octave_eq_8
plain-language theorem explainer
The theorem confirms that the octave period defined as 2 raised to the spatial dimension D equals exactly 8. Researchers deriving the coherence energy exponent from the Fibonacci constraint on dimension would cite this to anchor the relation 2^D = F_6. The proof is a direct unfolding of the local definition followed by numerical normalization.
Claim. The octave period defined by $2^D$ equals 8.
background
The Coherence Exponent module proves that the coherence energy exponent -5 is fixed by the Fibonacci constraint on dimension D. Here the octave is defined locally as the natural number 2^D. Upstream results supply the base octave as the ratio 2 in musical scales and as 8 ticks in constants, but the module specializes it to the power of D to connect with the Fibonacci sequence.
proof idea
The proof is a one-line wrapper that unfolds the definition of octave as 2^D and applies norm_num to reduce the arithmetic directly to 8.
why it matters
This result is used by the downstream theorem octave_is_fib_6 to equate the octave with the sixth Fibonacci number. It supplies the concrete step 2^D = 8 = F_6 in the module's main theorem, which combines with D = 3 = F_4 to produce the deficit 5 and thereby fixes the coherence exponent at phi^{-5}. The equality aligns with the eight-tick octave period in the forcing chain.
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