five_pow_2
plain-language theorem explainer
Five squared equals twenty-five is recorded as the base case in the product recognition lattice for cross-domain state spaces. Researchers constructing bounds on combined cognitive and oncological recognition states cite this equality when scaling to higher products such as five to the sixth. The verification relies on direct numerical computation.
Claim. $5^{2} = 25$
background
The Product Recognition Lattice module organizes cross-domain products of recognition state spaces as a hierarchy of powers of five. Five squared corresponds to a pair of five-dimensional domains and serves as the starting point for the lattice. The module documentation states that this structure combines C1 cognitive and C3 oncology domains to produce a joint state space of five to the sixth, constrained below two to the fourteenth.
proof idea
A one-line wrapper applying the decide tactic to confirm the arithmetic equality.
why it matters
This equality anchors the lattice hierarchy in the module documentation and supports the structural claim that five to the sixth yields a 15625-state space fitting in 14 bits. It supplies the initial numerical fact required for the sequence of higher powers listed as sibling declarations.
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