626.639 ✓
λmax=8.0631

Historic suite: 21/21 PASS
Anti-circ. AC1–AC5: ENFORCED
354+ tests · mpmath dps=80