significance
plain-language theorem explainer
The definition enumerates four interpretive statements on the φ³⁴ connection linking τ₀ to the Planck time t_P. Researchers examining scale hierarchies and Fibonacci relations in quantum gravity cite these points to motivate connections between biological and Planck regimes. It is implemented as a direct list definition without computation or lemmas.
Claim. The significance of the φ³⁴ connection is given by the list: $34 = F_9$ (Fibonacci number), $34$ rungs from τ₀ to t_P, connects biological to Planck scale, and may explain gauge hierarchy.
background
The PlanckScale module derives Planck length l_P = c × τ₀ × φ^{-n}, Planck mass, and Planck time from RS principles, with the φ-ladder supplied by the upstream scale function scale(k) := φ^k. Voxel is the fundamental discrete unit Quantity VoxelUnit. PrimitiveDistinction.from reduces seven axioms to four structural conditions plus three definitional facts. The local setting targets QG-009 and QG-010, where the Planck scale emerges from φ-forcing and the eight-tick octave.
proof idea
The definition is a direct enumeration of four strings. No lemmas or tactics are applied; it constructs the List String with the listed interpretive claims.
why it matters
This definition supplies interpretive context for downstream results in CircuitZCapacity, DAMAModulation, and Xenon1TExcess. It fills the QG-010 target by noting the Fibonacci number F₉ and the 2×17 relation to the eight-tick structure (T7). It touches the open question of exact matching between φ³⁴ and the observed Planck hierarchy.
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