defectIterate_zero_param
plain-language theorem explainer
The theorem states that the iterated defect vanishes at zero deviation for every iteration count. Researchers applying the Recognition Composition Law to zeta zeros cite this to fix the critical-line baseline before deriving amplification bounds. The proof is a one-line simplification that unfolds the defectIterate definition and applies the identity cosh(0) = 1.
Claim. For every natural number $n$, if $d_n(t) := 2^n t$ and $d_n(t) = 2^n t - 1$, then $d_n(0) = 0$.
background
The module develops the composition law for zeta zero defects induced by the Recognition Composition Law on J. The iterated defect is defined by defectIterate(t, n) = cosh(2^n t) - 1, where t = 2η for real-part deviation η from the critical line. On the critical line η = 0 the input t vanishes and every iterate must remain zero.
proof idea
The proof is a one-line wrapper that unfolds the definition of defectIterate and invokes Real.cosh_zero.
why it matters
This anchors the zero-deviation case inside the composition law for zeta zeros. It supports the module's main results on recurrence, four-fold amplification, and exponential lower bounds for off-critical zeros. Within Recognition Science it confirms that only nonzero deviation (away from T5 J-uniqueness) can generate the RCL cascade.
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