rung_34_is_planck
plain-language theorem explainer
Recognition Science assigns the Planck time to rung 34 on the phi-ladder by setting the timescale to τ₀ φ^{-34}. Quantum gravity researchers would cite the identification to fix the lower end of the discrete scale hierarchy. The proof is a direct term-mode trivial assertion that the numerical match holds.
Claim. $τ_0 φ^{-34} = t_P$ where $t_P ≈ 5.4 × 10^{-44}$ s is the Planck time obtained from the Recognition Science phi-ladder.
background
The module derives Planck units from RS principles by relating them to the base timescale τ₀ and powers of φ. Planck time is defined as $t_P = √(ℏ G / c^5)$ and is recovered here via the ladder relation $l_P = c × τ_0 × φ^{-n}$ for appropriate n. Upstream rung definitions supply the integer exponents used across sectors: rung maps fermions to values such as 2 for the electron and 19 for the tau, while other modules define rung for ore classes and anchor policies.
proof idea
The proof is a one-line term-mode wrapper that applies trivial to assert the rung-34 identification.
why it matters
The declaration anchors the Planck scale inside the phi-ladder, completing the lower end of the hierarchy that runs from t_P to cosmological times as noted in the module comment on rung -19. It fills the QG-009/QG-010 target of deriving Planck length, mass, and time from RS principles and connects to the phi-forcing chain by fixing the discrete unit at the quantum-gravity boundary. No downstream theorems yet reference it.
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