max_rate_pos
plain-language theorem explainer
Recognition Science establishes that the maximum computation rate is strictly positive by deriving it as the reciprocal of the fundamental time quantum. Researchers bounding information processing speeds in discrete-time models cite this result when confirming that the tick imposes a finite positive upper limit on operations per unit time. The proof is a direct term-mode reduction that unfolds the rate definition and invokes division positivity on the known positive tick value.
Claim. Let $1/τ_0$ denote the maximum computation rate, where $τ_0$ is the fundamental time quantum. Then $1/τ_0 > 0$.
background
The module IC-002 derives fundamental computation limits from Recognition Science, with the central source being temporal discreteness: the tick $τ_0$ is the minimum time quantum, so the maximum bit rate equals $1/τ_0$ in RS-native units. The definition max_computation_rate is introduced as the reciprocal of the fundamental tick, which itself equals the constant tick value of 1. Upstream results supply the positivity of this tick (tick_pos) together with the standard positivity of 1, allowing the rate to inherit strict positivity via division.
proof idea
The term proof unfolds the definition of max_computation_rate to expose the division $1$ over the fundamental tick, then applies the div_pos lemma instantiated with one_pos and tick_pos.
why it matters
This theorem supplies the positivity half of the IC-002 status certificate, confirming that the tick-derived rate bound is strictly positive rather than merely non-negative. It anchors the temporal-discreteness clause in the computation-limits structure and feeds directly into the certificate string that records all IC-002 components. Within the broader framework it realizes the first of the four listed sources of computation limits by making the inverse-tick rate manifestly positive.
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