We investigate the two-observer disagreement $\mathbb{E}|S_A - S_B|$ in AEHPV non-isometric holographic codes with observers included via the HUZ cloning rule. The central result is a structural identity, here stated in its corrected form: at leading order in $1/d_{\rm eff}$, the Haar-$V$-averaged observer-reduced state equals the diagonal of the bulk $A$-marginal in the observer's cloning basis, $\mathbb{E}_V[\rho_{R_A}] = \operatorname{diag}(\rho_A^{\rm bulk}) + O(1/d^2)$. Bulk-marginal coherences across distinct pointer values are projected out by the combination of HUZ cloning and Haar-$V$ averaging. This reduces the disagreement problem to a moment calculation of the bulk-marginal diagonal, whose scaling with $d_B$ depends on the bulk state class. For random product states we obtain $\mathbb{E}|S_A - S_B| \to \sqrt{4(\pi^2/3-3)/\pi}\,d_B^{-1/2} \approx 0.608\,d_B^{-1/2}$; for Haar-random states, $\sqrt{2/\pi}\,/(d_M\, d_B^{3/2})$. The exponent gap is exactly $1$. We verify the identity and both scalings against full simulation, including out-of-sample tests at sub-$\sigma$ precision.
Paper I had a small but real crack in its foundation. It said that, on average, what an observer sees equals the "marginal" of the bulk state – the full reduced description. Paper II shows that is not quite right: what the observer sees on average equals only the diagonal of that marginal – the bar chart of probabilities, with the off-diagonal "interference" entries erased. And the erasing is not an approximation we impose; it falls out of the physics, from the way the observer is cloned plus the randomness of the code. Fixing this made the rest of the machinery exact instead of approximate, and made plain exactly which object the scaling laws describe. What Paper II did not yet do was prove that this diagonal object actually controls the true quantum disagreement – that step is Paper III.
Featured-mold cards. Equation, plain gloss, section pointer + evidence.
The averaged observer state equals the diagonal of the bulk marginal, not the marginal. Off-diagonal coherences across pointer values collapse at first moment, by the combination of HUZ cloning and Haar averaging – not by hand.
Slow decay for low-entanglement states. Analytic prefactor; matches simulation.
Fast decay for maximally scrambled states. The black-hole-interior regime.
One whole power of $d_B$ between the classes. Stable across deformations.
AEHPV code with Haar $V$; HUZ observer cloning.
First-moment Haar integration shows the off-diagonal collapse and yields the corrected diagonal identity.
Each class reduces to a moment of the bulk-marginal diagonal – Dirichlet for product, Gaussian-limit for Haar.
Full-simulation checks at the diagonal-entry level, the variance asymptote, the prefactor convergence, and end-to-end, with out-of-sample tests.
A correct foundation and a sharp, unanswered question: does the diagonal model govern the true observer entropy? Paper III answers it with the entropy-replacement theorem.