entrainmentConfidence_zero
plain-language theorem explainer
Engineers specifying transcranial neuromodulation devices cite this result to fix the baseline of the entrainment confidence function at unity. The function is defined to return one over phi to the rung index, so the zero-rung case is identically one. The proof is a one-line wrapper that unfolds the definition and simplifies.
Claim. The entrainment confidence at rung zero equals one: $C(0) = 1$, where the function $C(k) := 1 / phi^k$ for natural-number rung $k$.
background
The module derives a cortical neuromodulation device operating at cortical-column resonance $5 phi$ Hz with pulse spacing $1/(5 phi)$ s. The entrainment confidence function supplies a phi-ladder scaling of relative confidence, defined directly as one divided by phi to the power of the rung index. This zero-rung theorem is the base case required by the device certification record.
proof idea
One-line wrapper that unfolds the definition of entrainment confidence and applies simp to reduce the power to one.
why it matters
The result populates the zero-confidence field inside the cortical neuromodulation device certificate. It anchors the phi-ladder scaling for the engineering specification at the $5 phi$ Hz resonance, consistent with the self-similar fixed point of the recognition framework. The module falsifier is an EEG study placing optimal entrainment outside the interval [7.5, 8.1] Hz.
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