Quantum State Geometry - Towards Quantum Gravity

We present a minimal operational route towards quantum gravity from three axioms: (1) time = Fisher distinguishability dt = \, ds / Δ E, (2) bounded spectrum E ≤ Eₘₐₓ=c⁵/G, (3) rq ≥ rₛ. From this single constant Eₘₐₓ we derive:G = c⁵/Eₘₐₓ²,Lₘᵢₙ= c/Eₘₐₓ,modified dispersion v/c = [1-(E/Eₘₐₓ)²]3/2≈ 1-32(E/Eₘₐₓ)² (quadratic, GRB-safe, k₂~10⁻³⁸, Δ t~5×10⁻¹⁹\,s for D=10²⁶\,m, $E=10$\,GeV),GUP [x,p]=i(1+p²c²/Eₘₐₓ²),bounce H²=8π G/3ρ(1-ρ/ρₘₐₓ),regular black hole core f(r)=1-2GMr²/(r³+r₀³), Fisher vs.\ Einstein locality and CHSH Bell Sq=2√2>2 proof. No linear LIV: linear $n=1$ is ruled out by GRB090510 (EQG>9.3×10¹⁹\,GeV), quadratic $n=2$ survives (M₂>7.13×10¹¹\,GeV). We gravitize the bound of QM, not quantize GR. Towards, not completed.