molecularQuantumStateClasses_le_2pow5
plain-language theorem explainer
The number of prepared molecular quantum state classes is bounded above by 32. A physicist working on RS-derived quantum molecular design would cite this bound to confirm that five bits suffice to index the full set of classes. The proof is a one-line wrapper that reduces the inequality to the explicit count of 25 and verifies it numerically.
Claim. Let $N$ be the number of molecular quantum state classes, defined as the product of the number of molecular energy levels and the number of quantum gate types. Then $N$ satisfies $N ≤ 2^5$.
background
The C4 module on quantum molecular design depth counts prepared state classes as the product of the cardinalities of the molecular energy level type and the quantum gate type. Upstream results establish that this product equals exactly 25 by unfolding the definition and rewriting with the separate counts for energy levels and gate types. The module sets the local context that five bits suffice for indexing under the RS model, while reachability of specific targets remains an empirical claim outside the Lean certification.
proof idea
The proof is a one-line wrapper that applies the upstream equality theorem reducing the state class count to 25, then uses numerical normalization to confirm the inequality 25 ≤ 32 holds.
why it matters
This bound supplies the addressable-by-five-bits component of the quantum molecular depth certificate. It completes the C4 claim that 25 classes fit inside a 5-bit space, supporting the Recognition Science framework's five-bit addressing depth in the context of the phi-ladder and forcing chain. The downstream certificate combines this with the exact count and the four-bit strict inequality.
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