rsKernelParams_C
plain-language theorem explainer
The theorem fixes the amplitude C in the RS-canonical ILG kernel parameters at exactly φ to the power -3/2. Researchers deriving kernel forms for infra-luminous gravity or CPM coercivity constants would cite this explicit prefactor. The proof is a direct reflexivity step that follows from the hardcoded value inside the rsKernelParams construction.
Claim. Let τ₀ > 0. For the RS-canonical kernel parameters built from τ₀, the amplitude constant satisfies C = φ^{-3/2}.
background
The ILG kernel takes the form w(k, a) = 1 + C · (a / (k τ₀))^α, with α = (1 - 1/φ)/2 the self-similarity exponent and C the amplitude linked to coercivity slack. The module works in RS-native units where τ₀ is the fundamental tick duration (one tick equals 1 in these units) and φ is the golden-ratio fixed point. Upstream, rsKernelParams constructs the full parameter record by setting C directly to φ^{-3/2} while importing the tick definition of τ₀ from Constants.
proof idea
The proof is a one-line wrapper that applies reflexivity to the definition of rsKernelParams, which already records C as φ^{-3/2}.
why it matters
This pins the explicit value of the kernel amplitude C required by the ILG formalization and the Recognition Science constants (phi from the forcing chain, eight-tick octave). It supports the module's main results on kernel positivity and reduction to 1 at reference scale, feeding the broader CPM core even though no direct used-by edges appear in the current graph.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.