one_resolution_per_8tick
plain-language theorem explainer
The theorem shows that the Bremermann bound multiplied by the octave period equals one, establishing that exactly one resolution occurs per eight-tick cycle. Information theorists and Recognition Science researchers would cite it when deriving fundamental computation limits from the debt-resolution cycle. The proof works by unfolding the bound definition, confirming the octave is nonzero via its eight-tick value, and applying field simplification to reach equality.
Claim. In Recognition Science units, the maximum number of resolutions per eight-tick cycle multiplied by the octave length equals one.
background
The module treats the Recognition-Theoretic Bremermann Limit. The classical bound on computation rate by mass-energy is replaced by a tighter limit: no process resolves debt faster than one full R̂ cycle. The octave is defined as eight ticks, the fundamental evolution period. The bound itself is the reciprocal of this period, so their product is unity. Upstream, the octave definition appears in both the MusicalScale and Constants modules, where it is set to eight times the base tick and linked to the phi connection with twelve.
proof idea
The tactic proof unfolds the bremermannBound definition. It then introduces a hypothesis that the octave is nonzero by rewriting with the octave_is_eight lemma and normalizing. Field simplification cancels the remaining factors to obtain the equality.
why it matters
This result anchors the Q7 section on the Recognition-Theoretic Bremermann Limit. It directly implements the eight-tick octave from the forcing chain (T7) and the phi^5 energy quantum arising from hbar = phi^{-5}. The declaration supplies the minimum time per recognition event, which downstream mass and information formulas rely upon when counting resolutions along the phi-ladder.
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