dft8_eq_8
plain-language theorem explainer
The equality fixes the DFT-8 mode count at exactly eight inside the J-cost quantum error correction module. Researchers constructing phi-harmonic pulse schedules for below-threshold correction cite it to anchor the eight-mode structure that follows from three spatial dimensions. The proof is a direct reflexivity step on the explicit definition of the count as eight.
Claim. The number of modes in the discrete Fourier transform of order eight equals 8.
background
The module Quantum Error Correction from J-Cost implements RS patent 015 on phi-harmonic QEC scheduling. It defines the DFT-8 mode count locally as eight to support threshold analysis where the error rate crosses the band J(φ) ∈ (0.11, 0.13). Upstream the mathematics module introduces the same count as 2^3 and proves the equality by decision procedure; the physics module redeclares the count explicitly as the numeral 8 to keep the QEC certificate self-contained.
proof idea
This is a one-line wrapper that applies reflexivity directly to the definition of the DFT-8 mode count.
why it matters
The result supplies the dft8_count field inside the QEC certificate that also records the five code families and the threshold crossing conditions. It instantiates the eight-tick octave (period 2^3) from the forcing chain and the spatial dimension D = 3. The downstream qecCert and the Fourier certificate both reference it to complete the certification of 5φ Hz scheduling.
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