dft8ModeCount
plain-language theorem explainer
The definition assigns the constant eight to the DFT-8 mode count, realizing the eight-tick octave from the Recognition Science forcing chain for phi-harmonic scheduling. Quantum error correction researchers cite it when confirming that the protocol runs at the fundamental frequency 5φ/8 Hz below the J-cost threshold band. It is introduced as a direct constant definition that matches the upstream Fourier analysis result of 2^3.
Claim. The number of modes in the eight-point discrete Fourier transform for the quantum error correction protocol equals eight: $dft8ModeCount = 8$.
background
In the Recognition Science framework the eight-tick octave is fixed by the forcing chain at T7 with period 2^3, which T8 combines with three spatial dimensions. The module Quantum Error Correction from J-Cost (RS patent 015) implements phi-harmonic QEC scheduling that applies DFT-8 pulses at 5φ Hz. Error correction is effective once the J-cost of the error rate drops below J(φ) in the interval (0.11, 0.13). The upstream Fourier analysis result defines the identical count as 2^3 and supplies the value used here.
proof idea
The definition is a direct constant assignment of the natural number eight. It is consistent with the upstream Fourier analysis definition that sets the count to two raised to the power three.
why it matters
This constant populates the QECCert structure that records five code families, zero J-cost at unit rate, strictly positive error costs for nonzero rates, and the DFT-8 mode count. It is referenced by the local dft8_eq_8 theorem and by the FourierCert structure in the mathematics module. The definition therefore supplies the concrete realization of the eight-tick octave required for the phi-harmonic QEC protocol.
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