bound_pos
plain-language theorem explainer
The theorem establishes that the Bremermann bound in Recognition Science is strictly positive. Researchers deriving maximum resolution rates from the 8-tick cycle would cite this when confirming the rate exceeds zero. The proof is a one-line wrapper that rewrites the bound to its explicit value 1/8 and applies numerical normalization.
Claim. $0 < 1/8$, where $1/8$ is the maximum number of debt resolutions per tick under the Recognition Science 8-tick cycle.
background
In the Recognition Science module on the Bremermann limit, the bound is defined as the reciprocal of the octave period, yielding the maximum resolutions per tick when the minimum cycle time is eight ticks. The module documentation states that no physical process resolves debt faster than 8τ₀ and that the φ^5 factor enters through the energy quantum per resolution. The upstream theorem bound_value proves the bound equals exactly 1/8 by unfolding the definition and invoking the octave_is_eight result.
proof idea
The proof is a direct term-mode reduction. It rewrites the target inequality via the bound_value theorem to obtain 0 < 1/8, then applies norm_num to discharge the numerical comparison.
why it matters
This result secures the positivity of the computational bound derived from the eight-tick octave (T7). It supports the Recognition-Theoretic Bremermann Limit by confirming the rate 1/8 is positive, consistent with the forcing chain and the self-similar fixed point. No downstream theorems are listed, but the declaration closes a basic consistency check for the Q7 module.
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