bremermann_limit_pos
plain-language theorem explainer
The result shows that the Bremermann limit constant is positive. Physicists and information theorists working within the Recognition Science framework cite it to establish finite computation bounds for systems with positive energy. The proof is a term-mode reduction that unfolds the relevant definitions and applies norm_num to verify the strict inequality.
Claim. $B > 0$ where $B$ is the Bremermann limit such that the maximum number of operations per second for a system of energy $E$ is at most $B E$.
background
Module IC-002 examines fundamental limits of computation in Recognition Science. These limits stem from the discrete tick time, the irrationality of the golden ratio preventing exact rational simulation, the Landauer energy cost for bit erasure, and the Bremermann limit arising from the relation $E t ≥ ħ/2$, which caps operations at $2E/ħ$ per second. The reduced Planck constant is supplied upstream as ħ = φ^{-5} in native units from the Constants module.
proof idea
The term proof unfolds the definition of the Bremermann limit together with that of ħ, exposing an expression whose positivity follows immediately, and then invokes norm_num to discharge the goal by simplification.
why it matters
This positivity result feeds the theorems max_ops_scales_with_energy and finite_energy_implies_finite_computation, which build energy-dependent bounds and finite computation guarantees. It corresponds to theorem IC-002.11 in the computation limits structure and supports the broader claim that computation is bounded by the temporal discreteness and the value of ħ from the forcing chain.
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