max_ops_scales_with_energy
plain-language theorem explainer
The maximum number of operations per second for a system grows linearly with its energy and remains positive for any positive energy. Workers on fundamental computation bounds in physics would reference this to guarantee a nonzero rate under the Bremermann scaling. The short proof multiplies the established positivity of the limit constant by the energy hypothesis.
Claim. Let $B > 0$ be the Bremermann limit constant. For every real number $E > 0$, $B E > 0$.
background
The module derives computation limits from temporal discreteness via the fundamental tick, irrationality of the golden ratio, Landauer erasure costs, and the Bremermann bound from the energy-time uncertainty. The maximum operations per second is defined as the product of the Bremermann constant and system energy. An upstream theorem states that the Bremermann limit is positive and finite, with the explicit claim that for a system with energy E the maximum operations per second is bounded by B times E.
proof idea
The proof is a one-line wrapper that applies the multiplication-positivity lemma to the upstream theorem on positivity of the Bremermann limit together with the hypothesis that energy is positive.
why it matters
This result supplies the scaling property IC-002.12 in the series on fundamental limits of computation. It confirms that the Bremermann bound derived from the Recognition Science forcing chain yields a strictly positive rate for any nonzero energy, consistent with the eight-tick octave and discrete time structure. No downstream uses are recorded, leaving open its integration with mass ladders or modal actualization.
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