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

Version of 24 September 2026: Technically refined preprint incorporating clarifications discovered post-submission. We derive a fundamental upper bound on the number of particles that can sustain quantum coherence in a maximally entangled state. The derivation uses a unified geometric framework in which the observable spacetime ℳ is a four-dimensional continuous embedding within a higher-dimensional substratum 𝒜 with quantized information interface. Three derivations converge to the canonical form N_crit = n_max ℏ / (2 |λ| |Ψ_max| V_3 τ). They are the direct application of action quantization, the quantum Cramér-Rao bound, and the quantum capacity of the ℳ–𝒜 information channel. These are the same action-quantization constraint expressed in action, metrological, and channel-capacity language. The Cramér-Rao route additionally supplies the metrological (Heisenberg 1/N) reading, but the ceiling N_crit follows in every case from action quantization, not from three independent principles. The bound predicts sharp coherence saturation independent of environmental isolation, distinguishing the framework from standard environmental decoherence. Discriminating signatures include a conjectured distinction between fermionic and bosonic systems, an abrupt knee in decoherence rate scaling at N_crit, and a trade-off N · τ ≤ K_AFT relevant to quantum computation. A natural reinterpretation of dynamical decoupling as embedding trajectory engineering connects the framework to established experimental techniques.