finite_energy_implies_finite_computation
plain-language theorem explainer
Finite positive energy E guarantees a positive finite upper bound on the maximum operations per second. Researchers deriving computational speed limits in discrete spacetime or Recognition Science models would cite this when applying the Bremermann bound. The proof is a one-line term that constructs the witness directly as max_ops_per_sec E, verifies positivity via scaled multiplication of positive constants, and closes the inequality by reflexivity.
Claim. For any real number $E > 0$, there exists a real number $B > 0$ such that the maximum operations per second permitted by energy $E$ satisfies that rate at $E$ is at most $B$.
background
The module IC-002 derives computation limits from temporal discreteness (tick as minimum time quantum), the irrationality of phi, Landauer erasure cost, and the Bremermann limit (maximum operations bounded by $2E/ℏ$ per second in RS units). The function max_ops_per_sec E encodes this energy-proportional rate. The local setting treats these as emergent from the Recognition framework rather than imposed externally.
proof idea
The proof is a one-line term that supplies the witness max_ops_per_sec E, applies mul_pos to bremermann_limit_pos and the hypothesis E > 0 to obtain positivity of the bound, and invokes le_refl to establish the required inequality.
why it matters
This result (IC-002.13) supplies the finite-energy implication inside the computation-limits section, directly supporting the Bremermann bound stated in the module documentation. It anchors the information-domain claims that link energy to bounded operations and prepares for later results on tick discreteness and phi irrationality. No downstream uses are recorded yet.
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