cLagLock_pos
plain-language theorem explainer
The positivity of the locked lag constant defined as the golden ratio raised to the power of negative five is established. Researchers deriving RS-native constants such as the reduced Planck constant cite this result to confirm that derived quantities remain positive. The proof is a direct term-mode reduction that invokes the positivity of the golden ratio and the preservation of positivity under real exponentiation.
Claim. The locked lag constant satisfies $0 < C_{lock}$ where $C_{lock} = phi^{-5}$ and $phi$ is the golden ratio.
background
The Constants module works in RS-native units where the fundamental time quantum tau_0 equals one tick. The locked lag constant is introduced as the canonical value phi to the power of negative five. Upstream results include the definition of cost for recognition events as the J-cost and the derived cost for multiplicative recognizers, both of which presuppose non-negative quantities in the recognition framework.
proof idea
The proof asserts positivity of phi from the phi_pos lemma, unfolds the definition of the locked lag constant, and applies the real-analysis fact that a positive base to any real power remains positive.
why it matters
This result is invoked directly by E_coh_pos and by hbar_pos, the latter stating that hbar equals phi^{-5} in RS-native units and corresponding to theorem C-004.1. It anchors the framework where hbar = phi^{-5}, c = 1, and G = phi^5 / pi, supporting the forcing chain from T5 J-uniqueness through the eight-tick octave to D = 3 spatial dimensions.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.