What is happening here

The thermofield double behaves exactly as ER=EPR describes a two-sided black hole: one side alone is perfectly thermal (trace distance 2.7e-15 from the Gibbs state), the two-sided correlations equal the imaginary-time bridge correlator to 3.3e-16, entanglement and correlations fa

A region of empty space has no state of its own: an 8-site block of the vacuum has nonzero entropy and is mixed (1 - Tr rho^2 = 0.988) while the whole ring is pure, and the mutual information with the complement equals exactly twice the block entropy - i.e. 100% of an empty regio

NEGATIVE RESULT bounding a popular claim: in a finite spin chain, operations confined to k sites reach exactly 4^k dimensions - the full local-algebra bound, versus only 2^k on an unentangled product state - but that is just 0.1-1.6% of the full 2^N space. A small patch does NOT

Entanglement transmits nothing: across 18 interventions on one half of a critical chain (Haar unitaries, projective measurements, non-unital channels, hard reset) the other half's state is unchanged to 9e-16, and its full eigenvalue SPECTRUM moves by 4e-16, so every observable is

The famous vacuum-energy discrepancy is not a number but a function of an assumption: computed against the observed 2.24 meV scale it is 10^120.7 at a Planck cutoff, 10^108.4 at GUT, 10^56.4 at 1 TeV, 10^41.6 at QCD, and 1 by construction at the observed scale - exactly 4 decades

The anthropic bound on the vacuum energy explains far less than advertised: a validated linear growth ODE gives collapsed fractions 0.561, 0.210, 7e-3, 6e-9 as Lambda grows by 1, 10, 100, 1000, putting the ceiling at 6.4x, 35.5x, 108x the observed value at 50%, 10%, 1% thresholds

Space can be reconstructed from entanglement alone: fed only the mutual-information matrix of a 64-site oscillator ring (blindness proven by permutation test), MDS recovers the ring at r=0.995 vs true geodesics with 93% of the spectrum in one Fourier pair. Removing entanglement t

The entanglement Hamiltonian of half the vacuum is a boost: at 200-digit precision the nearest-neighbour couplings ramp linearly with distance from the cut (R^2 = 0.998-0.999) with the exact near-cut value t1 = 3.141539, matching 2pi/v_F to 1.7e-5. This gives local temperature T(

Entanglement counts degrees of freedom: fitting the Calabrese-Cardy law to block entropies alone recovers the central charge c = 0.500062 for the critical Ising chain (CFT value 1/2, converging to 0.500013 on inner windows) and c -> 1 for the free boson as the regulator mass g

The first law of entanglement dS = d holds in an interacting transverse-field Ising ground state: the ratio reaches 0.9945 at eps=1e-3 and relative entropy is positive and quadratic (log-log slope 2.05). This is the identity from which linearized Einstein equations emerge in holo

A polymer with zero energy in every configuration exerts a real tension matching T dS/dx from pure state counting (Monte Carlo vs exact enumeration, max deviation 4.5e-4). Verlinde's holographic-screen composition (Unruh temperature + N = Ac^3/G hbar bits + equipartition) returns

In an exactly reversible HPP lattice gas (Loschmidt echo returns the initial state bit-for-bit), coarse-grained entropy rises in BOTH time directions away from a low-entropy initial state. The thermodynamic arrow of time lives in the boundary condition, not the dynamical laws (Bo

The vacuum of a free lattice scalar field carries entanglement entropy that scales with a region's boundary, not its volume: fitted 3D exponent 2.09±0.01 (area predicts 2, volume 3), 2D 1.05 (perimeter), 1D flat to 9 digits. Bekenstein–Hawking-like area scaling emerges from a bar

A globally static quantum state contains ordinary time evolution for internal observers: the solver-found null state of a clock+qubit constraint is stationary to machine precision ( ~ 6e-30, global qubit maximally mixed), yet conditioned on the clock the qubit Rabi-oscillates at