Abstract

We extrapolate the finite model of Hawk07-A by proving dimension-dependent recovery, operational-function, and composition theorems. The word “wormhole” denotes a declared quantum-return certificate, not a spacetime tunnel.

For a logical payload of dimension $d$, an independent maximally entangled early resource, one known Haar-sampled vault unitary, and nested release, we rederive the complete complementary moment and obtain a sufficient full-diamond recovery threshold

Here $r_{\ast }$ is the released quantum dimension, not the entire receiver dimension; $f$ is the blank-factor dimension; and $p$ is the allowed measure of uncertified devices. A positive-residual, multi-cut design is given explicitly. The proposed inverse-linear error scaling is corrected to the inverse-square scaling actually supplied by this certificate. No optimality claim is made.

The certified operational functions include referenced state return, entanglement transfer, classical message transmission, logical postprocessing, and privacy against the declared complete residual. For square-power payload dimensions, a new calculation proves coexistence of recovery and coherent entropy turnover on a family of Haar measure at least $1/(4d)$, with one physical residual qubit at the final cutoff. This extends, rather than silently reuses, Hawk07-A's dimension-$16$ calculation.

A finite convoy is constructed using separately prepared resources. Its joint error is bounded even for mutually entangled payloads. A different theorem states a sufficient complete memory-reset contract for reuse; small previous leakage alone does not supply that contract. Noise, batch workspace, classical communication, terminal discard, and the distinction between a quantum payload and a classical log are accounted for separately.

These are conditional predictions of finite quantum-information models. They predict neither transport of a material spacecraft through spacetime nor a metric, travel time, energy condition, fuel cost, gravitational Page curve, or geometric wormhole.