bound_value
plain-language theorem explainer
The theorem establishes that the Recognition Science Bremermann bound equals one eighth resolutions per tick. Researchers deriving fundamental computation limits from the eight-tick cycle would cite this when evaluating information-processing rates. The proof is a direct term reduction that unfolds the bound definition and substitutes the octave length.
Claim. The maximum number of resolutions per tick satisfies $bremermannBound = 1/8$, where the bound is the reciprocal of the eight-tick octave period.
background
Recognition Science sets the Bremermann limit by requiring each debt resolution to complete within one full eight-tick cycle. The definition bremermannBound is introduced as one divided by the octave length, with the upstream theorem octave_is_eight proving that this length equals eight in fundamental ticks. This yields a maximum rate of one resolution per eight ticks, or 1/8 per tick in RS-native units where the fundamental tick is normalized to one.
proof idea
The term proof unfolds the definition of bremermannBound and rewrites the octave symbol using the upstream theorem octave_is_eight, which itself reduces the octave to eight by unfolding tick and applying ring.
why it matters
This supplies the explicit numerical value invoked by the downstream positivity result bound_pos. It completes the concrete evaluation step inside the Recognition-Theoretic Bremermann Limit, directly tying the eight-tick octave (T7) to the information rate bound. The module positions the result as a tighter constraint than classical Bremermann limits because the phi^5 energy quantum per resolution enforces the eight-tick minimum.
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