Information-Theoretic Bound on Macroscopic Quantum Coherence from Topological Embedding Geometry

We derive a fundamental upper bound on the number of particles that can sustain quantum coherence in a maximally entangled state. Using a unified geometric framework in which the observable space-time $\mathcal M$ is a four-dimensional continuous embedding within a higher-dimensional substratum $\mathcal A$ with quantized information interface, three structurally independent derivations -direct application of action quantization, the quantum Cramér-Rao bound, and the quantum capacity of the $\mathcal M$-$\mathcal A$ information channel- converge to the canonical form $N_{\text{crit}} = n_{\max} \hbar / (2 |\lambda \Psi_{\max}| V_3(B) \,\tau)$. The bound predicts sharp coherence saturation independent of environmental isolation, distinguishing the framework from standard environmental decoherence. Discriminating signatures include distinct effective bounds for fermionic versus bosonic systems, an abrupt knee in decoherence rate scaling at $N_{\text{crit}}$, and a trade-off $N \ \tau \leq K_{\text{AFT}}$ relevant to quantum computation. A natural reinterpretation of dynamical decoupling as embedding trajectory engineering connects the framework to established experimental techniques.